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FCC Econometric Analysis of

Potential Discrimination

Utilization Ratios for Minorityand Women-Owned Companies

in FCC Wireless Spectrum

Auctions

December 5, 2000

A Study Prepared by

Ernst & Young LLP

for the

Federal Communications Commission

FCC Econometric Analysis of Potential Discrimination

Utilization Ratios for Minority- and Women-Owned Companies in FCC

Wireless Spectrum Auctions
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1. Introduction and Executive Summary

Utilization ratios are a means of measuring the participation and success of minority- and

women-owned businesses in the Federal Communications Commission (FCC) wireless

spectrum auctions. In this context, a utilization ratio indicates the share of, say, minorityowned companies that were successful in obtaining a spectrum license through an auction

out of all minority-owned companies that participated in the auction. Comparison of

these ratios across groups highlights any potential systematic differences in auction

outcomes.

There are different ways of calculating utilization ratios, depending on how success and

participation are measured. Perhaps the simplest way of calculating utilization ratios for

spectrum auctions is to determine the number of auction participants who won at least

one license as a percentage of all participants. While conceptually straight-forward, this

measure does not capture, for example, potential differences in the rates at which

participants qualified to bid1, or any differences in the value of the licenses won2. In order

to develop a more thorough understanding of auction outcomes for minority- and womenowned companies, this report presents a number of different utilization ratio measures:

• General Utilization Ratio. Percentage of auction winners (those who won at least one

license) among all auction applicants.

• Qualifying Ratio. Percentage of applicants who qualify to bid among all auction

applicants.

• Success Ratio. Percentage of auction winners (those who won at least one license)

among all qualified auction applicants.

• Economic Value Ratio.3 An alternative way of assessing the extent to which minorityand women-owned companies are able to secure wireless spectrum licenses is to

evaluate their share of the total economic value of the licenses auctioned. The

Economic Value Ratio is defined as the economic value of licenses secured by

applicants in a particular group, for example minority-owned companies, expressed as

a percentage of the total economic value of licenses auctioned.

• Average Revenue per Winner. If the number of winners in a group is small, then the

Economic Value Ratio for that group would naturally be low, even if there were no

systematic differences in the values of licenses obtained across groups. Average

revenue per winner provides another measure of auction outcomes for different

groups, while controlling for the number of winners.

 

1

 Throughout this report, an auction applicant is defined as a company (or an individual) who submitted

Form 175 (“Short Form”) indicating an interest to participate in an auction. In order to bid in an auction,

applicants had to qualify by paying an upfront payment. Not all applicants qualified to bid.

2

 As measured by the FCC’s net revenue. Net revenue is the revenue collected from the winning bidder,

after deducting bidding credits, if any.

3

 For the purposes of this report, “economic value of a license” is defined as the net revenue the FCC

received for the license. Net revenue equals the winning bid, minus bidding credits, if any.
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• Return on Payment Ratio. Another approach to scaling the revenues generated by

various groups is to use the upfront payments as a scaling factor. The upfront

payments determine bidding eligibility and hence affect auction outcomes. The return

on payment ratio is calculated as the percentage of net FCC revenues relative to the

percentage of upfront payments. For example, suppose that minority-owned

companies generated 15% of net FCC revenues and paid 10% of the upfront payments

in a particular auction. Then the Return on Payment Ratio for minority-owned

companies is 1.5, indicating that the minority share of revenues is 1.5 times the

minority share of upfront payments.

Each of these ratios presents a different view on how minority- and women-owned

companies obtain licenses through the spectrum auction process. In general, these ratios

can be classified into two categories: measures of auction outcomes, and measures of

financial implications of those outcomes.

The general utilization ratio provides an overall view of the auction outcomes, based on

the number of applicants and winners. The qualifying and success ratios refine this

concept further, by breaking the auction process into two parts: qualifying to bid, and

winning after qualifying. Contrasting these two measures will identify whether any

differences found in the general utilization ratios are attributable to differences in

qualifying or in succeeding after qualifying, thus providing insights into where in the

auction process there may be differences across groups of applicants.

The other measures are more financial measures of auction outcomes. Simply counting

winners and losers may obscure the fact that some licenses are more valuable than others,

and that there may be differences in the value of licenses acquired across groups of

applicants. The financial measures of auction outcomes address these issues by

examining revenue shares, and scaling them by numbers of applicants or by upfront

payments.

Both types of measures are useful in evaluating the ability of minority- and womenowned companies to acquire spectrum licenses through auctions, as they provide different

points of view. Taken together, they will provide a more comprehensive picture of

auction outcomes across different groups of auction applicants.

Our main findings, by ratio type, from this analysis are:

Aggregate Utilization Ratios:
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• When participation and success is measured by counting the percentages of winners

from all auction participants (general utilization ratio), minority and women

applicants appear to be somewhat less likely to win at least one license relative to

other applicants. These differences are statistically significant.4

• Examination of the qualifying ratio indicates that minority and women applicants tend

to qualify at lower rates than other applicants and that these differences are

statistically significant. On the other hand, analysis of success ratios reveals that

among qualified applicants, there are no statistically significant differences between

women and other applicants in their likelihood of winning licenses. Success ratios

also indicate that on average, qualified minority applicants are more likely to win than

qualified non-minority applicants. This difference is statistically significant. These

findings would suggest that the difference in general utilization ratios may be largely

attributable to the differences in qualifying ratios where minority applicants face a

lower likelihood of qualifying. However, once qualified, minorities appear to have

higher odds of success in auctions.

• Figure 1 presents the differences in average5 general utilization, qualifying, and

success ratios between minority and non-minority applicants.

∗ Indicates that differences in the ratios across non minority and minority

groups were statistically significant at the 95% level

Impact of Installment Plans

• When the various utilization ratios are analyzed separately for auctions with and

without installment plans, it appears that installment plans generally increase the rate

at which minority and women applicants win licenses. Figure 2 presents the same

ratios as Figure 1 but calculated separately for auctions with installment plans and

without installment plans. Although the utilization and qualifying ratios are still

lower for minorities than for non-minorities for both auctions with and without

installment plans, in auctions with installment plans the success ratio is higher for

minorities than for non-minorities and the difference is statistically significant.

 

4

 See pages 9-10 for a discussion of the concept of statistical significance.

5

 Calculated across all auctions.

Utilization

Ratios

Qualifying Ratios Success Ratios

0%

10%

20%

30%

40%

50%

60%

70%

80%

Utilization

Ratios

Qualifying Ratios Success Ratios

Figure 1

General Utilization Ratio, Qualifying Ratio, and Success 

Ratio over all Auctions

Non Minority Minority

*

*

*
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0%

10%

20%

30%

40%

50%

60%

70%

80%

Figure 2

Installment Plan vs. No Installment Plan

Non Minority Minority

Utilization Ratios Qualifying Ratios Success Ratios

Installment

No

 Installment

Installment

No

 Installment

No

 Installment

Installment

*

*

*

*

*

∗ Indicates that differences in the ratios across non minority and minority

groups were statistically significant at the 95% level

• The difference in outcomes for minorities between auctions with and without

installment plans may reflect various factors. Installment plans may relax potential

capital constraints, or, alternatively, they may lead to inflation of the price of the

license and aggressive bidding. Further study is required to definitively evaluate the

effects of installment plans.

Economic Value Analysis

• The analysis of economic value shares (i.e., shares of net FCC revenue generated

from the auctions) revealed that in the aggregate, the value of licenses acquired by

minority winners is approximately 12% of the total value of licenses. However, in

auctions with installment plans, the minority share of total value increases to

approximately 19% (see Figure 3). The value shares for women winners exhibit a

similar pattern.

Figure 3

Economic Value Shares

Net Revenue Share

 All Auctions

Net Revenue Share 

Installment Plans

Net Revenue Share 

No Installment Plans

Minority

12%

Non 

Minority

88%

Minority

19%

Non 

Minority

81%

Non 

Minority

99.99%

Minority

.01%
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• When the economic value of licenses acquired is examined on a per winner basis

(average economic value per winner), there are no statistically significant differences

between minority and women applicants, and other applicants at the aggregate level.

In other words, while the number of minority and women winners is relatively small,

compared to the number of other winners, the value of their licenses won is

comparable to that of other winners, on average.

• When economic value of licenses relative to the upfront payments is compared across

different applicant groups (return-on-payment ratio), minority and women applicants

tend to obtain a larger share of the economic value of the licenses than their share of

upfront payments. If upfront payments are taken as a measure of the value and

number of licenses applicants are interested in winning, this finding would seem to

indicate that minority and women applicants tend to win at least as many and/or as

valuable licenses as they are interested in winning. However, upfront payments may

be an imperfect indicator of interest, if applicants are unable to make upfront

payments in the amounts they desire. Figure 4 illustrates the average return-onpayment ratios for minorities across all auctions.

Non

Minority

Minority

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Non

Minority

Minority

Figure 4

Return on Payment Ratio for all Auctions

• When return-on-payment ratios are analyzed separately for auctions with and without

installment plans (Figure 5), the ratios for minorities are much higher in auctions with

installment plans. Ratios for women have a similar pattern.
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Other findings

• The analysis by industry groups revealed few statistically significant patterns across

industries6 in the comparison of utilization ratios between minority and women

applicants, and other applicants. In advanced paging/data auctions all three measures

of utilization (general utilization, qualifying, and success ratios) are significantly

lower for minorities than for non-minorities.

