T Tests

Page 1

T-Test in a nutshell

Looking at the differences in the Mean of two groups in relation to the Variance of the groups

t = Mean Group A - Mean Group B / Standard Error of the Mean

Variance

σ^2

An example:

Take these scores: 1, 4, 5, 6, 9, 11

Calculate the mean score: 6

Calculate the deviation of each score from the mean:

1-6 = -5^2=25

4-6 = -2^2=4

5-6 = -1^2=1

6-6 = 0^2=0

9-6 = 3^2=9

Now what happens if you add all of

the SQUARED DEVIATIONS up? =64

Then

take the mean of the deviations=64/6=10.67

Standard Deviation

...is the square root of Variance. That's it.

Page 2

Standard Error

The degree to which the sample differs from the population

The lower, the better

Independent Samples t-test (or between groups, unrelated t-test)

Are the two samples drawn from the same population or from different populations?

- 2 sets of observations, each from different participants

Steps:

1. Analyse -> Explore -> Click Normality Plots at "Plots"

-> For smaller sample size ( <50 ) look at Shapiro-Wilk, if bigger use Kolmogorov-Smirnov

-> Look for insignificance

2. Analyse -> Compare Means -> Independent Samples T Test

-> Put Dependent Variable in "Grouping Variable" and don't forget to specify group codes! (dogs=0, cats=1)

Cohen's d

d= Mean1 - Mean2 / Mean Standard Deviation

Gives an indication of the MAGNITUDE of the observed effect

Dependent Samples t-test (or within groups, related, correlated, paired samples t-test)

Steps:

1. Transform -> Compute New Variable -> Difference between two variables (ONLY FOR NORMALITY)

2. Explore Normality of new computed variable

3. Analyse -> Compare Means -> Paired Samples T Test

-> Report t, df, p and Cohen's d

4. Cohen's d formula:

d = Mean / Standard Deviation (Both directly in Paired Samples Test Table!!!!)

Page 3

Correlation and Partial Correlation

Steps:

1. Check Normality

-> Analyse -> Explore -> Check "Normality Plots"

2. Check Linearity

-> Graphs -> Legacy Dialogs -> Scatter (simple)

3. Correlate

-> Analyse -> Correlate -> Bivariate

4. R^2

-> Take Correlation Coefficient and square it and multiply by 100

5. Partial Correlation

-> Correlate -> Partial - > "Options", then check zero order