Does the amount of time spent studying influence scores on an exam? Below are th

Question

Does the amount of time spent studying influence scores on an exam? Below are the test scores of 35 students who studied for either 2, 6, 10,14 or 20 hours. Test for an overall significant effect for hours of stuody on test scores. Provide a verbal statement explaining your resalts, If there is a main effect, use the Tukey HSD Test to identify which pairwise differences are significant at the 05 level. Provide a verbal statement explaining your results. Calculate omega squared for the main effect of hours of study. Provide a verbal staterment explaining your results, Include a computer-generated figure (histogram or polygon) of the group means. You may submit the graph from SPSs, or use Excel to gencrate the graph. After solving by calculator, repeat the ANOVA and Tukey analyses on SPSS Test Scores Following the Different Number of Hours of Study 2h 35 32 502: 25 6h 45 37 48 22/ 52 10h 14h20h 45 57 67 92 65 81 81 71 81 84 78 75 TP 77 7-2229 2: j0763| 2184 7 2G209 | 54731 | 40807 ? 38.13 | 5443 | 5qs7|84.86 | 7GI4 :1-15635 :1033728|273728|24841,281 5G520.111 4058414 1:, 2229-M1955556367 3gBG: I 1111-119555 : 9291855 :1071141 12: N 35 tor : 154357-79. GI; 150277 39 df SS MS F G 30 94781 30192 Toral 31 Fcrit 2.80 Fobs ? Ferit reject Ho St Catherine Universily

Explanation / Answer

Here we have to test the hypothesis that,

H0 : All means are equal.

H1 : Atleast one of the mean is differ than 0.

Assume alpha= level of significance = 5% = 0.05

Here we have to test more than two means so we use one way anova.

Descriptive statistics of your k=5 independent treatments:

Treatment

A

B

C

D

E

Pooled Total

observations N

7

7

7

7

7

35

sum xi

269.0000

381.0000

417.0000

629.0000

533.0000

2,229.0000

mean x¯

38.4286

54.4286

59.5714

89.8571

76.1429

63.6857

sum of squares x2i

10,763.0000

21,847.0000

26,209.0000

56,731.0000

40,807.0000

156,357.0000

sample variance s2

70.9524

184.9524

227.9524

35.1429

37.1429

423.5748

sample std. dev. s

8.4233

13.5997

15.0981

5.9281

6.0945

20.5809

std. dev. of mean SEx¯

3.1837

5.1402

5.7065

2.2406

2.3035

3.4788

One-way ANOVA of your k=5 independent treatments:

source

sum of
squares SS

degrees of
freedom

mean square
MS

F statistic

p-value

treatment

11,064.6857

4

2,766.1714

24.8693

3.7298e-09

error

3,336.8571

30

111.2286

total

14,401.5429

34

The p-value corresponing to the F-statistic of one-way ANOVA is lower than 0.05, suggesting that the one or more treatments are significantly different.

Now we have to find which mean differs so we can use post hoc test to find which mean differs.

Tukey HSD Test:

We have k=5 treatments, for which we shall apply Tukey's HSD test to each of the 10 pairs to pinpoint which of them exhibits statistically significant difference.

We first establish the critical value of the Tukey-Kramer HSD Q statistic based on the k=5 treatments and =30 degrees of freedom for the error term, for significance level = 0.05 (p-values) in the Studentized Range distribution.

Qcritical=0.05,k=5,=30 = 4.1020,

Next, we establish a Tukey test statistic from our sample columns to compare with the appropriate critical value of the studentized range distribution.

We calculate a parameter for each pair of columns being compared, which we loosely call here as the Tukey-Kramer HSD Q-statistic, or simply the Tukey HSD Q-statistic, as:

Qi,j=|x¯ix¯j|/ si,j

where the denominator in the above expression is:

si,j=^ / sqrt(Hi,j)i,j=1,…,k;ij.

The quantity Hi,j is the harmonic mean of the number of observations in columns labeled i and j.

The quantity ^ = 10.5465 is the square root of the Mean Square Error = 111.2286 determined in the precursor one-way ANOVA procedure. Note that ^ is same across all pairs being compared. The only factor that varies across pairs in the computation of si,j=^sqrt(Hi,j) is the denominator, which is the harmonic mean of the sample sizes being compared.

We present below color coded results of evaluating whether Qi,j>Qcritical for all relevant pairs of treatments.

Tukey HSD results :

treatments
pair

Tukey HSD
Q statistic

Tukey HSD
p-value

Tukey HSD
inferfence

A vs B

4.0138

0.0575097

insignificant

A vs C

5.3040

0.0062820

** p<0.01

A vs D

12.9017

0.0010053

** p<0.01

A vs E

9.4612

0.0010053

** p<0.01

B vs C

1.2902

0.8847634

insignificant

B vs D

8.8878

0.0010053

** p<0.01

B vs E

5.4474

0.0048236

** p<0.01

C vs D

7.5976

0.0010053

** p<0.01

C vs E

4.1572

0.0457901

* p<0.05

D vs E

3.4404

0.1340901

insignificant

Treatment

A

B

C

D

E

Pooled Total

observations N

7

7

7

7

7

35

sum xi

269.0000

381.0000

417.0000

629.0000

533.0000

2,229.0000

mean x¯

38.4286

54.4286

59.5714

89.8571

76.1429

63.6857

sum of squares x2i

10,763.0000

21,847.0000

26,209.0000

56,731.0000

40,807.0000

156,357.0000

sample variance s2

70.9524

184.9524

227.9524

35.1429

37.1429

423.5748

sample std. dev. s

8.4233

13.5997

15.0981

5.9281

6.0945

20.5809

std. dev. of mean SEx¯

3.1837

5.1402

5.7065

2.2406

2.3035

3.4788

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.