• The differences in utilization ratios between minority and women applicants, and

other applicants are typically less pronounced among small companies than among

large companies. Among small companies, auction outcomes are generally more

comparable across applicant groups than among large companies.

• In the first three auctions, minority and women applicants were eligible for bidding

credits. In these auctions, the economic value shares tended to be generally larger for

minority and women applicants than in other auctions.

When interpreting the utilization ratio calculations, it is important to keep in mind that

they are based on a high-level analysis that does not control for many important applicant

characteristics that may affect auction outcomes and may provide explanations for the

observed differences across applicant groups. For example, the findings suggest that

installment plans increase the likelihood of winning for minority applicants, which may

reflect the easing of capital constraints, if any, or inflation in the value of licenses. These

results may also be the artifacts of differing auction strategies employed by different

participants. For example, large companies may strategically place upfront payments

across a wider array of spectrum than their business needs, and focus their interest as the

auction proceeds, leading to a lower return-on-payments. We are currently developing

further more detailed analysis into the determinants of auction outcomes.

 

6

 Advanced paging/data; mobile voice and data; interactive data; wireless cable; multichannel video.

Installment No

Installment

0

0.5

1

1.5

2

Installment No

Installment

Figure 5

Return on Payment Ratios for Installment vs. 

No Installment Plan Auctions

Non Minority Minority
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The remaining sections of this report provide a more detailed discussion of our analysis.

2. Data

The FCC provided Ernst & Young LLP (E&Y) with data on 19 auctions7 that E&Y used

to calculate preliminary utilization ratios.8 For each auction applicant, the data include

the following information:

• Indicator for Qualifying Applicant

• Name

• Indicator for Small Business

• Indicator for Rural Business

• Indicator for Woman-owned Business

• Indicator for Minority-owned Business

• Number of High Bids

• Total Population in Areas for each winning bid

• Sum of High Bids $ (Net)

• Sum of High Bids $ (Gross)

• Upfront Payment

• Bidding Eligibility

The indicators for minority-owned, women-owned, and small businesses are based on

self-reported data. It is our understanding that the FCC has not asked applicants to verify

their minority- or women-owned status, but when an auction applicant identified itself as

a small business, it also had to provide some verification to the FCC of its small business

status.9 10

3. Utilization Ratio Calculations

Each of the utilization ratios is calculated separately for each auction, as well as for

groups of auctions. Aggregating data across auctions allows us to detect general highlevel patterns, if any, that might not emerge in an auction-by-auction view. Two natural

groupings of auctions are by rule structure and by industry type. Auction rules have

varied considerably, and in particular, some auctions have provided special installment

plans for small businesses while others have not. An interesting question is whether these

special programs had an impact on participation of minority/women-owned businesses.

 

7

 Auctions 1-21, with the exception of auctions 13 and 19, which were never held.

8

 E&Y has not conducted an independent audit of the data and makes no representations of the accuracy of

the data.

9

 The type of verification has varied over time.

10 In the very first auctions (Auctions 1 through 3), minority and women owned businesses were granted

bidding credits, but subsequently, only small businesses have qualified for bidding credits. Hence, in most

auctions applicants have not had a direct reason to identify themselves as minority- or women-owned

businesses. On the other hand, bidding credits for small businesses have been in place in many auctions

(Auctions 3, 4, 5, 6, 7, 10, 11, 14, 16, 17, 18, 20, 21).
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Similarly, the licenses have been sold in a number of distinct industries, and there might

be some industry-specific factors influencing the extent of minority/women-owned

business participation in auctions. The groups of auctions are11:

• Auction Rule Structures Group

Group 1: Installment Plans (auctions # 2,3,5,6,7,10,11)

Group 2: No Installment Plans (auctions # 1,4,8,9,12,14,15,16,17,18,20,21)

• Industry Groups

Group 1: Advanced Paging/Data (auctions # 1,3,18)

Group 2: Mobile Voice and Data (auctions # 4,5,7,10,11,12,14,15,20,21)

Group 3: Interactive Data (auction # 2)

Group 4: Wireless Cable (auction # 6,17)

Group 5: Multichannel Video (auction # 8,9)

In another grouping, applicants are grouped on the basis of their self-reported size into

small and large companies12, and utilization ratios are calculated separately for each

group. Company size may be one of the determinants of auction outcomes, and hence it

is instructive to conduct utilization ratio comparisons for groups of companies that are

similarly sized.13

In addition to presenting the utilization ratios for the various groups, the report lists

aggregate (or average) utilization ratios. These are calculated in two ways: simple

averages, and revenue-weighted averages. First, we calculate the aggregate utilization

ratios by using the total numbers of auction applicants and winners across all auctions.

Second, we calculate average utilization ratios from the per-auction ratios that are

weighted by auctions’ revenue shares. For example, suppose that Auction 1 generated

10% of revenues from all auctions combined, and that Auction 2 generated 15% of all

revenues. Then, in the calculation of the average revenue-weighted utilization ratio for,

say, minority applicants, the minority utilization ratio from Auction 1 would receive a

weight of 10%, and the ratio from Auction 2 would receive a weight of 15%.14 Both

average utilization ratio measures are reported at the bottom of each table for reference.

For each ratio, E&Y conducted tests to determine whether the differences in the ratios

across groups were statistically significant. In these tests, minority applicants are

compared to non-minority applicants (i.e., all other applicants who did not identify

themselves as minority applicants), and women applicants are compared to all other

applicants (who did not identify themselves as women-owned companies). The concept

 

11 The auction rule structures groups are based on the information provided to us by the FCC. The industry

groups are based on our understanding of the information in the bidder packages provided to us by the FCC.

12 For the purposes of this report, a company is considered large, if it has not identified itself as a small

company on the auction application.

13 It should be noted, though, that the category ‘large’ may encompass very wide differences in company

size, given the way it has been defined.

14 Auctions or auction groups without any minority/women applicants are omitted from these averages.
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of statistical significance is used to differentiate between systematic patterns and chance

occurrences. Even in the absence of any systematic differences auction outcomes

between, say, minority and non-minority auction applicants, one would not expect the

utilization ratios for the two groups to be exactly the same. The question is then whether

a difference in the ratios indicates a systematic pattern. Statistical significance tests are a

common approach to determining this. For example, when the statistical significance test

indicates a 95% level of confidence, there is a 95% chance that a difference in utilization

ratios is due to a systematic pattern and only a 5% chance that there is no true difference.

The 95% level is typically used as the threshold level for deeming a result statistically

significant, i.e. if the confidence level is at least 95%, the result is considered statistically

significant; otherwise it is not.15 The confidence level of a test is affected by not only the

absolute magnitude of the difference in utilization ratios, but also by other factors, such as

the number of applicants on which the utilization ratios are calculated. Hence, a small

difference may at times be statistically significant, while a large one might not.

Although the full population of auction applicants is used in the calculations presented in

the body of this report, tests of statistical significance are a good benchmark for

comparison across groups, given the interest in examining utilization ratios in the auction

process in general, rather than in a specific auction at a specific point in time. Since the

auctions are an on-going process, the populations that participated in each of the auctions

can be viewed as draws from a “superpopulation,” and statistical testing of hypotheses is

appropriate.

A. General Utilization Ratio

The general utilization ratio is an overall measure of the extent to which

minority/women-owned businesses participate in auctions. It is calculated as the

percentage of winners among all auction applicants. Table 1 shows the general utilization

ratios by auction as well as for all auctions as a whole. For all auctions as a whole, there

are some differences across general utilization ratios across demographic groups: 37.40%

of non-minority applicants and 31.97% of minority applicants win licenses, while the

shares are 32.01% for women-owned applicants and 37.35% for other applicants. Both

of these differences are statistically significant, indicating that on average, minority- and

women-owned firms win licenses at slightly lower rates than other firms. The revenueweighted average general utilization ratios provide similar information: 28.89% for nonminorities vs. 22.02% for minorities, and 18.81% for women applicants vs. 29.18% for

other applicants.

In the auction-by-auction comparison, the percentage of winning minorities is sometimes

larger (e.g., auctions 2 and 7) and sometimes smaller (e.g., auctions 6 and 17) than the

corresponding percentage for non-minority applicants. Similarly, women applicants

sometimes win licenses more frequently than other applicants (e.g., auction 17) and

 

15 A Chi-square test was applied when the ratios were based on counts, such as number of auction winners.

A t-test was applied when the ratios were based on continuous variables, such as revenue amounts.

Appendices A and B describe the calculation of these statistics in detail.
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sometimes less frequently (e.g., auction 11). However, the number of minority and

women applicants and/or winners is too small in most auctions (13 out of 19) to allow the

use of statistical tests, so for most auctions, it is unclear what, if any, underlying patterns

these differences represent on a per-auction basis. In the auctions where the number of

minority and women applicants and/or winners permits the calculation of valid tests, none

of the differences are statistically significant.

When auctions are analyzed by auction groups based on auction rules (Table 2),

minorities appear to be just as likely to win licenses in auctions with installment plans,

whereas there is a statistically significant difference between minorities and nonminorities in auctions without installment plans, with minorities winning licenses less

frequently than non-minorities. In other words, it appears that the presence or absence of

installment plans does affect the outcomes for minorities, as measured by the general

utilization ratio. On the other hand, installment plans appear to make less of a difference

for the outcomes for women auction applicants. Women are less likely than other

applicants to win licenses in auctions with installment plans. This difference is

statistically significant.

