Adept SPSS Statistical Analysis Homework Helpers

Computing Central Tendency, Variance and Standard Deviation

The first data set includes two tables representing two classes of a college course.

Calculate and report the following for the quiz, midterm exam, final exam, and total grade for class one – mean, median, mode, range, variance, and standard deviation.

*Quiz*		*Midterm Exam*		*Final Exam*		*Total Grade*

Mean	7.55	Mean	77.40	Mean	78.20	Mean	81.72
Median	7.00	Median	77.00	Median	76.00	Median	80.64
Mode	7.00	Mode	77.00	Mode	73.00	Mode	#N/A
Standard Deviation	1.36	Standard Deviation	11.39	Standard Deviation	11.02	Standard Deviation	8.66
Sample Variance	1.84	Sample Variance	129.62	Sample Variance	121.43	Sample Variance	75.02
Range	5.00	Range	37.00	Range	37.00	Range	29.11

Paired Sample T-test

Determine if there is a meaningful difference between midterm exam scores and final exam scores for the students in class one.

Paired sample t-test for the midterm and final score show that the difference between the scores are not statistically significant as the p-value is 0.52 which is greater than level of significance.

t-Test: Paired Two Sample for Means
	Midterm Exam	Final Exam
Mean	77.40	78.20
Variance	129.62	121.43
Observations	20.00	20.00
Hypothesized Mean Difference	-
df	19.00
t Stat	(0.65)
P(T<=t) two-tail	0.52
t Critical two-tail	2.09

Two-sample T-test Analysis

Determine if there is a meaningful difference between the average midterm exam scores for class one and class two. Determine if there is a meaningful difference between the average final exam scores for class one and class two.

The two-sample t-test indicates that the difference between averages of two midterm exam scores are not statistically significant.

t-Test: Two-Sample Assuming Equal Variances
	Midterm Exam	Midterm Exam
Mean	77.40	74.80
Variance	129.62	114.37
Observations	20.00	30.00
Pooled Variance	120.41
Hypothesized Mean Difference	-
df	48.00
t Stat	0.82
P(T<=t) two-tail	0.42
t Critical two-tail	2.01

The two-sample t-test indicates that the difference between averages of two midterm exam scores are not statistically significant as p-value 0.22 is greater than 0.05.

t-Test: Two-Sample Assuming Equal Variances
	Final Exam	Final Exam
Mean	78.20	74.30
Variance	121.43	119.32
Observations	20.00	30.00
Pooled Variance	120.16
Hypothesized Mean Difference	-
df	48.00
t Stat	1.23
P(T<=t) two-tail	0.22
t Critical two-tail	2.01

ANOVA F-statistics

Using the scores for both class one and class two together (treating them collectively as a cohort), determine if midterm exam score is a significant predictor of final exam score. In roughly what percent of cases would knowing someone’s midterm exam score allow us to predict their final exam score?

Yes. The midterm score can be used to predict the final score of students with pretty high confidence. The mid term score explains around 69% of variance in final score and the ANOVA F-statistic yields statistically significant result (F = 108.64, p <0.001) indicating that the midterm score is statistically significant in predicting the final exam score.

ANOVA
	df	SS	MS	F	Significance F
Regression	1.00	4,126.72	4,126.72	108.64	0.00
Residual	48.00	1,823.30	37.99
Total	49.00	5,950.02

	Coefficients	Standard Error	t Stat	P-value
Intercept	12.22	6.17	1.98	0.05
Midterm Exam	0.84	0.08	10.42	0.00

The regression model also gives an estimate of coefficient which means for each unit increase in midterm score, average increase in final exam score is 0.84.

Bonus: Using only the scores from class one, and looking at the three variables quiz score, midterm exam score, and final exam score, which of these variables are significant predictors of total grade in the course?

Yes. The quiz score, midterm score, final exam score is highly efficient in predicting the total score with R2 of 0.91 indicating that regression model was able to explain 91% of variance in the data. The ANOVA F-statistic also yields significant result with F = 52.07, p<0.001.

ANOVA
	df	SS	MS	F	Significance F
Regression	3.00	1,292.87	430.96	52.07	0.00
Residual	16.00	132.42	8.28
Total	19.00	1,425.29

	Coefficients	Standard Error	t Stat	P-value
Intercept	22.66	4.82	4.70	0.00
Quiz	0.01	0.73	0.02	0.99
Midterm Exam	0.39	0.14	2.76	0.01
Final Exam	0.37	0.13	2.94	0.01

Among the three predictors, midterm score and final exam score were statistically significant in predicting the total grade, but the quiz score was not!

The second data set includes one table providing data on students in four college majors, including scores on an anxiety inventory, GPA in major, and GPA overall.

What are the frequencies of each major?In looking at the frequency of each major, do you observe any potential issue? How do you think that issue might be resolved?

Major	Count of Major
Business	8
Philosophy	6
Pre-Med	14
Psychology	12
Grand Total	40

There are total of four major – Business (8), Philosophy (6), Pre-Med (14), and Psychology (12). The issue here is that the number of samples for Business and Philosophy is quite small as compared to Pre-Med and Psychology. It can be resolved by either getting more data or resampling the data from respective samples.

