Assignment 10 Alternative
PSY 07301: Statistics in Psychology
Instructions: For each question, answer all items. Make sure that you are detailed when you answer the questions. As a rule of thumb, when you are answering any questions using statistics, you should include all statistics in the answer (e.g. if it asks about the mean, put the actual value of the mean in the sentence).
Type your answers out underneath each question either bolded or in a different font color (or both). Please do not delete the questions or the output. When you are finished with the assignment, upload it as a .doc, .docx, or .pdf to the assignment on Canvas.
The analyses come from the high school exam data set. This data set includes information about how students in NY State performed on a bunch of standardized tests. In addition to the test scores, there is demographic information (ethnicity/race, gender) and school information (type of school, type of program). The analyses below use a variety of tests that look at the relationships between variables.
Note: There are 5 parts to this assignment each one on a separate page. Make sure to answer all parts.
Part I: One-Way ANOVA
This analysis is looking at the relationship between ethnicity/race and freshman year science scores. Use the tables and graph included below to answer the following questions:
1. What are the null and alternative hypotheses for this analysis?
2. In a few sentences, describe the descriptive data for each ethnicity/race group (include N, mean, standard deviation, minimum, & maximum).
3. Did we violate the assumption of homogeneity in this analysis? Include evidence for your answer (i.e. how do you know?).
4. Were there significant differences in science scores between the different ethnicities?
5. Based on the results of your analysis, should you analyze the post hoc tests?
a. If yes, which groups are significantly different from each other? (List all).
b. Explain what the post hoc tests tell us about the relationship between ethnicity and science scores.
6. Complete Step 4 of hypothesis testing. Include your decision about the null hypothesis, a sentence describing the results (including post hoc tests), and the APA-style string of statistics.
7.
In your own words
, what is the relationship between ethnicity and science scores?
Descriptives
freshman yr science score
N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Lower Bound
Upper Bound
hispanic
24
45.3750
8.21881
1.67766
41.9045
48.8455
26.00
63.00
asian
11
51.4545
9.49067
2.86154
45.0786
57.8305
34.00
66.00
african-amer
20
42.8000
9.44569
2.11212
38.3793
47.2207
29.00
61.00
white
145
54.2000
9.09487
.75529
52.7071
55.6929
33.00
74.00
Total
200
51.8500
9.90089
.70010
50.4694
53.2306
26.00
74.00
Test of Homogeneity of Variances
freshman yr science score
Levene Statistic
df1
df2
Sig.
.565
3
196
.639
ANOVA
freshman yr science score
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
3446.748
3
1148.916
14.021
.000
Within Groups
16060.752
196
81.943
Total
19507.500
199
Post Hoc Tests
Multiple Comparisons
Dependent Variable: freshman yr science score
LSD
(I) Ethinicy/Race
(J) Ethinicy/Race
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
hispanic
asian
-6.07955
3.29600
.067
-12.5797
.4206
african-amer
2.57500
2.74069
.349
-2.8300
7.9800
white
-8.82500*
1.99484
.000
-12.7591
-4.8909
asian
hispanic
6.07955
3.29600
.067
-.4206
12.5797
african-amer
8.65455*
3.39801
.012
1.9532
15.3559
white
-2.74545
2.83098
.333
-8.3285
2.8376
african-amer
hispanic
-2.57500
2.74069
.349
-7.9800
2.8300
asian
-8.65455*
3.39801
.012
-15.3559
-1.9532
white
-11.40000*
2.15922
.000
-15.6583
-7.1417
white
hispanic
8.82500*
1.99484
.000
4.8909
12.7591
asian
2.74545
2.83098
.333
-2.8376
8.3285
african-amer
11.40000*
2.15922
.000
7.1417
15.6583
*. The mean difference is significant at the 0.05 level.
8.
Part II: Correlation
Using the output below (investigating the relationship between different exam scores), describe all 3 different pairs of relationships (reading-writing; reading-math; math-writing). For each, make sure to include the following information:
Whether the relationship was significant.
If it was significant, whether it was a positive/negative relationship.
Describe the relationships (As X increases/decreases, Y increases/decreases).
APA string of statistics [
r=
r value,
p=______]
You can do this in bullet format, but make sure to use whole sentences.
Correlations
Correlations
reading score
writing score
math score
reading score
Pearson Correlation
1
.597**
.658**
Sig. (2-tailed)
.000
.000
N
200
200
200
writing score
Pearson Correlation
.597**
1
.056
Sig. (2-tailed)
.000
.190
N
200
200
200
math score
Pearson Correlation
.658**
.056
1
Sig. (2-tailed)
.000
.190
N
200
200
200
**. Correlation is significant at the 0.01 level (2-tailed).
Looking at the scatterplot below, describe the relationship between math scores (X) and social studies scores (Y). Make sure to describe the
strength and direction of the relationship. You do not need to include an APA string of statistics for this question.
Part III: Regression
The output below is the result of investigating the predictive relationship between freshman year science scores and senior year science scores. Researchers wanted to see if they can predict senior year science scores from each students freshman year scores. Answer the following questions using the output below:
What is the correlation coefficient (r) for the relationship between senior and freshman year scores?
Does freshman year science scores significantly predict senior year science scores?
Write out the F statistical string associated with this relationship. [F(
dfreg, dfres)=
F value, p=________]
Write out the line of best fit equation for this relationship (Y=bX+a, substituting the b & a with values from the table).
If someone scored a 70 on their freshman year science test, based on the line of best fit, what would their predicted senior year score be?
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.878a
.771
.770
5.80149
a. Predictors: (Constant), freshman yr science score
ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
22478.445
1
22478.445
667.862
.000b
Residual
6664.150
198
33.657
Total
29142.595
199
a. Dependent Variable: senior yr science score
b. Predictors: (Constant), freshman yr science score
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
-2.613
2.192
-1.192
.235
freshman yr science score
1.073
.042
.878
25.843
.000
a. Dependent Variable: senior yr science score
Part IV: Chi Square Goodness of Fit Test
For this study, participants were split into 3 groups based on the type of exercise they engage in (martial arts, general exercise, or no exercise). I wanted to see if there were more people who do one type of exercise compared to the others. To do so, I ran a chi square goodness of fit test to determine whether there was a different number of participants in the groups. Answer the following questions using the output below:
How many people did I sample total?
Which of the exercise groups had more than the expected N?
Which of the exercise groups had less than the expected N?
Was there a significant difference in the number of participants in each group? How do you know?
Write out the statistical string of information for this test. It should be formatted like this: 2(df, N=##)= Chi-square value,
p=###
a. Make sure that you put the actual number in for the df, the chi-square value, and the ## after N and p
In your own words, what do the results of this test tell you about the distribution of participants in these exercise groups?
Part V: Chi Square Test of Independence
For this study, participants were split into 3 groups based on the type of exercise they engage in (martial arts, general exercise, or no exercise). I wanted to see if there was a difference in the proportion of male and female participants in the different exercise types. To do so, I ran a chi square test of independence to determine whether there was a significant relationship between the variables. Answer the following questions using the output below:
How many people did I sample total?
Which of the exercise groups had the same amount of male and female participants?
Which gender had higher numbers in general exercise?
Which gender had higher numbers in the no exercise group?
Which exercise group had the highest number of people total in it?
Was there a significant relationship between exercise type and gender? How do you know?
Write out the statistical string of information for this test. It should be formatted like this: 2(df, N=##)= Chi-square value,
p=###
a. Make sure that you put the actual number in for the df, the chi-square value, and the ## after N and p
In your own words, what do the results of this test tell you about these 2 variables?
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