The analysis by industry group (Table 3) shows that minority applicants win licenses at

significantly lower rates than non-minority applicants in advanced paging/data auctions

but not in other industry groups. Women applicants also win licenses less frequently than

other applicants in advanced paging/data auctions, as well as in mobile voice and data

auctions.

When auction applicants are grouped by size (Table 4), there are no systematic

differences in outcomes between minority/non-minority and women/other applicants

among small companies. In contrast, both minority- and women-owned applicants have

significantly lower general utilization ratios among large companies.

B. Qualifying Ratio

In order to bid in the auctions, applicants must qualify by submitting Form 175 (“short

form”) and an upfront payment. The upfront payment depends on desired bidding

eligibility. Bidding eligibility is measured in bidding units, and each license to be

auctioned requires a certain number of bidding units. For example, an applicant who

provides an upfront payment that qualifies him for 100 bidding units is able to bid on any

combination of licenses such that the total bidding eligibility requirement does not exceed

the 100 units. Failure to make the upfront payment or to complete the “short form” will

result in disqualification. A potential reason explaining the differences in general

utilization ratio between minority and non-minority applicants and between women and

other applicants, described above, is differences in rates at which minorities and women

qualify to bid, relative to other applicants. To examine the impact of the qualifying

process, we study the qualifying ratio separately from the general utilization ratio.
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The qualifying ratio is defined as the percentage of minority/non-minority and

women/other applicants that qualify to bid. Table 5 shows qualifying ratios by auction as

well as for all auctions as a whole. The average qualifying ratios across all auctions

indicate significant differences between the outcomes of minority and women applicants,

relative to other applicants. The average qualifying ratio for minority applicants is

48.3%, while it is 67.5% for non-minority applicants. Similarly, the average qualifying

ratio for women applicants is 51.9%, and 66.6% for other applicants. Both of these

differences are statistically significant, indicating that there are systematic differences in

qualifying rates between minorities and women applicants as compared to other

applicants.

In eight of the 19 auctions, the number of minority/women applicants and/or qualified

applicants is too small to permit the calculation of statistical tests regarding the

significance of the difference in qualifying ratios. In other auctions, the tests indicate

some statistically significant differences in qualifying ratios. Minorities qualify at

significantly lower rates than non-minority applicants in auctions 3, 5, 6, 10, and 11.

Women qualify at significantly lower rates than other applicants in auctions 5, 10, and 11.

Table 6 presents the qualifying ratios when auctions are grouped by auction rules, i.e.,

whether auctions had installment plans or not. Minorities qualify at significantly lower

rates regardless of whether auctions had installment plans or not. Women qualify at

significantly lower rates in auctions with installment plans, but no such difference appears

in auctions without installment plans.

In the analysis by industry group, minorities again qualify at significantly lower rates in

three of the five industry groups (advanced paging/data, mobile voice and data, and

interactive data). The number of minorities is too small to permit statistical tests in

wireless cable auctions, and there are no statistically significant differences in qualifying

ratios in the fifth industry group, multichannel video. For women applicants, the only

industry group with statistically significant differences in qualifying ratios is mobile voice

and data. As for minority applicants, the number of women applicants is too small in

wireless cable auctions to permit the calculation of statistical tests.

Company size appears to make no difference in qualifying ratios. When large

minority/women companies are compared to other large companies, they qualify at

statistically lower rates. The same holds in the comparison of small minority/women

companies to other small companies.

These findings from the study of the qualifying ratio indicate that at least some of the

differences evident in general utilization ratios between minority/women applicants and

other applicants can be attributed to differences in qualifying ratios. In general, minority

and women applicants tend to qualify at significantly lower rates than other applicants. A

possible reason for the lower qualifying rates may be differential access to capital, which

may hinder the ability of minorities and women to make the necessary upfront payments.
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However, a more in-depth analysis is required to arrive at authoritative conclusions about

the reasons behind this apparent disparity.

The next step in the analysis is to evaluate success rates for qualified applicants to

determine whether after qualifying there are differences in auction outcomes between

minority and women applicants relative to other applicants.

C. Success Ratio

The success ratio is a measure of qualified applicants who win bids, and is calculated as

the percentage of winners among qualified applicants.

Table 9 shows the success ratios by auction as well as the average success ratios. After

having qualified to bid, minority applicants in fact win licenses at a higher rate than nonminority applicants (66.1% vs. 55.4%), and this difference is statistically significant.

Qualified women applicants also win licenses at a higher rate than other applicants

(61.7% vs. 56.1%), although this difference is not statistically significant. Again, in 13 of

the 19 auctions, the number of minority and women qualified applicants and winners is

too small to permit the calculation of statistical tests. In auctions where testing is

possible, however, minorities often win at significantly higher rates (auctions 2, 5, and

11). No such systematic pattern appears in the comparison of women applicants and

other applicants on a per auction basis.

When success ratios are examined by auction group, minority and women applicants are

more likely to win than other applicants in auctions with installment plans. However, in

auctions without installment plans minorities win less frequently than non-minorities and

the difference is statistically significant. Women applicants also win less frequently but

the difference is not statistically significant. These results mirror those from the analysis

of general utilization ratio: again, installment plans appear to enhance the ability of

minorities in particular to secure wireless spectrum licenses, while the difference is less

marked for women applicants.

Analysis of auctions by industry groups reveals some differences across industries. While

minority applicants are statistically more likely to win in mobile voice and data auctions

than non-minority applicants, they are less likely to win other industry groups (with the

exception of wireless cable, for which the low number of minority qualified applicants

precludes the use of statistical tests). For women applicants, the only significant

difference emerges in mobile voice and data auctions, in which they are less likely to win

than other applicants.

When applicants are grouped by size, there are no differences in success ratios among

large companies, either between minority and non-minority applicants or between women

and other applicants. However, among small companies, minority applicants win licenses

more frequently than non-minorities, and the difference is statistically significant.
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In sum, the success ratios indicate that among qualified applicants, minorities and women

tend to win licenses just as frequently as other applicants, if not more frequently. This is

in marked contrast to the findings from the analysis of qualifying ratios. Those findings

showed that minority applicants in particular tend to qualify less frequently than other

applicants. On the basis of these results, the lower general utilization ratios for minority

and women applicants appear to be related to hurdles in qualifying to bid, but that among

those who qualified, the ability of minority and women applicants to secure licenses is

comparable to that of other applicants.

D. Economic Value Ratio

The preceding measures of utilization (general utilization ratio, qualifying ratio, and

success ratio) have measured utilization as qualifying to bid for or winning at least one

license, relative to the number of applicants. These calculations omit any considerations

of the economic value of the licenses obtained.16

An alternative measure of the extent to which minority/women-owned businesses win

FCC licenses is their share of the total economic value of licenses.

Table 13 presents the Economic Value Ratios by auction as well as for all auctions as a

whole. For all auctions as a whole, the value of the licenses won by minority applicants

was 11.9% of the total value of licenses. For women applicants, the share was 7.9%. In

other words, minority (women) applicants secured roughly a tenth of the licenses, when

measured by the economic value of the licenses.17 In the auction-by-auction analysis, the

value shares for minority applicants have ranged from a low of 0.0% to a high of 31.6%.

The range for women applicants is from 0.0% to 45.2%.

Economic value ratios by auction group are provided in Table 14. In auctions with

installment plans, the economic value ratios for both minority and women applicants are

higher than on average (19.4% and 12.7%, respectively). Consistent with the evidence

from the general utilization ratios and success ratios, these figures indicate that in

auctions with installment plans, minority and women applicants tend to acquire larger

shares of the spectrum for sale, as measured by the economic value of the spectrum.

The economic value shares by industry group are shown in Table 15. In terms of

economic value, minority and women applicants obtain their largest shares of the total

value of spectrum auctioned in multichannel video auctions.

In table 16, economic value shares are calculated by company size. Among small firms,

minority and women applicants obtain higher value shares than on average (22.1% and

 

16 Recall that for the purposes of this report, economic value of a license is defined as the winning bid for

that license, minus any bidding credits, i.e., the FCC’s net revenue for the license.

17 No statistical tests of significance are reported for these shares. If the minority share of economic value is

X% then the non-minority share is by definition (100-X)%, and testing for statistical significance in the

shares is not meaningful.
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14.6%, respectively). In contrast, their shares are very low among large firms (less than

1%).

The findings from the analysis of economic value shares indicates that in general,

minority and women applicants acquire approximately a tenth of the licenses, as

measured by their economic value. However, in auctions with installment plans and

among small firms, their shares of economic value are larger.

E. Economic Value Per Winner

The economic value ratio calculations show that the bulk of the revenues collected from

auctions come from non-minority owned companies, or companies not owned by women.

However, this reflects at least partially the fact that the number of minority and women

winners is smaller than the number of other winners. In order to evaluate the economic

value of licenses acquired by minority and women applicants while controlling for the

number of winners, we calculated the average economic value per winner.

Table 17 displays the results on a by-auction basis, and also gives the averages across all

auctions. On a per winner basis, the differences in economic value of licenses obtained

between minority and women applicants on one hand, and other applicants on the other,

appear to be less distinct than in the preceding analysis of overall value shares. The

average value per winner for minority applicants is $22.5 million, while it is $32.0

million for non-minority applicants. When comparing women applicants to other

applicants, the average values are $15.4 million for women and $33.2 million for others.

Neither of these differences is statistically significant. In the analysis by auction, the

average value of a license per winner is significantly lower for minorities in two auctions

(Auctions 6 and 11). In 10 out of the 19 auctions, there are not enough minority winners

to perform a valid test of statistical significance for the average value of licenses won.

