Could you please set an exam paper with 30 multiple choice questions with 4 possible answers.

Here are rules you need to follow when setting the paper:

1. The scope of these questions must be loosely based on topics discussed in the slides from your previous lecture.
2. For each question you must indicate the correct option.

Here are the slides from your past lecture:

Variance = how far a

set of numbers

(random) are spread
out from their average

value (mean)

Social scientists cannot always
do two sample group
comparisons. Often comparisons

between three or more groups
is necessary.
e.g. Say we wanted to find out
how small classroom size
impacts academic achievement
between races. There are more
than 2 races in this class and
thus there will be more than 2
sample groups to compare.
In these cases, we use a
statistical test known as the
analysis of variance (we analyse
the variance within the groups
AND between the groups)

If we have 3 sample groups with
the following raw data:
• 8, 10, 11
• 15, 18, 20
• 23, 24, 27
What are we looking at when we
look at variation within groups
and variation between groups?
Let’s watch a video to explain

The F ratio looks at the size of
the between-groups mean
square relative to the size of the
within group mean square:

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Note: You will not be required to
do an F-ratio as it is far more
technical than you would expect
BUT do know what this formula
means and what it is used for

• A comparison between three
or more means from
independent samples

• Interval data is usually used
and not categorised or ranked
data
• Samples should be selected
randomly
• The characteristics we are
comparing are normally
distributed in the underlying
populations
• Equal variance (homogeneity
of variance) which means that
the variance among the
groups should be
approximately equal (requires
that the variance within each
sample be equal for all
samples) .

Marketing Communication

MCP125

• Theme 9 Outcomes
(Chapter 9): Non-
parametric tests of
significance

• Discuss situations in
which nonparametric
tests can be applied

• Summarise the

application possibilities
for the chi-square test

We first need to know what a
parametric test is (so far, we
have been discussing these
without you knowing it) before

we can discuss what a
NONparametric test is.

So, what is a parametric test?

When a test of significance (t-
ratio or f-ratio) requires:

• Normality in the population (or
at least large samples so that
the sampling distribution of
means is normal)
• And interval-level measure
(where there is order and the
difference between two
values is meaningful)
It is referred to as a parametric
test because it makes
assumptions about the nature of
population parameters

What about a researcher who
cannot assume normality
(working with skewed data),
does not work with large

numbers of cases (large sample
groups) or with data that has
been categorised and counted
(nominal level) or ranked (ordinal

level)?

The researcher uses a
nonparametric test of

significance – tests whose list of
requirements does not include
normality or the interval level of

measurement

Power of a test = the probability
of rejecting the null hypothesis
when it is actually false and

should be rejected.

Power varies from one test to
another. The most powerful
tests are tests that have the
strongest or most difficult
requirements to satisfy e.g.
parametric tests such as t- and f-

ratios.

By contrast, nonparametric tests
are not so demanding but are

less powerful.

Chi-square ( ﷐��﷮� ﷯)
A test used to determine
whether frequencies observed
differ significantly from an even
distribution.

Chi-square allows us to test the
significance of difference
between a set of observed
frequencies (﷐��﷮0﷯) and expected
frequencies (﷐��﷮��﷯)

Let me explain on the next
slide…

﷐��﷮2﷯ is calculated by
﷐﷮﷮﷐﷐﷐﷐��﷮0﷯−����﷯﷮2﷯﷮﷐��﷮��﷯﷯﷯

Don’t panic!

You WILL BE required to do this
calculation so I will explain it to you in
a simplified way so that you can
grasp the basic concept and
understand what you are attempting

to learn

Let’s say that we wanted to
study whether the travel
methods have changed in the
past 7 years in South Africa.
Let’s pretend we have data from
7 years ago (which would be the
basis of our null hypothesis)

In other words, we want to know
whether modes of transport have
altered between the following:
Bus
Train
Car
Taxi
• Always start by defining the
hypothesis
Step 1: Define the ﷐��﷮0 ﷯������
1﷯:
• The ﷐��﷮0 ﷯always states that
the observed data of the
random variable fits the
proposed theoretical or user-
defined probability pattern of

outcomes (commuting patterns
7 years ago)
Please note:
• ﷐��﷮o﷯= observed frequencies
• ﷐��﷮��﷯= expected frequencies
• What our hypothesis would
look like
• ﷐��﷮0﷯:﷐��﷮0﷯=﷐��﷮��﷯ (the null
hypothesis)

OR

• ﷐��﷮0﷯: commuting patterns are
the same as they were seven
years ago

• ﷐��﷮1﷯:﷐��﷮o﷯≠﷐��﷮��﷯ (research
hypothesis)

OR

• ﷐��﷮1﷯: commuting patterns are
not the same as they were
seven years ago

Let us jump a few steps and
pretend we have gathered all the
data required to work out the
﷐��﷮2﷯

This would include factors such
as:
• the degrees of freedom (the
number of independent pieces
of information used to
calculate a statistic) which is 4
• level of significance (the
probability of rejecting the null

hypothesis when it is true,
which we will state as .05
• Then we would come up with
this frequency table
For the significance level of .05,
the critical value for chi-square
with 4 degrees of freedom is
9.488.
This is the value we must
exceed before we can reject the
null hypothesis.
9.956 DOES exceed 9.488 thus
we reject the null hypothesis and
accept the research hypothesis
that commuting patterns have
changed from 7 years ago

We have previously sought
to discover whether a
difference between two or
more samples could be
regarded as statistically
significant (and not due to

sampling error)

Now we turn our attention to
the existence and strength of
relationship between two
variables – their co-
relationship or their

correlation

e.g. we know there is a
correlation between height

and weight, right?

• Correlations vary in their
strength and these are
visualised in a scatter plot
– a graph that shows the
way scores on any two

variables (X and Y) are
scattered throughout the
range of possible score
values
• X variable is always along
the horizonal (generally the
independent variable) and
Y is on the vertical
(dependent variable)

• Pearson’s r does more than
just consider if subjects are
simply taller or heavier than
other subjects – it considers
exactly HOW MUCH MORE.
• Pearson’s r focuses on the
product of the X and Y
deviations from their
respective means.
• The deviation (X-Y) tells how
much taller or shorter than the
average
• The deviation (Y-X) tells how
much heavier or lighter than
the average

You will NOT be expected to
know this for the exams but let’s
test our brains and see if you
could figure it out. Pretend we
have taken the height (X) and
weight (Y) of 8 children: