Mathematics and statisitcs1

Running head: MATHEMATICS AND STATISTICS 1
Mathematics and Statistics
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MATHEMATICS AND STATISTICS 2
Mathematics and Statistics
Exercise 33
1. Do the data meet criteria for homogeneity of variance? Provide a rationale for your
answer.
According to the homogeneity of variance assumption, the independent t-test
assumes the variances of the two groups you are measuring are equal in the
population. From the chart below, p=0.455 is greater that the p-value, p=0.05
hence the test of homogeneity of variance is significant at p=0.455. Thus, the data
meets the criteria for homogeneity of variance.
Levene's Test of Equality of Error Variances
a
Dependent Variable: Post_treatment_hours
F
df1
df2
Sig.
.840
2
12
.455
Tests the null hypothesis that the error variance of
the dependent variable is equal across groups.
a. Design: Intercept + Group
MATHEMATICS AND STATISTICS 3
The distribution is roughly normal in shape with slight skewness to the right.
Tests of Normality
Statistic
df
Sig.
Statistic
df
Sig.
Post_treatment_hours
.206
15
.085
.934
15
.314
a. Lilliefors Significance Correction
From the Shapiro-Wilk test of normality, the distribution is normal since p=0.314 is
greater than (p>0.05).
3. What are the means for three groups’ hours worked on a job?
The means of the three groups are
Supported mean=14.60
TAU Observational mean=15.20
TAU Randomized mean=26.60
MATHEMATICS AND STATISTICS 4
4. What are the F value and the group and error df for this set of data?
From the ANOVA chart below, F=6.162, group df=12 and error df=2
ANOVA
Post_treatment_hours
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
457.200
2
228.600
6.162
.014
Within Groups
445.200
12
37.100
Total
902.400
14
5. Is the F significant at α = 0.05? Specify how you arrived at your answer.
F is significant at an alpha of 0.05 because p value of 0.014 is below the α=0.05.
6. If using SPSS, what is the exact likelihood of obtaining an F value at least as
extreme as or as close to the one that was actually observed, assuming that the
null hypothesis is true?
The exact likelihood of obtaining an F value is equivalent to p-value which is 1.4%
7. Which group worked the most weekly job hours post-treatment? Provide a
rationale for your answer.
The randomized treatment as usual group worked the most hours post treatment. This
would be probable because these individuals would have to be more resilient and less
dependent than other treatment groups.
8. Write your interpretation of the results as you would in an APA-formatted
journal.
MATHEMATICS AND STATISTICS 5
A one-way ANOVA was conducted to compare the effect of spinal cord injuries on the
number of hours worked. An analysis of variance showed that the effect of spinal cord
injuries on the number of hours worked was significant, F= (2,12) =6.162, p=0.014
9. Is there a difference in your final interpretation when comparing the results of the
LSD post hoc test versus Tukey HSD test? Provide a rationale for your answer.
In comparing LSD post hoc and Turkey HSD post hoc, the differences in my final
interpretation are not significant since they both show the same significant values. Both
support groups and TAU Observational have similar means but TAU Randomized have a
slightly higher mean number of hours worked than both groups.
10. If the researcher decided to combine the two Treatment as Usual groups to
represent an overall “Control” group, then there would be two groups to compare:
Supported Employment versus Control. What would be the appropriate statistic to
address the difference in hours worked between the two groups? Provide a
rationale for your answer.
In that scenario, the most appropriate test statistics to be used would be t-tests since it is
used in comparing the means of two nominal groups that have ratio or interval data.

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