The findings for women applicants are quite similar. In Auctions 6 and 11, there are

statistically significant differences between women and other winners in the average

economic value of licenses won, with women having lower values. In 9 of the 19

auctions, there are not enough women winners for the calculation of statistical tests.

When auctions are grouped by auction rules (Table 18), differences in the average values

of licenses per winner are not statistically significant in auctions with installment plans,

but they are in auctions without installment plans. This finding echoes those from the

previous calculations in which minority and women applicants had higher general

utilization and success ratios, and higher economic value shares in auctions with

installment plans.

In the analysis of average economic value per winner by industry group (Table 19), the

only significant difference is found in the comparison between minority and non-minority

winners in interactive data auctions. No significant differences are found in other

industry groups, or in the comparison between women and other winners. However, there
16 12/05/00

are no minority or women winners in wireless cable auctions so the tests cannot be

calculated for this industry group.

Table 20 presents the average economic values per winner by company size. Again, the

differences are significant among large companies (i.e., large minority- and womenowned companies pay on average significantly less for their licenses than other large

companies), but not among small companies. In fact, for minority small companies, the

average economic value per winner is higher than for non-minority small companies.

Taken together, the findings from the analysis of average economic values per winner

suggest that in general, there appear to be no systematic differences in the average values

between minority and women winners, and other companies. While in some auctions the

differences are significant, as they are also among large companies, this is offset by the

fact that in other auctions and among small companies, the differences are small enough

to be statistically insignificant.

F. Return-on-Payment Ratio

The final utilization ratio analyzed in this report is the return-on-payment ratio. The idea

behind this ratio is to scale the economic value of licenses won by the upfront payments.

Upfront payments determine the number of licenses the applicant is able to bid on, and

are indicative of the number and value of licenses the applicant is interested in

acquiring.18 Therefore we would expect applicants who made larger upfront payments to

win more licenses and/or more valuable licenses. Differences in the value of licenses

won might then be related to differences in upfront payments, and it is interesting to

examine to what extent the value of licenses won, relative to upfront payments, differs

across groups of applicants.

The return-on-payment ratio is calculated as the percentage of net revenues from

minority/women winners relative to the percentage of upfront payments from

minority/women applicants. For example, if minority applicants generated 15% of the

total FCC net revenue, and paid 10% of the total upfront payments, then this ratio would

be 15%/10%=1.5. The calculations of this ratio are limited to 11 of the 19 auctions

because we did not have data on upfront payments for all auctions.

Table 21 presents the overall return-on-payment ratios as well as the ratios by auction.

Overall, the value share of licenses won by minority applicants is nearly twice as large as

the minority share of upfront payments, as indicated by the return-on-payment ratio of

1.86. For non-minority applicants this ratio is close to 1. Similarly, for women

applicants the ratio exceeds 2, whereas for other applicants it is nearly 1. In other words,

minority and women winners tend to generate relatively more revenue than their share of

upfront payments. If upfront payments are taken as a measure of the number and/or value

of licenses applicants are interested in winning, this finding would seem to indicate that

 

18 Other factors, such as ability to raise capital for upfront payments, may also play a role in the amount of

the upfront payment.
17 12/05/00

qualified minority and women applicants win at least as many and/or as valuable licenses

as they are interested in winning. Of course, if minority and women applicants are not

able to make as large upfront payments as they would like, upfront payments are an

imperfect indicator of the extent of their interest in licenses. Nevertheless, throughout

this analysis of utilization ratios it is important to keep in mind that differences in the

number and value of licenses won reflect at least partly differences in applicants’ interest

in licenses.

In the analysis by auction, the ratio has been relatively constant and close to 1 for nonminorities across all auctions, while for minorities the ratio has varied from 0 to nearly 4.

Similarly, while the ratio varies from nearly 0 to almost 2 for women winners, it has been

close to 1 for other winners.

When auctions are examined by auction group (Table 22), again minorities and women

tend to generate relatively more revenue than their share of the upfront payments in

auctions with installment plans. This result again shows that the outcomes for minority

and women applicants appear to be influenced by the existence of installment plans.

Table 23 presents the results from the analysis by industry group. Because of lack of

data, we were unable to calculate the return-on-payment ratio for two of the five industry

groups. In the remaining three groups, the ratios exceed one for minorities in two groups

and are well below one in one group, while they are close to one for non-minorities in all

groups. The ratios are greater than one for women in all groups, and consistently close to

one for other applicants. Again, minority and women winners appear to generally secure

licenses with a greater share of the total value of licenses than their share of the upfront

payments.

The same pattern is repeated in the analysis of return-on-payment ratios by company size

(Table 24): minorities and women have return-on-payment ratios in excess of one, while

for other applicants the ratios are close to one.

The analysis of the return-on-payment ratios illustrates that among qualified applicants,

minorities and women win licenses of generally the same, or higher, value than other

applicants, relative to their upfront payments.
10/05/00

18

Table 1

General Utilization Ratios of All Applicants by Auction

GROUPS APPLIED WINS UTILIZATION RATIOS STATISTICAL SIGNIFICANCE

Auction

Auction 

Group

Industry 

Group Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwnedNon MinorityOwnedMinorityOwnedWomenOwnedNot WomenOwned

Non Minority/ 

MinorityOwned

Not Women/WomenOwned

1 2 1 24 6 4 4 0 0 22.22% 0.00% 0.00% 20.00% + +

2 1 5 522 164 195 178 63 70 32.12% 38.41% 35.90% 33.03% 84.10% 49.70%

3 1 1 69 35 24 9 2 3 20.59% 5.71% 12.50% 13.33% + +

4 2 2 78 8 5 18 0 0 25.71% 0.00% 0.00% 24.66% + +

5 1 2 376 89 61 89 25 15 22.30% 28.09% 24.59% 23.49% 73.80% 14.70%

6 1 3 196 21 17 67 5 4 35.43% 23.81% 23.53% 35.20% 71.10% 66.80%

7 1 2 167 7 13 80 4 5 47.50% 57.14% 38.46% 48.70% 38.30% 52.20%

8 2 4 4 1 1 1 0 0 33.33% 0.00% 0.00% 33.33% + +

9 2 4 4 1 1 1 0 0 33.33% 0.00% 0.00% 33.33% + +

10 1 2 33 5 6 7 2 1 17.86% 40.00% 16.67% 22.22% + +

11 1 2 202 27 18 125 16 8 62.29% 59.26% 44.44% 63.59% 23.70% 89.00%

12 2 2 22 1 3 10 0 1 47.62% 0.00% 33.33% 47.37% + +

14 2 2 43 2 0 17 1 0 39.02% 50.00% - 39.53% + +

15 2 2 4 0 0 2 0 0 50.00% - - 50.00% + +

16 2 2 95 5 8 14 2 2 13.33% 40.00% 25.00% 13.79% + +

17 2 3 210 13 12 104 4 8 50.76% 30.77% 66.67% 48.48% 83.70% 60.80%

18 2 1 71 5 9 44 1 4 65.15% 20.00% 44.44% 64.52% + +

20 2 2 11 1 1 4 0 0 40.00% 0.00% 0.00% 40.00% + +

21 2 2 6 0 0 4 0 0 66.67% - - 66.67% + +

Total NA NA 2,137 391 378 778 125 121 37.40% 31.97% 32.01% 37.35% 95.60%* 95.00%*

Revenue-Weighted Averages** 28.89% 22.02% 18.81% 29.18%

+ Not enough minority or women winners or applicants for valid chi-square test.

* Significant at the 95% level.

** Auctions where women or minorities did not participate are excluded from weight calculations.

^ See Appendix A for details on chi-square tests.

Auction group 1: With installment plans Auction group 2: Without installment plans

Industry group 1: Advanced paging/data Industry group 2: Mobile voice&data Industry group 3: Interactive data Industry group 4: Wireless cable

Industry group 5: Multichannel video
10/05/00

19

Table 2

General Utilization Ratios of All Applicants by Auction Group

APPLIED WINS UTILIZATION RATIOS STATISTICAL SIGNIFICANCE^

Auction 

Group Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwnedNon MinorityOwnedMinorityOwnedWomenOwnedNot WomenOwned

Non 

Minority/ 

MinorityOwned

Not 

Women/WomenOwned

1 1,565 348 334 555 117 106 35.99% 33.62% 31.74% 36.47% 58.48% 99.90% *

2 572 43 44 223 8 15 40.64% 18.60% 34.09% 39.39% 99.56% * 51.16%

Total 2,137 391 378 778 125 121 37.40% 31.97% 32.01% 37.35% 95.63% * 94.97%

Revenue-Weighted Averages** 28.89% 22.02% 18.81% 29.18%

 

- Auction group 1 = With installment plans (consists of auctions 2, 3, 5, 6, 7, 10, 11).

 - Auction group 2 = No installment plans (consists of auctions 1, 4, 8, 9, 12, 14, 15, 16, 17, 18, 20, 21).

 * Statistically significant at the 95% level.

