The t-test for correlational groups is used to compare two groups whose measurements are interval or ratio in nature, where the samples are observed before and after the introduction of an independent variable. It is used for pre-test and post-test designs, repeated measures within subject designs, and matched sample designs. The two-tailed test is used to test whether the means of the two groups (before and after manipulation) are equal or different. The test involves calculating the t-critical value, t-calculated value, and comparing the two to determine whether to reject or fail to reject the null hypothesis that the means are equal.

1. T-TEST FOR CORRELATIVEGROUPS
- Usedto compare twogroupswhose measurementsare interval orration,where the
samplesare observedbefore andafterthe introductionof the independentvariable
- Usedin:
 Pre-testandpost-testof samples
 Repeatedmeasures withinsubjectdesigns
 Matched sample designs
* two-tailedtestof significance isused( ±)
*assume normal distribution
How to use:
1. State hypotheses.
Ho (null hypothesis) : Ma = Mb
Ha (alternative hypothesis):Ma= Mb
2. Findthe critical areaor t critical.
a. State 𝛼, or the level of significance.
b. Finddf,where df=n -1, where n= numberof samples  n-1 because onlyone groupof
samplesisused
c. Look upthe critical/tabularvalue of ton the table.
3. Set upthis table:
Sample/s Numerical
measurement
before
manipulation
Numerical
measurement
aftermanipulation
D D2
Where:
D = measurementsbefore –measurementsafter * noabsolute value
𝐷2 = (measurements before – measurements after)2
4. Calculate forthe test statistic,ort calc
a. Calculate the sumof squaresof the difference score,or ∑ 𝑑²
∑𝑑² = ∑ 𝐷² −
(∑ 𝐷)²
𝑛
 n = numberof samples
b. Calculate the standarderrorof meandifference,or 𝑆 𝐷
𝑆 𝐷 = √
∑ 𝑑²
𝑛(𝑛 − 1)

2. c. Calculate 𝐷
𝐷 =
∑ 𝐷
𝑛
d.Calculate t
𝑡 =
𝐷
𝑆 𝐷
* the final value of tmust be ±, since it’sa two-tailedtest.
5. Formulate the conclusion.
If:t calc > t critical
acceptHa, rejectHo the manipulationhasa significanteffect.
If:t calc < t critical
acceptHo, rejectHa  the manipulationhasnosignificanteffect.