EPS - 525 - Assignments 3, 4 and 5 (Total 19 Questions with Multiple Parts problems included)-Dependent Sample t test, Independent Sample T test and One-Way ANOVA
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question_eps525_assignment5_q9.docEPS 525 – Introduction to Statistics
Assignment No. 5 – One-way Analysis of Variance
Name:
A researcher conducted a study to examine the effects of secure, anxious, and avoidant attachment styles on the physiology of sleep. Participants were selected using a stratified random sampling approach to ensure representation of each of the three styles. The sleep patterns of 30 secure, 30 anxious, and 30 avoidant children were monitored. Of primary importance to the researcher was the overall percentage of time each child spent in deep (delta) sleep. Following is the average amount of time that each child spent in delta sleep, expressed as a percentage of total sleep time (ranging from 0.0 to 100.0). For the attachment styles, 1 = secure, 2 = anxious, and 3 = avoidant.
Data Output for this Assignment is found on the last four pages.
The gray boxes for your answers will expand as necessary for your responses.
1. (2 points) What would the null hypothesis be for this study? Show/write the appropriate symbols and expression in words.
H0:
.
2. (2 points) What would the alternative hypothesis be for this study? Show/write the appropriate symbols and expression in words.
Ha:
3. Prior to examining whether the group means differ; you need to test the underlying assumptions of the one-way analysis of variance.
3.a. (2 points) Has the assumption of independence been met for this data?
FORMCHECKBOX Yes FORMCHECKBOX No (check your answer selection)
Indicate how you made your determination.
3.b. (3 points) Has the assumption of normality been met for this data, using an alpha level of .001?
FORMCHECKBOX Yes FORMCHECKBOX No (check your answer selection)
Indicate how you made your determination. Be sure to include all applicable values and symbols.
3.c. (3 points) Has the assumption of homogeneity of variance been met for this data, using an alpha level of .05? That is, is this assumption met or not met?
FORMCHECKBOX Yes FORMCHECKBOX No (check your answer selection)
Indicate how you came to your conclusion. Be sure to include all applicable values and symbols.
4. (2 points) The next question that needs to be answered is whether all of the groups are the same in their percentage of time in deep (delta) sleep using an alpha level of .05. If applicable (or indicate why not), use the Welch statistic. What is your conclusion (at this point) from this analysis? Indicate how you came to your conclusion. Be sure to include all applicable values and symbols.
5. (3 points) Calculate the measure of association and interpret its meaning.
W
T
W
B
MS
SS
MS
K
SS
+
-
-
=
)
1
(
2
w
Where SSB = K = MSW =SST = MSW =
Therefore, (2 =
This means:
6. (1 point) Write the statistical strand for this one-way ANOVA analysis.
7. (4 points) Assuming that you found a significant F, which pairs of groups differ? Indicate which post hoc procedure you used and why. Indicate your findings from the post hoc analysis. That is, how did you determine the pair to be significant or not (this must go beyond the * as an indication)? Be sure to discuss all unique pairwise comparisons.
Post hoc and why:
Pairwise comparisons:
8. (4 points) For each of the significant pairwise comparisons (be sure to indicate the pair), calculate and report the effect size.
W
k
i
MS
X
X
ES
-
=
Wherew
MS
=As applicable, for each significant pairwise comparison report your findings like:
Group 1 and Group 2 Mean Difference = 1.23, ES = .45
9. (4 points) Complete the three tables on the next page that present your statistical results from these analyses. Use the values reported in the SPSS output – you do not need to round.
Table 1
Means and Standard Deviations of Percentage of Time in Deep (Delta) Sleep
|
Attachment Style |
n |
Mean |
SD |
|
Secure |
|
|
|
|
Anxious |
|
|
|
|
Avoidant |
|
|
|
|
Total |
|
|
|
Table 2
Analysis of Variance for Percentage of Time in Deep (Delta) Sleep by Attachment Style
|
Source |
SS |
df |
MS |
F |
p |
|
Between |
|
|
|
|
|
|
Within |
|
|
|
|
|
|
Total |
|
|
|
|
|
Table 3
Post Hoc Results for Percentage of Time in Deep (Delta) Sleep by Attachment Style
|
Attachment Style |
Mean |
Mean Differences ( k i X X - )(Effect Sizes are indicated in parentheses) |
||
|
|
|
1 |
2 |
3 |
|
1. Secure |
|
( ( |
|
|
|
2. Anxious |
|
|
( ( |
|
|
3. Avoidant |
|
|
|
( ( |
*Significant at ( = .05
Explore
Attachment Style
Oneway
Post Hoc Tests
Means Plots
Assignment No. 5 – One-Way ANOVA
Page 2