** Auctions where women or minorities did not participate are excluded from weight calculations.

^ See Appendix A for details on chi-square tests.
10/05/00

20

Table 3

General Utilization Ratios of All Applicants by Industry Group

APPLIED WINS UTILIZATION RATIOS STATISTICAL SIGNIFICANCE^

Industry 

Group Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwnedNon MinorityOwned

MinorityOwnedWomenOwned

Not WomenOwned

Non 

Minority/ 

MinorityOwnedNot Women/WomenOwned

1 164 46 37 57 3 7 45.76% 6.52% 18.92% 39.37% 99.90%* 97.80%*

2 1,037 145 115 370 50 32 35.87% 34.48% 27.83% 36.66% 25.40% 93.80%*

3 406 34 29 171 9 12 43.55% 26.47% 41.38% 42.18% 94.60% 6.70%

4 8 2 2 2 0 0 33.33% 0.00% 0.00% 33.33% + +

5 522 164 195 178 63 70 32.12% 38.41% 35.90% 33.03% 84.10% 49.70%

Total 2,137 391 378 778 125 121 37.40% 31.97% 32.01% 37.35% 95.60%* 95.00%*

Revenue-Weighted Averages** 28.89% 22.02% 18.81% 29.18%

- Industry group 1 = Advanced paging/data (consists of auctions 1, 3, 18).

- Industry group 2 = Mobile voice and data (consists of auctions 4, 5, 7, 10, 11, 12, 14, 15, 16, 20 , 21).

- Industry group 3 = Interactive data (consists of auctions 6, 17).

- Industry group 4 = Wireless cable (consists of auctions 8, 9).

- Industry group 5 = Multichannel video (consists of auction 2).

Table 4

General Utilization Ratios of All Applicants by Company Size

APPLIED WINS UTILIZATION RATIOS STATISTICAL SIGNIFICANCE^

Size Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwned

Non 

MinorityOwnedMinorityOwnedWomenOwnedNot WomenOwned

Non 

Minority/ 

MinorityOwnedNot Women/WomenOwned

Non-Small 400 32 30 139 6 5 36.14% 18.75% 16.67% 36.22% 95.20%* 96.90%*

Small 1,737 359 348 639 119 116 37.74% 33.15% 33.33% 37.65% 89.20% 86.50%

Total 2,137 391 378 778 125 121 37.40% 31.97% 32.01% 37.35% 95.60%* 95.00%*

Revenue-Weighted Averages** 28.89% 22.02% 18.81% 29.18%

+ Not enough minority or women winners or applicants for valid chi-square test.

* Significant at the 95% level.

** Auctions where women or minorities did not participate are excluded from weight calculations.

^ See Appendix A for details on chi-square tests.
10/05/00

21

Table 5

Qualifying Ratios By Auction

GROUPS APPLICANTS QUALIFIED QUALIFYING RATIOS STATISTICAL SIGNIFICANCE^

Auction

Auction 

Group

Industry 

Group Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwned

Non 

MinorityOwnedMinorityOwnedWomenOwned

Not 

WomenOwned

Non 

Minority/ 

MinorityOwned

Not Women/WomenOwned

1 2 1 24 6 4 23 6 4 94.44% 100.00% 100.00% 95.00% 44.50% 35.20%

2 1 5 522 164 195 241 73 91 46.93% 44.51% 46.67% 45.87% 39.30% 14.00%

3 1 1 69 35 24 28 10 8 52.94% 28.57% 33.33% 44.44% 96.10%* 62.90%

4 2 2 78 8 5 30 0 0 42.86% 0.00% 0.00% 41.10% + +

5 1 2 376 89 61 255 46 34 72.82% 51.69% 55.74% 70.16% 99.90%* 97.30%*

6 1 3 196 21 17 155 13 12 81.14% 61.90% 70.59% 79.89% 95.90%* 63.20%

7 1 2 167 7 13 128 5 10 76.88% 71.43% 76.92% 76.62% 26.10% 2.00%

8 2 4 4 1 1 3 0 0 100.00% 0.00% 0.00% 100.00% + +

9 2 4 4 1 1 2 0 0 66.67% 0.00% 0.00% 66.67% + +

10 1 2 33 5 6 32 4 5 100.00% 80.00% 83.33% 100.00% 98.40%* 96.90%*

11 1 2 202 27 18 153 16 8 78.29% 59.26% 44.44% 78.80% 96.80%* 99.90%*

12 2 2 22 1 3 22 1 3 100.00% 100.00% 100.00% 100.00% + +

14 2 2 43 2 0 24 1 0 56.10% 50.00% - 55.81% + +

15 2 2 4 0 0 4 0 0 100.00% - - 100.00% + +

16 2 2 95 5 8 62 4 5 64.44% 80.00% 62.50% 65.52% 52.30% 13.60%

17 2 3 210 13 12 139 6 8 67.51% 46.15% 66.67% 66.16% 88.50% 2.90%

18 2 1 71 5 9 54 3 7 77.27% 60.00% 77.78% 75.81% 61.70% 10.30%

20 2 2 11 1 1 8 1 1 70.00% 100.00% 100.00% 70.00% + +

21 2 2 6 0 0 5 0 0 83.33% - - 83.33% + +

Total NA NA 2,137 391 378 1,368 189 196 67.53% 48.34% 51.85% 66.63% 99.90%* 99.90%*

Revenue Weighted Averages** 66.14% 37.43% 38.38% 64.35%

+ Not enough minority or women winners or applicants for valid chi-square test.

* Statistically significant at the 95% level.

** Auctions where women or minorities did not participate are excluded from weight calculations.

^ See Appendix A for details on chi-square tests.

Auction group 1: With installment plans Auction group 2: Without installment plans

Industry group 1: Advanced paging/data Industry group 2: Mobile voice&data Industry group 3: Interactive data Industry group 4: Wireless cable

Industry group 5: Multichannel video
10/05/00

22

Table 6

Qualifying Ratios by Auction Group

APPLICANTS QUALIFIED QUALIFYING RATIOS STATISTICAL SIGNIFICANCE^

Auction 

Group Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwned

Non 

MinorityOwnedMinorityOwnedWomenOwned

Not 

WomenOwned

Non 

Minority/ 

MinorityOwned

Not 

Women/WomenOwned

1 1,565 348 334 992 167 168 67.79% 47.99% 50.30% 66.94% 99.99% * 99.90% *

2 572 43 44 376 22 28 66.92% 51.16% 63.64% 65.91% 96.37% * 23.97%

Total 2,137 391 378 1,368 189 196 67.53% 48.34% 51.85% 66.63% 99.99% * 99.99% *

Revenue Weighted Averages** 66.14% 37.43% 38.38% 64.35%

- Auction group 1 = With installment plans (consists of auctions 2, 3, 5, 6, 7, 10, 11).

 - Auction group 2 = No installment plans (consists of auctions 1, 4, 8, 9, 12, 14, 15, 16, 17, 18, 20, 21).

 * Statistically significant at the 95% level.

** Auctions where women or minorities did not participate are excluded from weight calculations.

^ See Appendix A for details on chi-square tests.
10/05/00

23

Table 7

Qualifying Ratios by Industry Group

APPLICANTS QUALIFIED QUALIFYING RATIOS STATISTICAL SIGNIFICANCE^

Industry 

Group Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwned

Non 

MinorityOwnedMinorityOwnedWomenOwned

Not 

WomenOwned

Non 

Minority/ 

MinorityOwnedNot Women/WomenOwned

1 164 46 37 105 19 19 72.88% 41.30% 51.35% 67.72% 99.90%* 93.20%

2 1,037 145 115 723 78 66 72.31% 53.79% 57.39% 71.26% 99.90%* 99.80%*

3 406 34 29 294 19 20 73.92% 55.88% 68.97% 72.68% 97.60%* 33.40%

4 8 2 2 5 0 0 83.33% 0.00% 0.00% 83.33% + +

5 522 164 195 241 73 91 46.93% 44.51% 46.67% 45.87% 39.30% 14.00%

Total 2,137 391 378 1,368 189 196 67.53% 48.34% 51.85% 66.63% 99.90%* 99.90%*

Revenue Weighted Averages** 66.14% 37.43% 38.38% 64.35%

- Industry group 1 = Advanced paging/data (consists of auctions 1, 3, 18).

- Industry group 2 = Mobile voice and data (consists of auctions 4, 5, 7, 10, 11, 12, 14, 15, 16, 20 , 21).

- Industry group 3 = Interactive data (consists of auctions 6, 17).

- Industry group 4 = Wireless cable (consists of auctions 8, 9).

- Industry group 5 = Multichannel video (consists of auction 2).

Table 8

Qualifying Ratios by Company Size

APPLICANTS QUALIFIED QUALIFYING RATIOS STATISTICAL SIGNIFICANCE^

Size Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwned

Non 

MinorityOwnedMinorityOwnedWomenOwned

Not 

WomenOwned

Non Minority/ 

MinorityOwned

Not 

Women/WomenOwned

Non-Small 400 32 30 244 13 11 62.77% 40.63% 36.67% 62.97% 98.60%* 99.60%*

Small 1,737 359 348 1,124 176 185 68.80% 49.03% 53.16% 67.60% 99.90%* 99.90%*

Total 2,137 391 378 1,368 189 196 67.53% 48.34% 51.85% 66.63% 99.90%* 99.90%*

Revenue Weighted Averages** 66.14% 37.43% 38.38% 64.35%

+ Not enough minority or women winners or applicants for valid chi-square test.

* Statistically significant at the 95% level.

^ See Appendix A for details on chi-square tests.

