KIN 4310 1st Edition Lecture 16 Outline of Last Lecture I Review Questions Outline of Current Lecture I Exam 3 Topics II The t test III The t test Steps IV T test Example V Question VI ANOVA VII F distribution VIII ANOVA cont Current Lecture I Exam 3 Topics a Dependent t Test b One way ANOVA c Two way ANOVA d Significant Correlations e Measurement of i Health Status ii Aerobic Fitness iii Body Composition iv Diet Physical Activity II The t test a A hypothesis test that is used to determine if there is a significant difference between two groups These 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 b c d e f i This is called the t test for independent means The t test can also be used when there is only one group of subjects and they are tested under two conditions i This is called the t test for dependent means T test for dependent means i Requires paired data ii Two sets using the same measurement scale Examples i Body mass index is measured before and after a special diet program ii Grip strength is measured in the dominant hand and the non dominant hand The t test for dependent means i You have two groups of scores ii Each score in group A is paired with a score in group B iii The t test is based on difference values You need the following i n number of pairs of measurements ii III The t test Steps a Step 1 Calculate the t value for dependent means i Equation b c d e ii 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 1 Step 3 Determine the critical value of t i Use table B2 of your textbook ii Critical t value for df 3 alpha 0 05 1 One tailed tcrit 2 353 2 Two tailed tcrit 3 182 Step 4 Compare your t value to the critical value i One tailed tcrit 2 353 ii Two tailed tcrit 3 182 iii t 2 93 Step 5 Make a decision i 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 Example a 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 Question a What can a t test be used for i Determining correlations between two variables ii Determining if there is a significant difference between two groups iii Catching Type 2 errors iv Making scatter plots VI ANOVA a 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 sample ii Scores in each group are normally distributed iii The variances of each group population are homogenous c New test statistic i F score ii The F distribution is not symmetric it is skewed positively iii The values of F can be 0 or positive they cannot be negative iv The F distribution changes shape with respect to degrees of freedom v 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 distribution a VIII ANOVA Cont a Test Statistic for One Way ANOVA i ii An excessively large F test statistic is evidence against equal population means iii Note F is sometimes called the F ratio iv F is sometimes called the F ratio b Assumption i Group populations are normally distributed ii Group variances are equal iii 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 groups 2 Variance WITHIN groups d Variance i ii e Variance WITHIN groups i 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 2 2 Sum the squares ii Sum of squares WITHIN groups represents the spread of each data point within its own group iii Subtract each data value from its own group mean iv 1 Note the triangles are group means Variance between groups how much do the group means vary amongst the other means