Assumptions Behind Hypothesis Tests
Test
Type of data
One-sample Z
Quantitative – one variable
One-sample t
Quantitative – one variable
One-way 2
Qualitative – one variable
Two-way 2
Qualitative – two variables
Note: can have two DVs (like
a qualitative correlation) or
one IV and one DV (like a
qualitative independent t)
Quantitative – same variable
measured twice (same person
measured under two conditions
or matched subjects measured
under different conditions)
Note: this test is like a onesample t-test conducted on a
sample of difference scores
Quantitative (DV) and
Qualitative (true IV or
grouping variable) with only
two possible values for the
qualitative variable
Quantitative (DV) and
Qualitative (true IV or
grouping variable) with three
or more possible values for the
qualitative variable. Note: this
test is an extension of the
independent t-test to compare
3 or more groups.
Quantitative – two variables
Dependent t
(two-dependent
samples)
Independent t
(two independent
samples)
One-way F
(ANOVA)
Correlation
(Pearson r)
Assumptions & Non-directional Null
Known mean and SD for null hypothesis;
adequate sample size to meet central limit
theorem
H0: 1 = null
Known mean for null hypothesis; adequate
sample size to meet central limit theorem
(estimate SD from sample)
H0: 1 = null
Known pattern of proportions for null
hypothesis; adequate sample size to make
minimum expected frequency of 5 per cell
H0: a1 = anull ; b1 = bnull ; c1 = cnull
Adequate sample size to make minimum
expected frequency of 5 per cell
H0: the two variables are independent / notrelated to each other
Known mean for null hypothesis; adequate
sample size (of difference scores) to meet
central limit theorem; Note null hypothesis is
about the mean difference score
H0: diff = 0
Known mean for null hypothesis; adequate
sample size to meet central limit theorem;
Note null hypothesis is a about the difference
between two independent sample means
H0: 1 = 2 or H0: (1 - 2) = 0
Known mean for null hypothesis; adequate
sample size to meet central limit theorem;
Note null hypothesis is about the difference
between a set of independent sample means
H0: 1 = 2 = 4 = 4 …
Both variables are reasonably normally
distributed, the relationship between them is
linear and homoscedastic, the range of both
variables is appropriate to the research
question
H0:  = 0