en:statpqpl:porown2grpl:parpl:t_test2zalcpl

The -test for dependent groups is used when the measurement of an analysed variable you do twice, each time in different conditions (but you should assume, that variances of the variable in both measurements are pretty close to each other). We want to check how big is the difference between the pairs of measurements (). This difference is used to verify the hypothesis informing us that the mean of the difference in the analysed population is 0.

Basic assumptions:

- measurement on an interval scale,
- normality of distribution of measurements (or the normal distribution for an analysed variable in each measurement),

Hypotheses:

where:

, – mean of the differences in a population.

The test statistic is defined by:

where:

– mean of differences in a sample,

– standard deviation of differences in a sample,

– number of differences in a sample.

Test statistic has the t-Student distribution with degrees of freedom.

The p-value, designated on the basis of the test statistic, is compared with the significance level :

**Note**

**standard deviation of the difference**is defined by:

**standard error of the mean of differences**is defined by:

**Standardized effect size**.

The **Cohen's d** determines how much of the variation occurring is the difference between the averages, while taking into account the correlation of the variables.

.

When interpreting an effect, researchers often use general guidelines proposed by Cohen ^{1)} defining small (0.2), medium (0.5) and large (0.8) effect sizes.

The settings window with the `t-test for dependent groups`

can be opened in `Statistics`

menu→`Parametric tests`

→`t-test for dependent groups`

or in ''Wizard''.

**Note**

Calculations can be based on raw data or data that are averaged like: arithmetic mean of difference, standard deviation of difference and sample size.

A clinic treating eating disorders studied the effect of a recommended „diet A” on weight change. A sample of 120 obese patients were put on the diet. Their BMI levels were measured twice: before the diet and after 180 days of the diet. To test the effectiveness of the diet, the obtained BMI measurements were compared.

Hypotheses:

Comparing with a significance level we find that the mean BMI level changed significantly. Before the diet, it was higher by less than 2 units on average.

The study was able to use the Student's t-test for dependent groups because the distribution of the difference between pairs of measurements was a normal distribution (Lilliefors test, ).

Cohen J. (1988), Statistical Power Analysis for the Behavioral Sciences, Lawrence Erlbaum Associates, Hillsdale, New Jersey

en/statpqpl/porown2grpl/parpl/t_test2zalcpl.txt · ostatnio zmienione: 2022/09/13 22:34 przez admin

Wszystkie treści w tym wiki, którym nie przyporządkowano licencji, podlegają licencji: CC Attribution-Noncommercial-Share Alike 4.0 International