Which major has the highest average measured anxiety? Which major has the lowest average measured anxiety?Comparing each of the four majors against each other at once, is there a meaningful difference in the average anxiety score?

Row Labels	Average of Anxiety
Business	17.00
Philosophy	15.00
Pre-Med	18.93
Psychology	17.00

Pre-Med has highest level of anxiety and Philosophy has lowest level. The ANOVA test shows that there is not significant difference across groups in Anxiety levels

ANOVA
*Source of Variation*	SS	df	MS	F	*P-value*	*F crit*
Between Groups	70.45	3.00	23.48	1.18	0.33	2.87
Within Groups	718.93	36.00	19.97

Total	789.38	39.00

Comparing each of the four majors against each other at once, is there a meaningful difference in the average GPA in major? Comparing each of the four majors against each other at once, is there a meaningful difference in the average overall GPA?

No. There is no significant differences in Average GPA in majors across different majors.

ANOVA
*Source of Variation*	SS	df	MS	F	P-value	F crit
Between Groups	0.53	3.00	0.18	1.42	0.25	2.87
Within Groups	4.45	36.00	0.12

Total	4.98	39.00

The ANOVA F-test shows statistically insignificant result with F = 1.42, p = 0.25.

For the entire group of students, is there a meaningful difference between GPA in major and overall GPA? For the entire group of students, is anxiety a significant predictor of overall GPA?

Based on paired sample t-test, there is significant difference between GPA in major and overall GPA with t = 4.47, p<0.001.

t-Test: Paired Two Sample for Means
	GPA in Major	Overall GPA
Mean	3.48	3.33
Variance	0.13	0.15
Observations	40.00	40.00
Pearson Correlation	0.83
Hypothesized Mean Difference	-
df	39.00
t Stat	4.47
P(T<=t) two-tail	0.00
t Critical two-tail	2.02

We also use regression model to test if Anxiety is significant predictor of overall GPA or not. It turns out that Anxiety level is significant predictor of overall GPA with F = 7.74, p = 0.01. The model has multiple R2 = 0.17 indicating that Anxiety account for 17% of variance in the overall GPA.

ANOVA
	df	SS	MS	F	Significance F
Regression	1.00	0.97	0.97	7.74	0.01
Residual	38.00	4.75	0.13
Total	39.00	5.72

	Coefficients	Standard Error	t Stat	P-value
Intercept	2.72	0.23	12.05	0.00
Anxiety	0.04	0.01	2.78	0.01

The estimated coefficients show that the anxiety has significant positive relationship with the GPA. Each unit increase in Anxiety, on an average, increases overall GPA by 0.04.

Bonus: For the entire group of students, determine the magnitude and direction of the relationship between grade-point-average in major and grand-point-average overall. You should have been able to guess what you would find before calculating anything or even looking at a single value; why?

Based on my guess, I would say the GPA in Major would be highly correlated to the overall GPA and the relationship will be positive. This is because we expect student who score high for major, to score for other courses as well. Similarly, for students who are unable to score in majors, it is expected that they would score low in other courses as well.

The guess is verified by the data:

Regression Statistics
Multiple R	0.83
R Square	0.69
Adjusted R Square	0.68
Standard Error	0.22
Observations	40

The GPA in major is positively correlated with overall GPA.

Bonus: Is there another effect you think would be interesting to explore with these data? Why?

We can use Anxiety as control variable and then see if different majors have significantly different GPA after controlling for Anxiety levels.

Data Set 2 – Four Majors
Participant	Anxiety	GPA in Major	Overall GPA	Major
1	17	3.60	3.36	Pre-Med
2	12	3.33	3.00	Psychology
3	13	3.67	3.38	Philosophy
4	16	4.00	3.70	Pre-Med
5	13	3.50	3.30	Psychology
6	17	3.33	3.13	Business
7	13	3.50	3.45	Philosophy
8	21	3.80	3.75	Pre-Med
9	15	3.00	3.00	Pre-Med
10	23	2.50	2.70	Business
11	17	3.75	3.18	Psychology
12	24	3.80	3.89	Psychology
13	24	4.00	3.80	Philosophy
14	22	3.75	3.40	Psychology
15	18	3.67	3.60	Pre-Med
16	14	3.67	3.56	Psychology
17	23	3.50	3.50	Business
18	13	3.67	3.00	Business
19	17	3.60	3.36	Pre-Med
20	12	3.33	3.00	Business
21	22	3.50	3.18	Pre-Med
22	19	3.50	3.10	Psychology
23	23	3.00	3.00	Pre-Med
24	25	3.25	3.18	Pre-Med
25	23	3.33	3.09	Psychology
26	24	3.67	3.80	Psychology
27	13	2.75	2.40	Business
28	11	3.00	2.81	Psychology
29	16	3.60	3.36	Pre-Med
30	14	3.00	3.30	Business
31	8	3.00	2.77	Philosophy
32	19	3.80	3.89	Pre-Med
33	13	3.00	2.67	Philosophy
34	13	3.67	3.56	Psychology
35	21	4.00	3.89	Business
36	19	3.67	3.30	Philosophy
37	18	3.67	3.80	Pre-Med
38	21	4.00	4.00	Pre-Med
39	12	3.67	3.40	Psychology
40	17	3.25	3.60	Pre-Med