Question

1. ) The Scholastic Aptitude Test (SAT) contains three sections: critical reading, mathematics and writing. Each part is scored on a 500-point scale. Information on test scores for the 2018 version of SAT is available at the College Board website. Find the sample of SAT scores for 5 students bellow.

                                                                                                                       ANOVA Table

                SAT scores - 2018

                                                 

Student	Reading	Math	Writing
1	453	458	462
2	456	459	460
3	454	460	457
4	458	456	462
5	454	457	464
mean	455	458	461

Source of variation	Sum of Squares (SS)	Degrees of freedom	Mean Square (MS)	F
Treatment	90	2	45	10
Error	54	12	5
Total	144	14

1. (9pt) Conduct a Fisher’s LSD test allowing for 1% error.

2. (4pt) The level of difficulty for all the three sections of the SAT measured by the score are supposed to be the same. Do you agree with this after the results of the LSD test? WHY? Be specific for full credit.

Answer 1

MINITAB used

(9pt) Conduct a Fisher’s LSD test allowing for 1% error.

Fisher Individual Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	99% CI	T-Value	Adjusted P-Value
Math - Reading	3.00	1.34	(-1.10, 7.10)	2.24	0.045
Writing - Reading	6.00	1.34	(1.90, 10.10)	4.47	0.001
Writing - Math	3.00	1.34	(-1.10, 7.10)	2.24	0.045

Simultaneous confidence level = 97.49%

Fisher test shows that   Reading and Writing are significant at 1% level. (P=0.001).

The difference between Math and Reading, Writing and Math are not significant at 0.01 level of significance.

(4pt) The level of difficulty for all the three sections of the SAT measured by the score are supposed to be the same. Do you agree with this after the results of the LSD test? WHY? Be specific for full credit.

We are not agreeing that level of difficulty for all the three sections of the SAT measured by the score are the same. Mean score of writing is higher that shows that writing is easy compared to other sections.

One-way ANOVA: Reading, Math, Writing

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.01

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Factor	3	Reading, Math, Writing

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	90.00	45.000	10.00	0.003
Error	12	54.00	4.500
Total	14	144.00

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
2.12132	62.50%	56.25%	41.41%

Means

Factor	N	Mean	StDev	99% CI
Reading	5	455.000	2.000	(452.102, 457.898)
Math	5	458.000	1.581	(455.102, 460.898)
Writing	5	461.00	2.65	(458.10, 463.90)

Pooled StDev = 2.12132

Fisher Pairwise Comparisons

Grouping Information Using the Fisher LSD Method and 99% Confidence

Factor	N	Mean	Grouping
Writing	5	461.00	A
Math	5	458.000	A	B
Reading	5	455.000		B

Means that do not share a letter are significantly different.

Fisher Individual Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	99% CI	T-Value	Adjusted P-Value
Math - Reading	3.00	1.34	(-1.10, 7.10)	2.24	0.045
Writing - Reading	6.00	1.34	(1.90, 10.10)	4.47	0.001
Writing - Math	3.00	1.34	(-1.10, 7.10)	2.24	0.045

Simultaneous confidence level = 97.49%