Question

Use this table to answer the following questions:

	Text Message	X2	Video Chat	X2	Phone Conversation	X2
	4		10		5
	5		8		5
	5		7		4
	6		5		5
	5		6		6
	7		7		6
	6		8		5
	7		8		7
	5		9		6
	4		8		8
n							N
ΣX							ΣΣX
X							(ΣΣX)2/N
Σ(X2)							ΣΣ(X2)
(ΣX)2/n							Σ(ΣX)2/n

1. This one is tough! There are lots of steps we need to take before we can calculate the final test statistic. Let's break it down into steps. What is the Sum of Squares (SS) between? See the powerpoint for the formula for this one!

Group of answer choices

A. 28.47

B. 935.8

C. 40.9

D. 836.40

E. 17.27

2. Okay, now let's figure out what's the Sum of Squares (SS) within?

Group of answer choices

A. 58.20

B. 166

C. 91.3

D. 935.8

E. 40.9

3. Okay, what's the Mean Squares Within (MSwithin)? See the powerpoint for this formula. Remember, you'll need to calculate the DF to figure this one out!

Group of answer choices

A. 1.51

B. 3.381

C. 2.16

D. 4.98

4. What's the Mean Squares Between (MSBetween)?

Group of answer choices

A. 8.63

B. 2.16

C. 28.20

D. 14.23

5. Now we're ready to calculate the test statistic (yay!). Tell me the correct value of the test statistic, round to 2 decimals.

Group of answer choices

A. F = 9.40

B. F = 4.01

C. F = 13.39

D. F = 3.70

6. What is the df between (also known as the df Numerator)?

Group of answer choices

A. df = 30

B. df = 2

C. df = 27

D. df = 3

7. What is the df within (also known as the df Demominator)?

Group of answer choices

A. 2

B. 30

C. 27

D. 3

8. What is the critical value?

Group of answer choices

A. 2.87

B. 4.56

C. 3.36

D. 5.49

9. Based on the critical value and the obtained value, do you accept or reject the null hypothesis?

Group of answer choices

A. Fail to reject the null hypothesis

B. Reject the null hypothesis

10. Based on your answer to the previous question, should we run a post hoc test (don't worry, I won't make you calculate them, I just want to know if we should do a post hoc test in this situation).

Group of answer choices

A. No

B. Yes

11. Write up your results as you would see them in a research paper. Be sure that you include the means and standard deviations for each group in your write-up, as well as a sentence or two explaining the results! See the powerpoint for help with this. You do not need to calculate or include the post-hoc test here.

Answer 1

n	Text Message	Video Chat	Phone Conversation
1	4	10	5
2	5	8	5
3	5	7	4
4	6	5	5
5	5	6	6
6	7	7	6
7	6	8	5
8	7	8	7
9	5	9	6
10	4	8	8
Total	54	76	57
X^2	302	596	337
Grand total	187
Grand squared total	1235	N = 30

This is a test for single factor ANOVA

This is ANOVA - Single Factor. We first need to find the and . They are 'Total variance' and 'Variance in between the treatments' respectively.

We know

=

Grand total = 187 Sum of individual squares = 1235

= 69.367

=

Note: We have to separately sum for all the treatment.

=

= 1194.1

= 28.467

69.367 - 28.467

= 40.9

We can also use excel data analysis function

Steps:

1. Input data
2. Click on 'Data' on toolbar and then click on data analysis
3. Select 'Anova- Single Factor'
4. Input your range and other info accordingly and you will get your analysis.

: The means are equal

: At least one of the means is not equal.

We put the cacluated values in the ANOVA table

ANOVA
Source of Variation	SS	df	MS  (SS /df)	F
Between Groups	28.467	2.000  ( k -1)	14.233	9.396
Within Groups	40.900	27.000 (n- k)	1.515
Total	69.367	29.000

What is the Sum of Squares (SS) between? See the powerpoint for the formula for this one!

Group of answer choices

A. 28.47

B. 935.8

C. 40.9

D. 836.40

E. 17.27

2. Okay, now let's figure out what's the Sum of Squares (SS) within?

Group of answer choices

A. 58.20

B. 166

C. 91.3

D. 935.8

E. 40.9

3. Okay, what's the Mean Squares Within (MSwithin)? See the powerpoint for this formula. Remember, you'll need to calculate the DF to figure this one out!

Group of answer choices

A. 1.51

B. 3.381

C. 2.16

D. 4.98

4. What's the Mean Squares Between (MSBetween)?

Group of answer choices

A. 8.63

B. 2.16

C. 28.20

D. 14.23

5. Now we're ready to calculate the test statistic (yay!). Tell me the correct value of the test statistic, round to 2 decimals.

Test Stat = MSB / MSE

= 9.396

Group of answer choices

A. F = 9.40

B. F = 4.01

C. F = 13.39

D. F = 3.70

6. What is the df between (also known as the df Numerator: between)?

Group of answer choices

A. df = 30

B. df = 2

C. df = 27

D. df = 3

7. What is the df within (also known as the df Demominator: within)?

Group of answer choices

A. 2

B. 30

C. 27

D. 3

8. What is the critical value?

critical value at 5%

C.V. =

=

= 3.354 .......................found using f-dist tables with df1 = 2 df2=27 and p = 0.05

Critical value at 1%

C.V. =

=

=5.488 .......................found using f-dist tables with df1 = 2 df2=27 and p = 0.01

Group of answer choices

A. 2.87

B. 4.56

C. 3.36

D. 5.49 at 1%

9. Based on the critical value and the obtained value, do you accept or reject the null hypothesis?

Group of answer choices

Since Test Stat > C.V.

A. Fail to reject the null hypothesis

B. Reject the null hypothesis

Therefore we conclude that at least one mean is different.

10. Based on your answer to the previous question, should we run a post hoc test (don't worry, I won't make you calculate them, I just want to know if we should do a post hoc test in this situation).

Group of answer choices

A. No

B. Yes

It is done to check where the significant difference lies. So weare rejecting we know there is a difference so we can conduct pos hoc. But if we were to not reject it we wouldn't conduct.

We reject the null hypothesis at 5% level.