Question

A researcher decides to examine the effects of a new drug on the activity level of animals. Three samples of rats are selected with n=5 in each sample. One group gets no drug, one group gets a small dose, and a third group gets a large dose. The researcher records the activity level for each animal. The data from this experiment are presented below.

No drug	Small dose	Large dose
5	5	10
3	5	12
1	9	9
1	6	6
5	5	8
T = 15	T = 30	T =
SS = 16	SS = 12	SS =

                                    G = 90

                                    ΣX² = 678

NOTE: To save you some time, I have provided some calculations for the first two treatments; however, to make sure you retain the skill, I want you to calculate T and SS for the third treatment group! Remember, T stands for “treatment total,” and is just “ANOVA language” for ΣX for that treatment group. I have also provided G (the Grand total of all scores, the same as ΣX for all scores in the whole experiment) and ΣX².

1. Do these data indicate any significant differences among the three groups? Use α = .05. (Note that you will need to use – and clearly show – all 4 steps of hypothesis testing to answer this question.)

2. Please fill in the ANOVA source table below with values calculated in #1.

Source	SS	df	MS	F
Between treatments
Within Treatments
Total

Note: No values go into the boxes that are shaded.

3. Compute the value of ƞ² (percentage of variance accounted for by the treatment) for these data.

4. Write a sentence showing how the outcome of the hypothesis test and the measure of effect size would appear in a research report (i.e., in APA format). Note that you can find an example of APA format for a single-factor ANOVA (also called a one-way ANOVA) in your book on pages 349-350. Like the example in your book, I expect you to include a table showing means and standard deviations of each group. (This means you will have to calculate the means and standard deviations for each group, which should be pretty easy since you already have T and SS for each group!) I provided a blank below table to help you get the idea! This table should go AFTER your statement in words, like the example in the book.

Table 1. Activity level following drug exposure for each group.

	No drug	Small dose	Large dose
M
SD

Answer 1

1) Hypothesis:

Null hypothesis: H0:

Alternative hypothesis: H1: Not H0

2) Test:

Here we used One way ANOVA because we have 3 groups. it is the most powerful test to compare two or more means

3)Decision rule:

Reject H0 if F> F()((k-1)(N-k))

4) Test statistic:(Using Ms-Excel)

SUMMARY
Groups	Count	Sum	Average	Variance
No drug	5	15	3	4
Small drug	5	30	6	3
Large drug	5	45	9	5
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	90	2	45	11.25	0.001771	3.885294
Within Groups	48	12	4
Total	138	14

5)Conclusion:

Here F statistic>F critical

11.25>3.8852

so we reject H0

So there is a statistically significant difference between these three treatment groups.

	No drug	Small drug	Large drug
Mean	3	6	9
S.D	2	1.732	2.236