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Hypothesis Testing 1. Harris (2020) tested levels of well-being in subjects with chronic anxiety undergoing brief therapy with mild psychedelics three months before and again three months after the administration of a single session of therapy. The well- being scores for the 16 subjects are listed in the "Before" and "After" columns in the Table below: Well-Being Scores Subject Before After A 125 133 B 96 126 115 115 108 119 93 124 F 98 109 G 95 72 H 120 104 107 113 126 118 K 102 121 L 116 115 M 80 94 105 87 123 121 110 118 Use the data provided in the table to test whether well-being changed significantly from immediately before to 3 months after the session. Set alpha at .05. a) Write a null and alternative hypothesis b) Determine the critical value and draw the comparison distribution with the rejection region(s) indicated c) Compute the relevant statistic

Hypothesis Testing 1. Harris (2020) tested levels of well-being in subjects with chronic anxiety undergoing brief therapy with mild psychedelics three months before and again three months after the administration of a single session of therapy. The well- being scores for the 16 subjects are listed in the "Before" and "After" columns in the Table below: Well-Being Scores Subject Before After A 125 133 B 96 126 115 115 108 119 93 124 F 98 109 G 95 72 H 120 104 107 113 126 118 K 102 121 L 116 115 M 80 94 105 87 123 121 110 118 Use the data provided in the table to test whether well-being changed significantly from immediately before to 3 months after the session. Set alpha at .05. a) Write a null and alternative hypothesis b) Determine the critical value and draw the comparison distribution with the rejection region(s) indicated c) Compute the relevant statistic

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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t = n(E D)- (E D) n -1 n = number of pairs of scores (for example, if 8 people are measured at tl and t2, df = 8-1 = 7) D= the difference between each pair of scores ED = the sum of the differences (ED") = the sum of the squares of the differences (ED)= the sum of the differences squared t score: Independent Samples t-test (degrees of freedom = (ni – 1) + (n2 – 1)) Z. - Z. + Vn, -1'n, - 1 X - mean of first group (sample) X:- mean of second group (sample) s21 = sample variance of first group s?, = sample variance of second group n1 =number of subjects (or observations) in the first group n, = number of subjects in second group 2=r Be careful about computing the denominator; pay attention to whether you are working with sample variances or standard deviations to make sure your computations are correct. One Way ANOVA (see ANOVA table for degrees of freedom) Between Groups Sum of Squares: Subtract the grand mean from each group mean, square the deviation, multiply by n in each group and add the values together. SSu = En (X,- X n = the number of subjects or observations in a group X, - the mean for any group (1 through n) of subjects X = the overall, or grand, mean for all subjects or observations Within Groups Sum of Squares: Subtract each group's mean from the individual scores and add them all up. SSw - EE (X-X.j X = any single score within any particular group X,- the mean of any particular group nG = number of groups N= total # of subjects/observations df MS F Treatment (Between= B) SS. df, = MS, = ss, / df, MS= SSw/ dfw F = MS, /MSw n-1 dfw = N - ng Error (Within W) SS Total SStotal = ss, + SSw dfrotal = 3D N -1 = df,+ dfy Frequently Used Z Critical Scores a level One-tailed (left) Two-tailed One-tailed (right) a 0.05 2-1.64 21.64 21.96 a= 0.01 2=-2.33 z= 2.33 2= 2.57 a= 0.001 2=-3.08 z3.08 23.32
Transcribed Image Text:t = n(E D)- (E D) n -1 n = number of pairs of scores (for example, if 8 people are measured at tl and t2, df = 8-1 = 7) D= the difference between each pair of scores ED = the sum of the differences (ED") = the sum of the squares of the differences (ED)= the sum of the differences squared t score: Independent Samples t-test (degrees of freedom = (ni – 1) + (n2 – 1)) Z. - Z. + Vn, -1'n, - 1 X - mean of first group (sample) X:- mean of second group (sample) s21 = sample variance of first group s?, = sample variance of second group n1 =number of subjects (or observations) in the first group n, = number of subjects in second group 2=r Be careful about computing the denominator; pay attention to whether you are working with sample variances or standard deviations to make sure your computations are correct. One Way ANOVA (see ANOVA table for degrees of freedom) Between Groups Sum of Squares: Subtract the grand mean from each group mean, square the deviation, multiply by n in each group and add the values together. SSu = En (X,- X n = the number of subjects or observations in a group X, - the mean for any group (1 through n) of subjects X = the overall, or grand, mean for all subjects or observations Within Groups Sum of Squares: Subtract each group's mean from the individual scores and add them all up. SSw - EE (X-X.j X = any single score within any particular group X,- the mean of any particular group nG = number of groups N= total # of subjects/observations df MS F Treatment (Between= B) SS. df, = MS, = ss, / df, MS= SSw/ dfw F = MS, /MSw n-1 dfw = N - ng Error (Within W) SS Total SStotal = ss, + SSw dfrotal = 3D N -1 = df,+ dfy Frequently Used Z Critical Scores a level One-tailed (left) Two-tailed One-tailed (right) a 0.05 2-1.64 21.64 21.96 a= 0.01 2=-2.33 z= 2.33 2= 2.57 a= 0.001 2=-3.08 z3.08 23.32
Hypothesis Testing 1. Harris (2020) tested levels of well-being in subjects with chronic anxiety undergoing brief therapy with mild psychedelics three months before and again three months after the administration of a single session of therapy. The well- being scores for the 16 subjects are listed in the “Before" and “After" columns in the Table below: Well-Being Scores Subject Before After A 125 133 B 96 126 115 115 108 119 93 124 F 98 109 G 95 72 H 120 104 107 113 126 118 K 102 121 L 116 115 M 80 94 105 87 123 121 110 118 Use the data provided in the table to test whether well-being changed significantly from immediately before to 3 months after the session. Set alpha at .05. a) Write a null and alternative hypothesis b) Determine the critical value and draw the comparison distribution with the rejection region(s) indicated c) Compute the relevant statistic d) Make a statistical decision (regarding the null hypothesis) e) Write a conclusion based on the specific research question
Transcribed Image Text:Hypothesis Testing 1. Harris (2020) tested levels of well-being in subjects with chronic anxiety undergoing brief therapy with mild psychedelics three months before and again three months after the administration of a single session of therapy. The well- being scores for the 16 subjects are listed in the “Before" and “After" columns in the Table below: Well-Being Scores Subject Before After A 125 133 B 96 126 115 115 108 119 93 124 F 98 109 G 95 72 H 120 104 107 113 126 118 K 102 121 L 116 115 M 80 94 105 87 123 121 110 118 Use the data provided in the table to test whether well-being changed significantly from immediately before to 3 months after the session. Set alpha at .05. a) Write a null and alternative hypothesis b) Determine the critical value and draw the comparison distribution with the rejection region(s) indicated c) Compute the relevant statistic d) Make a statistical decision (regarding the null hypothesis) e) Write a conclusion based on the specific research question
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