** Auctions where women or minorities did not participate are excluded from weight calculations.
10/05/00

24

Table 9

Success Ratios of Qualified Applicants by Auction

GROUPS QUALIFIED WINS SUCCESS RATIOS STATISTICAL SIGNIFICANCE^

Auction

Auction 

Group

Industry 

Group Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwned

Non 

MinorityOwnedMinorityOwnedWomenOwned

Not 

WomenOwned

Non 

Minority/ 

MinorityOwnedNot Women/WomenOwned

1 2 1 23 6 4 4 0 0 23.53% 0.00% 0.00% 21.05% + +

2 1 5 241 73 91 178 63 70 68.45% 86.30% 76.92% 72.00% 99.60%* 80.90%

3 1 1 28 10 8 9 2 3 38.89% 20.00% 37.50% 30.00% + +

4 2 2 30 0 0 18 0 0 60.00% - - 60.00% + +

5 1 2 255 46 34 89 25 15 30.62% 54.35% 44.12% 33.48% 99.80%* 77.40%

6 1 3 155 13 12 67 5 4 43.66% 38.46% 33.33% 44.06% 28.30% 52.90%

7 1 2 128 5 10 80 4 5 61.79% 80.00% 50.00% 63.56% 59.00% 60.50%

8 2 4 3 0 0 1 0 0 33.33% - - 33.33% + +

9 2 4 2 0 0 1 0 0 50.00% - - 50.00% + +

10 1 2 32 4 5 7 2 1 17.86% 50.00% 20.00% 22.22% + +

11 1 2 153 16 8 125 16 8 79.56% 100.00% 100.00% 80.69% 95.50%* 83.10%

12 2 2 22 1 3 10 0 1 47.62% 0.00% 33.33% 47.37% + +

14 2 2 24 1 0 17 1 0 69.57% 100.00% - 70.83% + +

15 2 2 4 0 0 2 0 0 50.00% - - 50.00% + +

16 2 2 62 4 5 14 2 2 20.69% 50.00% 40.00% 21.05% 82.50% 90.90%

17 2 3 139 6 8 104 4 8 75.19% 66.67% 100.00% 73.28% + +

18 2 1 54 3 7 44 1 4 84.31% 33.33% 57.14% 85.11% + +

20 2 2 8 1 1 4 0 0 57.14% 0.00% 0.00% 57.14% + +

21 2 2 5 0 0 4 0 0 80.00% - - 80.00% + +

Total NA NA 1,368 189 196 778 125 121 55.39% 66.14% 61.73% 56.06% 99.40%* 86.30%

Revenue-Weighted Averages** 40.44% 59.65% 52.43% 42.41%

+ Not enough minority or women winners or applicants for valid chi-square test.

* Statistically significant at the 95% level.

** Auctions where women or minorities did not participate are excluded from weight calculations.

^ See Appendix A for details on chi-square tests.

Auction group 1: With installment plans Auction group 2: Without installment plans

Industry group 1: Advanced paging/data Industry group 2: Mobile voice&data Industry group 3: Interactive data Industry group 4: Wireless cable

Industry group 5: Multichannel video
10/05/00

25

Table 10

Success Ratios of Qualified Applicants by Auction Group

QUALIFIED WINS SUCCESS RATIOS STATISTICAL SIGNIFICANCE^

Auction 

Group Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwned

Non 

MinorityOwned

MinorityOwnedWomenOwned

Not 

WomenOwned

Non 

Minority/ 

MinorityOwned

Not 

Women/WomenOwned

1 992 167 168 555 117 106 53.09% 70.06% 63.10% 54.49% 99.99% * 95.94% *

2 376 22 28 223 8 15 60.73% 36.36% 53.57% 59.77% 97.60% * 47.93%

Total 1,368 189 196 778 125 121 55.39% 66.14% 61.73% 56.06% 99.44% * 86.25%

Revenue-Weighted Averages** 40.44% 59.65% 52.43% 42.41%

- Auction group 1 = With installment plans (consists of auctions 2, 3, 5, 6, 7, 10, 11).

 - Auction group 2 = No installment plans (consists of auctions 1, 4, 8, 9, 12, 14, 15, 16, 17, 18, 20, 21).

 

* Statistically significant at the 95% level.

** Auctions where women or minorities did not participate are excluded from weight calculations.

^ See Appendix A for details on chi-square tests.
10/05/00

26

Table 11

Success Ratios of Qualified Applicants by Industry Group

QUALIFIED WINS SUCCESS RATIOS STATISTICAL SIGNIFICANCE^

Industry 

Group Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwned

Non 

MinorityOwnedMinorityOwnedWomenOwned

Not 

WomenOwnedNon Minority/ 

Minority-Owned

Not 

Women/WomenOwned

1 105 19 19 57 3 7 62.79% 15.79% 36.84% 58.14% 99.90%* 93.20%

2 723 78 66 370 50 32 49.61% 64.10% 48.48% 51.45% 99.80%* 99.80%*

3 294 19 20 171 9 12 58.91% 47.37% 60.00% 58.03% 97.60%* 33.40%

4 5 0 0 2 0 0 40.00% - - 40.00% + +

5 241 73 91 178 63 70 68.45% 86.30% 76.92% 72.00% 99.60%* 80.90%

Total 1,368 189 196 778 125 121 55.39% 66.14% 61.73% 56.06% 99.40%* 86.30%

Revenue-Weighted Averages** 40.44% 59.65% 52.43% 42.41%

- Industry group 1 = Advanced paging/data (consists of auctions 1, 3, 18).

- Industry group 2 = Mobile voice and data (consists of auctions 4, 5, 7, 10, 11, 12, 14, 15, 16, 20 , 21).

- Industry group 3 = Interactive data (consists of auctions 6, 17).

- Industry group 4 = Wireless cable (consists of auctions 8, 9).

- Industry group 5 = Multichannel video (consists of auction 2).

Table 12

Success Ratios of Qualified Applicants by Company Size

QUALIFIED WINS SUCCESS RATIOS STATISTICAL SIGNIFICANCE^

Size Total

MinorityOwnedWomenOwned TotalMinorityOwnedWomenOwned

Non 

MinorityOwnedMinorityOwnedWomenOwned

Not 

WomenOwned

Non Minority/ 

MinorityOwned

Not 

Women/WomenOwned

Non-Small 244 13 11 139 6 5 57.58% 46.15% 45.45% 57.51% 58.20% 57.00%

Small 1,124 176 185 639 119 116 54.85% 67.61% 62.70% 55.70% 99.80%* 92.10%

Total 1,368 189 196 778 125 121 55.39% 66.14% 61.73% 56.06% 99.40%* 86.30%

Revenue-Weighted Averages** 40.44% 59.65% 52.43% 42.41%

* Statistically significant at the 95% level.

** Auctions where women or minorities did not participate are excluded from weight calculations.

^ See Appendix A for details on chi-square tests.
10/05/00

27

 Table 13

Economic Value Ratio by Auction

GROUPS NET REVENUE ($) NET REVENUE SHARE RATIO

Auction

Auction 

Group

Industry 

Group Total Minority-Owned Women-Owned

Non MinorityOwnedMinorityOwnedWomenOwnedNot WomenOwned

1 2 1 522,500,000 0 0 100.00% 0.00% 0.00% 100.00%

2 1 5 213,892,375 67,639,625 96,713,125 68.38% 31.62% 45.22% 54.78%

3 1 1 392,706,797 98,926,414 144,099,005 74.81% 25.19% 36.69% 63.31%

4 2 2 7,019,403,797 0 0 100.00% 0.00% 0.00% 100.00%

5 1 2 10,071,708,842 2,329,565,519 1,539,695,042 76.87% 23.13% 15.29% 84.71%

6 1 3 216,239,603 3,329,617 4,733,800 98.46% 1.54% 2.19% 97.81%

7 1 2 204,267,144 10,636,800 11,337,576 94.79% 5.21% 5.55% 94.45%

8 2 4 682,500,000 0 0 100.00% 0.00% 0.00% 100.00%

9 2 4 52,295,000 0 0 100.00% 0.00% 0.00% 100.00%

10 1 2 904,607,467 223,010,250 23,619,778 75.35% 24.65% 2.61% 97.39%

11 1 2 2,517,439,565 79,809,552 23,051,314 96.83% 3.17% 0.92% 99.08%

12 2 2 1,842,533 0 7,100 100.00% 0.00% 0.39% 99.61%

14 2 2 13,638,940 31,735 - 99.77% 0.23% - 100.00%

15 2 2 173,234,888 - - 100.00% - - 100.00%

16 2 2 96,232,060 521,885 521,885 99.46% 0.54% 0.54% 99.46%

17 2 3 578,663,029 417,475 16,912,510 99.93% 0.07% 2.92% 97.08%

18 2 1 21,650,301 390,608 417,323 98.20% 1.80% 1.93% 98.07%

20 2 2 7,459,200 0 0 100.00% 0.00% 0.00% 100.00%

21 2 2 3,438,294 - - 100.00% - - 100.00%

Total NA NA 23,693,719,833 2,814,279,480 1,861,108,457 88.12% 11.88% 7.85% 92.15%

Auction group 1: With installment plans Auction group 2: Without installment plans

Industry group 1: Advanced paging/data Industry group 2: Mobile voice&data Industry group 3: Interactive data Industry group 4: Wireless cable

Industry group 5: Multichannel video
10/05/00

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Table 14

Economic Value Ratio by Auction Group

NET REVENUE ($) NET REVENUE SHARE RATIO

Auction Group Total Minority-Owned Women-Owned

Non 

MinorityOwned

MinorityOwnedWomenOwnedNot WomenOwned

1 14,520,861,792 2,812,917,777 1,843,249,639 80.63% 19.37% 12.69% 87.31%

2 9,172,858,042 1,361,703 17,858,818 99.99% 0.01% 0.19% 99.81%

Total 23,693,719,834 2,814,279,480 1,861,108,457 88.12% 11.88% 7.85% 92.15%

- Auction group 1 = With installment plans (consists of auctions 2, 3, 5, 6, 7, 10, 11).

