Research Methods- Parametric tests of difference: Unrelated and related t-tests Flashcards
Why the unrelated t-test?
The unrelated t-test is a test of difference between two sets of data. It is used with interval-level data only. When an independent groups design is used, the test selected is the unrelated t-test.
What is the design and level of measurement in this example?
The design is independent groups (unrelated) because one group consists of girls and the other group consists of boys. The level of measurement is interval, as the time taken to complete a jigsaw puzzle is measured on a ‘safe’ scale with equal units. It is assumed that the participants are drawn from a normally distributed sample within the population, and there is homogeneity of variance as the standard deviations in both groups are similar.
What is the aim of the study?
The study investigates whether there is a difference in visuo-spatial ability between boys and girls. Ten girls and ten boys completed a simple jigsaw puzzle, and the time taken for each participant was recorded and compared.
What is the alternative hypothesis?
The alternative hypothesis is that there is a difference in the time taken by males and females to complete a jigsaw puzzle. (non-directional, two-tailed)
What is the null hypothesis?
The null hypothesis is that there is no difference in the time taken by males and females to complete a jigsaw puzzle.
What is Step 1 in the unrelated t-test analysis?
Step 1 involves creating a table of data and calculating the following:
- The sum of the scores for Group A (ΣX₁) and Group B (ΣX₂).
- The square of each value in Group A (X₁²) and Group B (X₂²).
What is Step 2 in the unrelated t-test analysis?
Step 2 involves calculating the value of t using the formula:
[ t = \frac{(\bar{X}_1 - \bar{X}_2)}{\sqrt{\frac{S_A + S_B}{N_A + N_B - 2} \times \left(\frac{1}{N_A} + \frac{1}{N_B}\right)}} ]
Where:
- ( S_A = \Sigma X_1^2 - \frac{(\Sigma X_1)^2}{N_A} )
- ( S_B = \Sigma X_2^2 - \frac{(\Sigma X_2)^2}{N_B} )
In this example, ( t = -0.116 ).
What is Step 3 in the unrelated t-test analysis?
Step 3 involves comparing the calculated value of t (-0.116) to the critical value of t (2.101) for a two-tailed test at the 0.05 level where degrees of freedom (df) = ( N_A + N_B - 2 = 18 ). Since the calculated value (ignoring the sign) is less than the critical value, the result is not significant (p > 0.05).
What conclusion is drawn from the unrelated t-test analysis?
The null hypothesis is accepted: There is no difference between males and females in the time taken to complete a jigsaw puzzle (p > 0.05).
Why the related t-test?
The related t-test is used when a repeated measures design is employed. Here, we are looking for a difference in the average heart rate before and after treatment (CBT).
What is the design and level of measurement in this example?
The design is repeated measures (related) because the same participants were tested twice. The level of measurement is interval, as heart rate (beats per minute, bpm) is measured on a ‘safe’ scale with equal units. It is assumed that participants were drawn from a normally distributed sample within the population, and homogeneity of variance is assumed.
What is the aim of the study?
The study investigates the effects of CBT on the physiological arousal of gamblers. Ten persistent gamblers underwent a six-week course of CBT. Their heart rate was monitored before and after treatment while playing a fruit machine for 20 minutes.
What is the alternative hypothesis?
The alternative hypothesis is that there is a reduction in heart rate activity when comparing heart rate before and after cognitive behaviour therapy. (directional, one-tailed)
What is the null hypothesis?
The null hypothesis is that there is no difference in heart rate activity comparing heart rate before and after cognitive behaviour therapy.
What is Step 1 in the related t-test analysis?
Step 1 involves creating a table of data and calculating the following:
- The difference (d) between scores for condition A (before treatment) and condition B (after treatment).
- The square of each difference (d²).
- The sum of the differences (Σd) and the sum of the squared differences (Σd²).
What is Step 2 in the related t-test analysis?
Step 2 involves calculating the value of t using the formula:
[ t = \frac{\Sigma d}{\sqrt{\frac{N \Sigma d^2 - (\Sigma d)^2}{N - 1}}} ]
In this example, ( t = 2.237 ).
What is Step 3 in the related t-test analysis?
Step 3 involves comparing the calculated value of t (2.237) to the critical value of t (1.833) for a one-tailed test at the 0.05 level where degrees of freedom (df) = ( N - 1 = 9 ). Since the calculated value is greater than the critical value, the result is significant (p ≤ 0.05).
What conclusion is drawn from the related t-test analysis?
The null hypothesis is rejected, and the alternative hypothesis is accepted: There is a reduction in heart rate activity comparing heart rate before and after cognitive behaviour therapy (p ≤ 0.05).
