Question

A study was conducted to determine if students in different college years differ on the number of hours of sleep they obtain. On a specified mid-semester Wednesday morning 25 Freshmen, 25 Sophomore, 25 Junior and 25 Senior college students reported the number of Hours of Sleep they had obtained on the previous evening. Answer the following question referring to the following tables. Descriptive Statistics Year Mean Std. Deviation N Freshmen 7.7080 1.86881 25 sophomore 7.1600 1.34412 25 Junior 7.4400 1.47422 25 Senior 5.8400 1.24766 25 Total 7.0370 1.64597 100 Tests of Between-Subjects Effects Source Sum of Squares df Mean Square F Sig. YEAR 51.515 3 17.172 7.607 .000 Error 216.698 96 2.257 Total 5220.150 100 Multiple Comparisons LSD Mean Difference (I-J) Std. Error Sig. (I) Year (J) Year Freshmen sophomore .5480 .42495 .200 Junior .2680 .42495 .530 Senior 1.8680* .42495 .000 sophomore Freshmen -.5480 .42495 .200 Junior -.2800 .42495 .512 Senior 1.3200* .42495 .002 Junior Freshmen -.2680 .42495 .530 sophomore .2800 .42495 .512 Senior 1.6000* .42495 .000 Senior Freshmen -1.8680* .42495 .000 sophomore -1.3200* .42495 .002 Junior -1.6000* .42495 .000

Based off of this data:

If we used multiple t-tests what would the overall alpha level be?

What is the Null Hypothesis for the one-way ANOVA?

Is the F test significant (give F and p)?

What do the multiple comparisons tell us? (i.e., what conclusions can be made about differences in attendance between classes?)

Answer 1

1.

There are four groups to be comapared. Number of comparisons (multiple t-tests) required is,

Overall alpha level = probability of observing at least one significant result just due to chance

= 1 - P(no significant results in 6 tests)

(assuming alpha level in each test is 0.05)

= 0.2649

2.

Null Hypothesis H0: Average number of hours of sleep of Freshmen, Sophomore, Junior and Senior college students are equal.

3.

From the Anova output,

F = 7.607

p = .000

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that F test is significant.

4.

Multiple Comparisons LSD

Mean Difference (I-J) Std. Error Sig. (I) Year (J) Year

Freshmen sophomore .5480 .42495 .200

Junior .2680 .42495 .530

Senior 1.8680* .42495 .000

sophomore Freshmen -.5480 .42495 .200

Junior -.2800 .42495 .512

Senior 1.3200* .42495 .002

Junior Freshmen -.2680 .42495 .530

sophomore .2800 .42495 .512

Senior 1.6000* .42495 .000

Senior Freshmen -1.8680* .42495 .000

sophomore -1.3200* .42495 .002

Junior -1.6000* .42495 .000

The data with * shows the significant differences.

Conclusions -

There is significant differences in average number of hours of sleep between Freshmen and Senior college students.

There is significant differences in average number of hours of sleep between Sophomore and Senior college students.

There is significant differences in average number of hours of sleep between Junior and Senior college students.

There are no significant differences in average number of hours of sleep between Freshmen, Sophomore and Junior college students.