 - Auction group 2 = No installment plans (consists of auctions 1, 4, 8, 9, 12, 14, 15, 16, 17, 18, 20, 21).
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Table 15

Economic Value Ratio by Industry Group

NET REVENUE ($) NET REVENUE SHARE RATIO

Industry 

Group Total Minority-Owned Women-Owned

Non 

MinorityOwnedMinorityOwnedWomenOwnedNot WomenOwned

1 936,857,098 99,317,022 144,516,328 89.40% 10.60% 15.43% 84.57%

2 21,013,272,729 2,643,575,741 1,598,232,694 87.42% 12.58% 7.61% 92.39%

3 794,902,632 3,747,092 21,646,310 99.53% 0.47% 2.72% 97.28%

4 734,795,000 0 0 100.00% - - 100.00%

5 213,892,375 67,639,625 96,713,125 68.38% 31.62% 45.22% 54.78%

Total 23,693,719,833 2,814,279,480 1,861,108,457 88.12% 11.88% 7.85% 92.15%

- Industry group 1 = Advanced paging/data (consists of auctions 1, 3, 18).

- Industry group 2 = Mobile voice and data (consists of auctions 4, 5, 7, 10, 11, 12, 14, 15, 16, 20 , 21).

- Industry group 3 = Interactive data (consists of auctions 6, 17).

- Industry group 4 = Wireless cable (consists of auctions 8, 9).

- Industry group 5 = Multichannel video (consists of auction 2).

Table 16

Economic Value Ratio by Company Size

NET REVENUE ($) NET REVENUE SHARE RATIO

Size Total Minority-Owned Women-Owned

Non MinorityOwnedMinorityOwnedWomenOwned

Not 

WomenOwned

Not Small 10,979,543,634 8,383,842 5,631,850 99.92% 0.08% 0.05% 99.95%

Small 12,714,176,199 2,805,895,638 1,855,476,607 77.93% 22.07% 14.59% 85.41%

Total 23,693,719,833 2,814,279,480 1,861,108,457 88.12% 11.88% 7.85% 92.15%
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Table 17

Average Economic Value per Winner by Auction

GROUPS WINS NET REVENUE ($) AVERAGE NET REVENUE PER WINNER ($) STATISTICAL SIGNIFICANCE^

Auction

Auction 

Group

Industry 

Group Total

MinorityOwnedWomenOwned Total Minority-Owned Women-OwnedNon MinorityOwnedMinorityOwnedWomenOwnedNot WomenOwned

Non Minority/ 

MinorityOwned

Not 

Women/WomenOwned

1 2 1 4 0 0 522,500,000 0 0 130,625,000 - - 130,625,000 + +

2 1 5 178 63 70 213,892,375 67,639,625 96,713,125 1,271,763 1,073,645 1,381,616 1,084,993 71.10% 71.61%

3 1 1 9 2 3 392,706,797 98,926,414 144,099,005 41,968,626 49,463,207 48,033,002 41,434,632 55.52% 59.64%

4 2 2 18 0 0 7,019,403,797 - - 389,966,878 - - 389,966,878 + +

5 1 2 89 25 15 10,071,708,842 2,329,565,519 1,539,695,042 120,970,989 93,182,621 102,646,336 115,297,484 62.15% 54.46%

6 1 3 67 5 4 216,239,603 3,329,617 4,733,800 3,434,032 665,923 1,183,450 3,357,235 99.64%* 96.56%*

7 1 2 80 4 5 204,267,144 10,636,800 11,337,576 2,547,768 2,659,200 2,267,515 2,572,394 51.67% 99.84%

8 2 4 1 0 0 682,500,000 - - 682,500,000 - - 682,500,000 + +

9 2 4 1 0 0 52,295,000 - - 52,295,000 - - 52,295,000 + +

10 1 2 7 2 1 904,607,467 223,010,250 23,619,778 136,319,443 111,505,125 23,619,778 146,831,282 56.23% +

11 1 2 125 16 8 2,517,439,565 79,809,552 23,051,314 22,363,578 4,988,097 2,881,414 21,319,558 98.68%* 99.63%*

12 2 2 10 0 1 1,842,533 0 7,100 184,253 - 7,100 203,937 + +

14 2 2 17 1 0 13,638,940 31,735 - 850,450 31,735 - 802,291 + +

15 2 2 2 0 0 173,234,888 - - 86,617,444 - - 86,617,444 + +

16 2 2 14 2 2 96,232,060 521,885 521,885 7,975,848 260,943 260,943 7,975,848 80.98% 84.17%

17 2 3 104 4 8 578,663,029 417,475 16,912,510 5,782,456 104,369 2,114,064 5,851,568 93.26% 88.51%

18 2 1 44 1 4 21,650,301 390,608 417,323 494,411 390,608 104,331 530,824 + 90.22%

20 2 2 4 0 0 7,459,200 0 0 1,864,800 - - 1,864,800 + +

21 2 2 4 0 0 3,438,294 - - 859,574 - - 859,574 + +

Total NA NA 778 125 121 23,693,719,833 2,814,279,480 1,861,108,457 31,974,641 22,514,236 15,381,062 33,230,763 74.15% 89.08%

* Statistically significant at 95% level.

+ Not enough minority or women winners or applicants for valid t-test.

^ See Appendix B for details on t-tests.

Auction group 1: With installment plans Auction group 2: Without installment plans

Industry group 1: Advanced paging/data Industry group 2: Mobile voice&data Industry group 3: Interactive data Industry group 4: Wireless cable

Industry group 5: Multichannel video
10/05/00

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Table 18

Average Economic Value per Winner by Auction Group

WINS NET REVENUE ($) AVERAGE NET REVENUE PER WINNER ($) STATISTICAL SIGNIFICANCE^

Auction 

Group Total

MinorityOwnedWomenOwned Total Minority-Owned Women-OwnedNon MinorityOwnedMinorityOwnedWomenOwnedNot WomenOwned

Non 

Minority/ 

MinorityOwned

Not 

Women/WomenOwned

1 555 117 106 14,520,861,792 2,812,917,777 1,843,249,639 26,730,466 24,042,032 17,389,148 28,235,216 56.51% 73.98%

2 223 8 15 9,172,858,042 1,361,703 17,858,818 42,658,123 170,213 1,190,588 44,014,419 99.82% * 99.77% *

Total 778 125 121 23,693,719,834 2,814,279,480 1,861,108,457 31,974,641 22,514,236 15,381,062 33,230,763 74.15% 89.08%

- Auction group 1 = With installment plans (consists of auctions 2, 3, 5, 6, 7, 10, 11).

 - Auction group 2 = No installment plans (consists of auctions 1, 4, 8, 9, 12, 14, 15, 16, 17, 18, 20, 21).

 * Statistically significant at the 95% level.

^ See Appendix B for details on t-tests.
10/05/00

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Table 19

Average Economic Value per Winner by Industry Group

WINS NET REVENUE ($) AVERAGE NET REVENUE PER WINNER ($) STATISTICAL SIGNIFICANCE^

Industry 

Group Total

MinorityOwnedWomenOwned Total Minority-Owned Women-OwnedNon MinorityOwnedMinorityOwnedWomenOwnedNot WomenOwned

Non 

Minority/ 

MinorityOwnedNot Women/WomenOwned

1 57 3 7 936,857,098 99,317,022 144,516,328 15,510,001 33,105,674 20,645,190 15,846,815 69.42% 63.03%

2 370 50 32 21,013,272,729 2,643,575,741 1,598,232,694 57,405,303 52,871,515 49,944,772 57,440,947 55.30% 56.27%

3 171 9 12 794,902,632 3,747,092 21,646,310 4,883,676 416,344 1,803,859 4,863,247 99.83%* 93.83%

4 2 0 0 734,795,000 - - 367,397,500 - - 367,397,500 + +

5 178 63 70 213,892,375 67,639,625 96,713,125 1,271,763 1,073,645 1,381,616 1,084,993 71.10% 71.61%

Total 778 125 121 23,693,719,833 2,814,279,480 1,861,108,457 31,974,641 22,514,236 15,381,062 33,230,763 74.15% 89.08%

- Industry group 1 = Advanced paging/data (consists of auctions 1, 3, 18).

- Industry group 2 = Mobile voice and data (consists of auctions 4, 5, 7, 10, 11, 12, 14, 15, 16, 20 , 21).

- Industry group 3 = Interactive data (consists of auctions 6, 17).

- Industry group 4 = Wireless cable (consists of auctions 8, 9).

- Industry group 5 = Multichannel video (consists of auction 2).

Table 20

Average Economic Value per Winner by Company Size

WINS NET REVENUE ($) AVERAGE NET REVENUE PER WINNER ($) STATISTICAL SIGNIFICANCE^

Size Total

MinorityOwnedWomenOwned Total Minority-Owned Women-OwnedNon MinorityOwnedMinorityOwnedWomenOwnedNot WomenOwned

Non 

Minority/ 

MinorityOwnedNot Women/WomenOwned

Non-Small 139 6 5 10,979,543,634 8,383,842 5,631,850 82,489,923 1,397,307 1,126,370 81,894,864 99.97%* 99.97%*

Small 639 119 116 12,714,176,199 2,805,895,638 1,855,476,607 19,054,386 23,578,955 15,995,488 20,762,332 65.41% 62.44%

Total 778 125 121 23,693,719,833 2,814,279,480 1,861,108,457 31,974,641 22,514,236 15,381,062 33,230,763 74.15% 89.08%

*Statistically significant at the 95% level.

