# Presentation: 245499

## Stats 101

**Leonard M. Gaines, Ph.D.**
**New York SDC**
**Empire State Development**
**LGAINES@EMPIRE.STATE.NY.US**
**518-292-5300 ext. 4**

## Overview

- Sampling
- Errors
- Identifying the middle
- Variation and Central Tendency
- Checking for Differences

## Sampling

- Simple Random Sample
- Select sample from population as one group
- Stratified Random Sampling
- Divide population into relevant sub-groups
- Select sample from each sub-group
- Ensures large enough sample from each sub-group
- Frequently need smaller total sample

## Errors

- Sampling Error
- Error that results from taking a sample
- Different samples of the same population give different results
- Nonsampling Error
- Errors that come from other sources
- Data entry errors
- Questions answered incorrectly
- Poorly worded questions
- Bias

## Finding the middle

- Mean
- Arithmetic or Weighted Average
- Median
- Rank order members of group
- Count halfway through group
- Can be calculated from grouped data
- Which measure is better?
- If symmetric distribution – mean is fine
- If distribution is skewed – median is usually better

## Variation

- Happens in the real world
- Questions to consider
- How much variation is there?
- How useful is your data?
- How does this affect your conclusions?
- Why do we need to worry about this?

## Slide 7

## Slide 8

## Margin of Error

## Measures of Central Tendency

- Measures of Variation
- Standard Deviation & Standard Error
- Margin of Error
- Confidence Interval
- Coefficient of Variation

## Standard Deviation & Standard Error

- Standard Deviation
- Average of the distance of each observation from the mean
- Standard Error
- Measure of the deviation of a sample estimate from the average of all possible sample estimates
- Estimates sampling error

## Margin of Error (MOE)

- Shows the range likely to contain the estimate from all possible samples
- Based on a predetermined probability of containing the estimate
- Related to the Standard Error
- 68 percent MOE = 1 times the standard error
**90 percent MOE = 1.645 times the standard error**
- 95 percent MOE = 2 times the standard error
- Usually reported as Estimate +/- MOE
- Census Bureau reports Estimate and MOE individually

## Confidence Interval

- The range that is likely to contain the average of an estimate based on all possible samples based on a given probability.
- A 90 percent Confidence Level has a 90 percent chance of containing the average estimate
- Higher confidence intervals give wider ranges
- Range from estimate +/- Margin of Error
- Usually shown as a range
- 90% CI – 1.0 to 2.0
- 95% CI – 1.5 to 2.5

## Coefficient of Variation

- Measure of relative variation
- Variation (standard deviation/standard error) as a percentage of estimate
- Quick way to compare the quality of two different measures
- Census Bureau uses this in deciding which ACS tables to publish

## Testing for Statistical Differences I

- Statistically Significant difference is _***NOT***_ the same as practically important difference
- Informal Quick and Dirty Method
- Both estimates inside the CI for the other estimate – no difference
- Neither estimate inside the CI for the other estimate – difference exists
- One estimate is inside the CI for the other estimate – inconclusive – must use formal procedures

## Testing for Differences II

- Formal Methods – more accurate than informal
- Four steps
- State hypotheses
- Null (H0) – no difference (measure 1 = measure 2)
- Alternate (Ha) – difference (Measure 1 ≠  measure 2)
- Calculate test statistic
- Compare test statistic to threshold value or find p-value
- Interpret result and state conclusion

## Slide 17