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# T test for independent variables

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### T test for independent variables

1. 1. AGUSTIN.DE VILLA.DOMINGO.VERZOSA III-BECQUEREL T-TEST FOR INDEPENDENT VARIABLES
2. 2. WHAT IS THIS TEST?  The t-test assesses whether the means of two groups are statistically different from each other. This analysis is appropriate whenever you want to compare the means of two groups, and especially appropriate as the analysis for the posttest-only two-group randomized experimental design.
3. 3. WHAT IS THIS TEST?  The test statistic in the t-test is known as the t-statistic. The t-test looks at the t- statistic, t-distribution and degrees of freedom to determine a p value (probability) that can be used to determine whether the population means differ. The t- test is one of a number of hypothesis tests. To compare three or more variables, statisticians use an analysis of variance (ANOVA). If the sample size is large, they use a z-test. Other hypothesis tests include the chi-square test and f-test.
4. 4. WHAT IS THIS TEST?  A statistical examination of two population means.  A two-sample t-test examines whether two samples are different and is commonly used when the variances of two normal distributions are unknown and when an experiment uses a small sample size. For example, a t-test could be used to compare the average floor routine score of the U.S. women's Olympic gymnastic team to the average floor routine score of China's
5. 5. WHERE IS IT USED?
6. 6. Hypothesis for the independent t-test  The null hypothesis for the independent t-test is that the population means from the two unrelated groups are equal:  H0: u1 = u2  In most cases, we are looking to see if we can show that we can reject the null hypothesis and accept the alternative hypothesis, which is that the population means are not equal:  HA: u1 ≠ u2  To do this, we need to set a significance level (alpha) that allows us to either reject or accept the alternative hypothesis. Most commonly, this value is set at 0.05.
7. 7. What do you need to run an independent t-test?  In order to run an independent t- test, you need the following:  One independent, categorical variable that has two levels.  One dependent variable.
8. 8. Unrelated groups  Unrelated groups, also called unpaired groups or independent groups, are groups in which the cases in each group are different. Often we are investigating differences in individuals, which means that when comparing two groups, an individual in one group cannot also be a member of the other group and vice versa. An example would be gender - an individual would have to be classified as either male or female - not both.
9. 9. STEPS Determine the null and alternative hypothesis. Determine α
10. 10. STEPS Create four columns: "x", "(x-Mx)2", "y", "(y-My)2" Put the raw data for group X in column x, and for group Y in column y
11. 11. STEPS Calculate the mean for both groups
12. 12. STEPS Calculate deviation scores for each group by subtracting each score from it's group mean and squaring it and put these in the columns "(x- Mx)2" and "(y-My)2"
13. 13. STEPS Sum the squared deviation scores for each group
14. 14. STEPS Calculate S2 for each group x = individual scores M = mean n= number of scores in group
15. 15. STEPS Set up formula Calculate t M = mean n = number of scores per group
16. 16. STEPS Check to see if t is statistically significant on probability table with df = N-2 and p < .05 (N = total number of scores)
17. 17. PROBLEM  Sam Sleepresearcher hypothesizes that people who are allowed to sleep for only four hours will score significantly lower than people who are allowed to sleep for eight hours on a cognitive skills test. He brings sixteen participants into his sleep lab and randomly assigns them to one of two groups. In one group he has participants sleep for eight hours and in the other group he has them sleep for four. The next morning he administers the SCAT (Sam's Cognitive Ability Test) to all participants. (Scores on the SCAT range from 1-9 with high scores representing better performance).
18. 18. DATA TABLE SCAT scores 8 hours sleep group (X) 5 7 5 3 5 3 3 9 4 hours sleep group (Y) 8 1 4 6 6 4 1 2
19. 19. STEP 1  Null hypothesis: People who are allowed to sleep for only four hours will not score significantly lower than people who are allowed to sleep for eight hours on a cognitive skills test.  Alternative Hypothesis: People who are allowed to sleep for only four hours will score significantly lower than people who are allowed to sleep for eight hours on a cognitive skills test.
20. 20. STEP 2 x (x-Mx)2 y (y - My)2 5 0 8 16 7 4 1 9 5 0 4 0 3 4 6 4 5 0 6 4 3 4 4 0 3 4 1 9 9 16 2 4
21. 21. STEP 3 x (x-Mx)2 y (y - My)2 5 0 8 16 7 4 1 9 5 0 4 0 3 4 6 4 5 0 6 4 3 4 4 0 3 4 1 9 9 16 2 4
22. 22. STEP 4 x (x-Mx)2 y (y - My)2 5 0 8 16 7 4 1 9 5 0 4 0 3 4 6 4 5 0 6 4 3 4 4 0 3 4 1 9 9 16 2 4 x=40 (x-Mx)2=32 y=32 (y-My)2=46 Mx=5 My=4
23. 23. STEP 5 CALCULATE FOR t.
24. 24. STEP 6 According to the t sig/probability table with df = 14, t must be at least 2.145 to reach p < .05, so this difference is not statistically significant
25. 25. INTERPRETATION Sam's hypothesis was not confirmed. He did not find a significant difference between those who slept for four hours versus those who slept for eight hours on cognitive test performance.
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