KIN 4310 1st Edition Lecture 16Outline of Last Lecture I. Review QuestionsOutline of Current Lecture I. Exam 3 TopicsII. The t-testIII. The t-test StepsIV. T-test ExampleV. QuestionVI. ANOVAVII. F-distributionVIII. ANOVA cont.Current LectureI. Exam 3 Topicsa. Dependent t-Testb. One-way ANOVAc. Two-way ANOVAd. Significant Correlationse. Measurement of:i. Health Statusii. Aerobic Fitnessiii. Body Compositioniv. Diet Physical ActivityII. The t-testa. A hypothesis test that is used to determine if there is a significant difference between two groupsThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.i. This is called the t-test for independent meansb. The t-test can also be used when there is only one group of subjects, and they are tested under two conditionsi. This is called the t-test for dependent meansc. T-test for dependent meansi. Requires paired dataii. Two sets using the same measurement scaled. Examplesi. Body mass index is measured before and after a special diet programii. Grip strength is measured in the dominant hand and the non-dominant hande. The t-test for dependent meansi. You have two groups of scoresii. Each score in group A is paired with a score in group Biii. The t-test is based on difference valuesf. You need the following:i. n: number of pairs of measurementsii.III. The t-test Stepsa. Step 1: Calculate the t-value for dependent meansi. Equation:ii.b. Step 2: After you know the t-value, you must determine the degrees of freedom (df)i. df = n-1 ii. df = number of pairs – 1c. Step 3: Determine the critical value of ti. Use table B2 of your textbookii. Critical t-value for df = 3, alpha = 0.051. One-tailed: tcrit = 2.3532. Two-tailed: tcrit = 3.182d. Step 4: Compare your t-value to the critical valuei. One-tailed: tcrit = 2.353ii. Two-tailed: tcrit = 3.182iii. t = 2.93e. Step 5: Make a decisioni.ii. Note: We would reject if it was a one-tailed test, but it is a two-tailed test so we would fail to reject. The two-tailed test is more conservative because it is harder to prove.IV. T-test Examplea. For the following, would we use a dependent or independent t-test?i. 130 adolescent boys and 156 adolescent girls are given the Eating Attitudes Test. Is there a difference between the scores of the boys and the girls?ii. It would be independent because we have two different sizes and we cannot pair them up.b. For the following, would we use a dependent or independent t-test?i. 156 adolescent girls are given the Eating Attitudes Test. Then, they are shown a series of images from a fashion magazine. After a short break, the test is repeated. Is there a difference between the girls’ test scores before and after viewing the imager?ii. This would be dependent because there is paired data.c. For the following, would we use a dependent or independent t-test?i. 156 adolescent girls are tested with the Eating Attitudes Test and the Goldfarb Fear of Fat Scale. Are the scores on these two tests related?ii. You would not use a t-test at all here because you are using two different scales. A requirement of t-test is that the data has to be paired and they have to be on the same scale.V. Questiona. What can a t-test be used for?i. Determining correlations between two variablesii. Determining if there is a significant difference between two groupsiii. Catching Type 2 errorsiv. Making scatter plotsVI. ANOVAa. Analysis of variance (ANOVA) is a method for testing the hypothesis that three or more population means are equal.i. For example:ii.iii. Note: This method is to test if more than two population means are equal is similar to the way we tested two population means equal in Chapter 9. b. Assumptions:i. Each group is comprised of a randomly selected sampleii. Scores in each group are normally distributed iii. The variances of each group population are homogenousc. New test statistic!i. F-scoreii. The F-distribution is not symmetric; it is skewed positivelyiii. The values of F can be 0 or positive; they cannot be negativeiv. The F-distribution changes shape with respect to degrees of freedomv. Note: When the null is true, when it is coming out of the same bag so to say, the F will be non-symmetric and positively skewed.VII. F-distributiona.VIII. ANOVA Cont.a. Test Statistic for One-Way ANOVAi.ii. An excessively large F test statistic is evidence against equal population meansiii. Note: F is sometimes called the F ratioiv. F is sometimes called the F ratiob. Assumption:i. Group populations are normally distributed ii. Group variances are equaliii.c. ANOVA asks:i. Judging from our samples, what is the probability that they all came from the same population?ii. ANOVA breaks the total variance, s2all, into two parts:1. Variance BETWEEN groups2. Variance WITHIN groupsd. Variancei.ii.e. Variance WITHIN groupsi. How spread out is the data in each group relative to its group mean?1. Square the differences between every data point and its group mean, (X-Xi)22. Sum the squares, ii. Sum of squares WITHIN groups represents the spread of each data point within its own groupiii. Subtract each data value from its own group meaniv.1. Note: the triangles are group means. Variance between groups – how much do the group means vary amongst the other