+ Not enough minority or women winners or applicants for valid t-test.

^ See Appendix B for details on t-tests.
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Table 21

Return on Payment Ratios for Qualified Applicants by Auction

GROUPS Upfront Payments ($) Net Revenue ($) Return On Payment

Auction

Auction 

Group

Industry 

Group Total Minority-Owned

WomenOwned TotalMinorityOwnedWomenOwnedNon MinorityOwnedMinorityOwnedWomenOwnedNot WomenOwned

1 2 1 No data No data No data Not included Not included Not included No data No data No data No data

2 1 5 No data No data No data 213,892,375 67,639,625 96,713,125 No data No data No data -

3 1 1 No data No data No data Not included Not included Not included No data No data No data No data

4 2 2 522,339,935 0 0 7,019,403,797 0 0 1.00 - - 1.00

5 1 2 767,591,100 157,243,732 66,206,561 10,071,708,842 2,329,565,519 1,539,695,042 0.97 1.13 1.77 0.93

6 1 3 15,028,291 270,311 366,383 216,239,603 3,329,617 4,733,800 1.00 0.86 0.90 1.00

7 1 2 41,144,002 660,077 1,168,397 204,267,144 10,636,800 11,337,576 0.96 3.25 1.95 0.97

8 2 4 No data No data No data Not included Not included Not included No data No data No data No data

9 2 4 No data No data No data Not included Not included Not included No data No data No data No data

10 1 2 49,716,127 7,365,238 4,100,238 904,607,467 223,010,250 23,619,778 0.88 1.66 0.32 1.06

11 1 2 763,199,365 13,996,809 10,122,758 2,517,439,565 79,809,552 23,051,314 0.99 1.73 0.69 1.00

12 2 2 170,000 5,000 15,000 1,842,533 0 7,100 1.03 0.00 0.04 1.09

14 2 2 232,789,217 137,850 - 13,638,940 31,735 - 1.00 3.93 - 1.00

15 2 2 No data No data No data Not included Not included Not included No data No data No data No data

16 2 2 18,358,604 146,851 94,347 96,232,060 521,885 521,885 1.00 0.68 1.06 1.00

17 2 3 359,693,769 6,044,815 7,455,432 578,663,029 417,475 16,912,510 1.02 0.04 1.41 0.99

18 2 1 14,947,467 212,455 246,611 21,650,301 390,608 417,323 1.00 1.27 1.17 1.00

20 2 2 No data No data No data Not included Not included Not included No data No data No data No data

21 2 2 No data No data No data Not included Not included Not included No data No data No data No data

Total NA NA 2,784,977,878 186,083,138 89,775,727 21,859,585,655 2,715,353,066 1,717,009,453 0.94 1.86 2.44 0.95

No data indicates that no data were available for these categories.

Not included indicates that data exist for these categories but have been omitted so that totals are calculated for auctions with valid upfront payment data only.

Auction group 1: With installment plans Auction group 2: Without installment plans

Industry group 1: Advanced paging/data Industry group 2: Mobile voice&data Industry group 3: Interactive data Industry group 4: Wireless cable

Industry group 5: Multichannel video
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Table 22

Return on Payment Ratios for Qualified Applicants by Auction Group

Upfront Payments ($) Net Revenue ($) Return On Payment

Auction 

Group Total

MinorityOwnedWomenOwned Total Minority-Owned Women-Owned

Non 

MinorityOwnedMinorityOwnedWomenOwned

Not 

WomenOwned

1 1,636,678,886 179,536,167 81,964,337 14,128,154,995 2,713,991,363 1,699,150,635 0.91 1.75 2.40 0.93

2 1,148,298,992 6,546,971 7,811,390 7,731,430,660 1,361,703 17,858,818 1.01 0.03 0.34 1.00

Total 2,784,977,878 186,083,138 89,775,727 21,859,585,655 2,715,353,066 1,717,009,453 0.94 1.86 2.44 0.95

- Auction group 1 = With installment plans (consists of auctions 2, 3, 5, 6, 7, 10, 11).

 - Auction group 2 = No installment plans (consists of auctions 1, 4, 8, 9, 12, 14, 15, 16, 17, 18, 20, 21).

 
10/05/00

35

Table 23

Return on Payment Ratios for Qualified Applicants by Industry Group

Upfront Payments ($) Net Revenue ($) Return On Payment

Industry 

Group Total

MinorityOwnedWomenOwned Total Minority-OwnedWomenOwned

Non 

MinorityOwnedMinorityOwnedWomenOwned

Not 

WomenOwned

1 14,947,467 212,455 246,611 21,650,301 390,608 417,323 1.00 1.27 1.17 1.00

2 2,395,308,351 179,555,557 81,707,301 20,829,140,347 2,643,575,741 1,598,232,694 0.94 1.69 2.25 0.96

3 374,722,060 6,315,126 7,821,815 794,902,632 3,747,092 21,646,310 1.01 0.28 1.30 0.99

4 No data No data No data Not Included Not Included Not Included No data No data No data No data

5 No data No data No data 213,892,375 67,639,625 96,713,125 No data No data No data No data

Total 2,784,977,878 186,083,138 89,775,727 21,859,585,655 2,715,353,066 1,717,009,453 0.94 1.86 2.44 0.95

- Industry group 1 = Advanced paging/data (consists of auctions 1, 3, 18).

- Industry group 2 = Mobile voice and data (consists of auctions 4, 5, 7, 10, 11, 12, 14, 15, 16, 20 , 21).

- Industry group 3 = Interactive data (consists of auctions 6, 17).

- Industry group 4 = Wireless cable (consists of auctions 8, 9).

- Industry group 5 = Multichannel video (consists of auction 2).

Table 24

Return on Payment Ratios for Qualified Applicants by Company Size

Upfront Payments ($) Net Revenue ($) Return On Payment

Size Total

MinorityOwnedWomenOwned TotalMinorityOwned Women-OwnedNon MinorityOwnedMinorityOwnedWomenOwnedNot WomenOwned

Non-Small 1,407,585,613 189,800 310,000 9,355,223,633 8,383,842 5,631,850 1.00 6.65 2.73 1.00

Small 1,377,392,265 185,893,338 89,465,727 12,504,362,022 2,706,969,224 1,711,377,603 0.91 1.60 2.11 0.92

Total 2,784,977,878 186,083,138 89,775,727 21,859,585,655 2,715,353,066 1,717,009,453 0.94 1.86 2.44 0.95

No data indicates that no data were available for these categories.

Not included indicates that data exist for these categories but have been omitted so that totals are calculated for auctions with valid upfront payment data only.
 10/05/00

36

Appendix A: Chi-Square Test of Statistical Significance

A chi-square test is used to determine whether there are systematic differences in

utilization ratios across demographic groups for each auction. The null hypothesis of the

chi-square test is that there are no such differences in ratios.

The chi-square test statistic is based on a frequency table. In the case of utilization ratios,

the frequency tables are 2x2 tables with demographic group (e.g. minority/non-minority)

along one dimension and auction outcome (e.g., winner/non-winner) along the other. The

chi square test statistic is calculated as:

 χdf

2

 =

i

C

i

R

= =

∑∑

1 1

( f e )

e

ij

ij

− ij

2

 

where fij is the observed frequency in the ij cell of the frequency table

eij is the expected frequency in the ij cell if the null hypothesis is true

R is the number of rows in the frequency table

C is the number of columns in the frequency table

The expected frequency under the null hypothesis is calculated as:

eij = 

( f )( f )

N

i j

where fi is the total in the ith row marginal

fj is the total in the jth row marginal

N is the total number of observations in the frequency table

The degrees of freedom for this test statistic are given by:

df = (R-1)(C-1)

Reference:

Knoke, David, and George W. Bohrnstedt, Statistics for Social Data Analysis, F.E.

Peacock Publishers Inc., Itasca IL.,1994.
 10/05/00

37

Appendix B: t test: Testing for the Difference Between Two Means

A t-test is used to determine whether two means are equal. The null hypothesis under the

t-test is that there are no differences in the means. To determine if the difference of the

average net revenues between the minority and non-minority license winners and the

male and female winners were significantly different, we used the following form of the

t-test:

tdf = 

x y

S

n

S

n

−

+

1

2

1

2

2

2

where x is the mean of the first group

 y is the mean of the second group

 S1

2 is the variance from the first group

 S2

2

 is the variance of the second group

 n1 is the total number of observations in the first group

 n2 is the total number of observations in the second group

The degrees of freedom can be approximated as follows:

df = 

(S S )

S

n

n

S

n

n

2

1

2

2

2

1

2

1

2

1

2

2

2

2

2

1 1

+













−

+













−

The null hypothesis that the mean difference is zero is rejected if the test statistic t is

greater than the critical value at a .05 level of significance. In other words, if the

calculated t is greater than the critical value, we would conclude that there is a statistically

significant difference between the two means.

Reference:

Dixon, Wilfrid J., and Frank J. Massey Jr., Introduction to Statistical Analysis, McGrawHill Company, New York, 1969.