ANOVA Table Fill in the blanks of the One Way ANOVA Table below with the appropriate values and answer the questions; assume alpha = 05. Sum of Source Squares df Mean Square F Between Groups Within Groups 116 24.527 Total 3645.24 120 Critical F value = Reject or Fail to Reject Ho ?
ANOVA Table Fill in the blanks of the One Way ANOVA Table below with the appropriate values and answer the questions; assume alpha = 05. Sum of Source Squares df Mean Square F Between Groups Within Groups 116 24.527 Total 3645.24 120 Critical F value = Reject or Fail to Reject Ho ?
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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Question
Transcribed Image Text:ANOVA Table
Fill in the blanks of the One Way ANOVA Table below with the appropriate values and answer the questions;
assume alpha = 05.
Sum of
Source
Squares
df
Mean Square
F
Between Groups
Within Groups
Total
116
24.527
3645.24
120
Critical F value =
Reject or Fail to Reject Ho ?.
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
120
104
107
113
J
126
118
K
102
121
L
116
115
M
80
94
N
105
87
123
121
P
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: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
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