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1. What is independent samples t-test?
1. What is independent samples t-test?
Independent samples t-test is to compare the means from TWO independent groups and see whether they are different. We use independent samples t-test when we have two groups of participants, each sampled from a population that is different from the other. For example, in a study on how cultures may affect behavior, we have one group of participants sampled in China and another group sampled in the US. To compare the means of some measurements (e.g., personality scores) between these two groups, we can use the independent samples t-test.
2. Example 1: Academic performance
2. Example 1: Academic performance
Some people believe that females have better academic performance than males. Suppose we use GPA as the measurement of academic performance to evaluate this belief.
Q: Do females have a higher GPA than males? (α = .05)
A: We used independent samples t-test (one-tailed) to examine.
Step 1: Set the research hypothesis: Female's GPA is higher than male's GPA.
Step 2: Assume that female is sample 1 and male is sample 2.
Step 3: Write down the null and alternative hypotheses:
H0 : μ1 - μ2 ≤ 0
H1 : μ1 - μ2> 0
Step 4: Perform the statistical analysis in jamovi (Please use full screen mode).
Example6.3_Independent T-Test_GPA.mp4Based on the results from jamovi, we can decide that there is no gender difference in GPA.
Conclusion / Interpretation (APA format)
Female's GPA (M = 3.02, SD = 0.512) was not higher than male's GPA (M = 3.03, SD = 0.522), t(198) = -0.162, p = . 564, d = -0.023.
3. Example 2: Lying tendency
3. Example 2: Lying tendency
There was a big controversy about who lies more, men or women? In order to find out the answer, we conducted a study to investigate the lying tendency of both genders. We used the scale of Lying Tendencies Survey (Mann , Garcia-Rada, Houser, Ariely, 2014), which consists of 16 items. Based on the scale, lying tendency is divided into four categories. Here, we focus on Antisocial Commission (AC) for our analysis.
Q: Do the genders differ on Antisocial Commission (AC) of lying tendency? (α = .05)
A: We used independent samples t-test (two-tailed) to examine.
Step 1: Set the research hypothesis: AC of male is different from AC of female.
Step 2: Assume that female is sample 1 and male is sample 2.
Step 3: Set the null and alternative hypotheses:
H0 : μ1 - μ2 = 0
H1 : μ1 - μ2 ≠ 0
Step 4: Perform the statistical analysis in jamovi (Please use full screen mode).
Example6.1 Independent T-Test.mp4Based on the results from jamovi, we can decide that male and female have different lying tendency in terms of antisocial commission.
Conclusion / Interpretation (APA format):
There was a significant difference in the antisocial commission between males (M = 4.26, SD = 0.702) and females (M = 3.99, SD = 0.738), t (198) = -2.70, p = 0.007, d = -0.383.
4. Equality of variances
4. Equality of variances
In order for the independent samples t-test to be valid, there is a mathematical assumption: the population variances of the two populations are assumed to be equal.
This is known as the equal-variance assumption (also known as the assumption of equality of variances).
In order to check whether this assumption is violated, we have to test for the homogeneity of variances of two samples.
Levene's test is a statistical test to check whether data from the two samples suggest that the variances from the two populations are significantly different.
Basically, Levene's test is similar to t-test, but the NULL hypothesis is that "the two population variances are equal". Suppose we set α = .05, which means that we need quite strong evidence from the samples in order for us to decide that the two population variances are different.
If p > α, we can decide that the two population variances are not significantly different, based on the sample data. In this case, we can assume that the variances are equal and proceed with interpreting the results from the independent-samples t-test.
However, if p < α, it means that evidence from the sample data is strong enough to convince us that the two population variances are different. In this case, we cannot directly interpret the results from the independent-samples t-test.
Now, let us look at an example below, in which the assumption of equal variances is NOT violated.
[For your interest: Levene's test can also test for variances of more than 2 samples. You will see it again in the later modules.]
[Challenge question: What if the assumption equal variances is VIOLATED? What are the possible consequences and potential remedies?]
5. Effect size for independent sample t-test
5. Effect size for independent sample t-test
Now we are interested in the standardized mean difference of a test value in one independent group and a test value in another group (for example, scores of the experimental group versus that of the control group).
Since we have two values from two independent groups, we need to pool these two groups SD. It's more difficult than one/paired sample to have the SD, because these separate groups may have different sample size and variation.
There is a shortcut that can calculate Cohen's d directly from the test statistic t-value and sample sizes.
Similarly, the interpretation of the independent samples Cohen's d is same as the one-sample/paired-samples Cohen's d.
Module Exercise
Module Exercise
Complete the exercise!
Complete the exercise!
Now, if you think you're ready for the exercise, you can check your email for the link.
Remember to submit your answers before the deadline in order to earn the credits!
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