stores in high promotion condition have higher average sales than stores in other conditionsReason: rejecting the null simply means that at least the average for one group is different from others, but didn’t say which group43

15Tests of Differences
1. One Sample
2. Two Independent
Samples
3. Paired
Samples
4. More Than
Two Samples
Which test to use? It depends on (1). the
number of variables and (2). Number of
groups involved
t tests
ANOVA
44
•
One-Sample t-test
–
One sample
•
Independent Samples t-test
–
Two independent samples
•
Paired samples t-test
–
Two dependent samples
•
ANOVA
–
Two or more samples
Summary
Average temperature in
August = 17
°
Sales in store A = Sales in
store B
Knowledge of statistics
after class = before class
Average fuel prices in
suburbs A,B and C are
different
45
Side topic - some further clarification of the
distinction between relational and comparative
RQs
46

16
47
So far we have suggested that there is a close
correspondence between the type of RQ and statistical
tests used
Hypothesis
Testing
Test of Association
(relational RQ)
Test of Differences
(comparative RQ)
Means
Proportions
Different forms of t test/ANOVA
•
Cross tabulation
•
Correlation
•
Multiple regression
48
It is important to recognize that the distinction is
artificial and sometimes not so clear-cut
Examples of a relational
RQ
1.Does genderaffect how frequently people eat fast-food?
2.Does education attainmentaffect how frequently people eat fast-food?
1.Do men and women differ in how frequently they eat fast-food?
2.
Does the
frequency of
fast-food consumption
differ across
people of
different levels of
education
?111
49
What characterizes these types of RQ is that the
independent variable (IV) is a categorical variable
while the dependent variable (DV) is metric
Example
Does
education attainment
affect
how frequently people eat fast-food
?
•
There is no test of association for this type of RQ (for test of associations
both variables need to be categorical or metric, but not one of each type)
•
What you need to do is to first
re-phrase
the relational RQ as the
corresponding comparative RQ and then choose the corresponding test
of differences (an independent-samples t test or one-way ANOVA)
IV is
categorical
DV is metric

17
Today’s agenda
50
•
Hypothesis testing – tests of differences
–
Different types of t tests
–
Two-tailed vs. one-tailed test
– ANOVA
•
How to write about hypothesis testing
•
A few words on assignment 2
How to write about hypothesis testing – the
formulaic approach
• 1
st
step – describe the test
– Which test did you use?
– What variables are involved?
–
What are the groups involved?