Two Independent samples
Data form
Independent variable (two levels)
Level 1
Level 2
𝑋1
𝑌1
⋮
⋮
𝑋𝑛1
𝑌𝑛2
Dependent (response) variable (continuous type)
H0: X1, …,Xn1 are coming from normal distribution (level 1)
H1: X1, …,Xn1 are not coming from normal distribution
Ho is rejected if sig(SPSS)=p-value < 𝛼
And
H0: Y1, …,Yn2 are coming from normal distribution (level 2)
H1: Y1, …,Yn2 are not coming from normal distribution
Ho is rejected if sig(SPSS)=p-value < 𝛼
Assumptions: Independent t-test
Assumption #1: Your dependent variable should be measured on
a continuous scale (interval or ratio level). Examples of variables: time
(measured in hours), intelligence (measured using IQ score), exam
performance (measured from 0 to 100), weight (measured in kg).
Assumption #2: Your independent variable should consist of two
categorical, independent groups. Example independent variables:
gender (2 groups: male or female), employment status (2 groups: employed
or unemployed), smoker (2 groups: yes or no), and so forth.
Assumption #3: Your dependent variable should be approximately
normally distributed for each group of the independent variable. You
can test for normality using the Kolmogorov-Smirnov or Shapiro-Wilk
test of normality
Assumption #4: There needs to be homogeneity of variances. You can
test this assumption in SPSS using Levene’s test for homogeneity of
variances.
𝐻0 : 𝜎12 = 𝜎22 vs 𝐻1 : 𝜎12 ≠ 𝜎22
The t test evaluates whether the mean value of the test variable (e.g., age)
for one group (e.g., boys) differs significantly from the mean value of the
test variable for the second group (e.g., girls).
When normality is not satisfied, the nonparametric procedures can be
much more efficient than their parametric equivalents.
Wilcoxon’s Rank Test (Mann-Whitney Test) for Two-Independent samples
H0: the two population distributions are the same
Ha: the two populations are in some way different
OR:
H0: the population distribution (histogram) for the continuous variable of
level 1 and the population distribution (histogram) for the continuous
variable of level 2 are the same (identical)
H1: the population distribution (histogram) for the continuous variable of
level 1 and the population distribution (histogram) for the continuous
variable of level 2 are not the same (identical)