Question

A) What is the DV? __________ What is the IV?

B) What analysis should be used to determine if there is a difference in balancing time as a function of treatment?

C) What is the result of that analysis? D) Given that result, can we conclude amphetamine caused a difference in balancing time? If so, what was the change (i.e., did amphetamine reduce or increase balancing time)?

E) Given the result of the test, can we conclude that amphetamine does not cause a change in balancing time? If so, explain how. If not, explain why not.

It is known that the effect of giving amphetamine after brain damage is to reduce tissue necrosis (death). A researcher is interested in whether this effect translates into better behavioral performance. The researcher lesions the brains of a group of 9 rats with a chemical injected into their motor cortex to simulate a stroke. The researcher then randomly assigns rats to one of 3 conditions. In Condition A, the rats are given no other treatment. In Condition B, the rats are given a saline solution intravenously immediately after the lesion. In Condition C, the rats are given amphetamine intravenously immediately after the lesion. The researcher then measures how long each rat can maintain balance on a thin bar before falling off 2 days later. The following data are obtained (all times are in seconds):

Rat Condition Time

1 A 8

2 A 6

3 A 10

4 B 12

5 B 10

6 B 7

7 C 18

8 C 21

9 C 20

Answer 1

A)

The dependent variable is the 'time for which rat can maintain balance on thin bar'.

And the independent variable is 'the treatment given to the rat'.

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B)

As there are three treatments, so we should perform an analysis of variance to compare the three sample means.

Null Hypothesis - H₀: There is no difference in the mean balancing time across treatments.

Alternate Hypothesis - H₁: At least one treatment has mean balancing time different from others.

It can be written symbolically as -

We get following output from excel for single factor ANOVA -

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	3	24	8	4
B	3	29	9.666666667	6.333333333
C	3	59	19.66666667	2.333333333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	238.8888889	2	119.4444444	28.28947368	0.000881392	5.14325285
Within Groups	25.33333333	6	4.222222222
Total	264.2222222	8

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C)

As the p-value is less than level of significance, so we reject the null hypothesis and conclude that at least one of the mean is significantly different from other.

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D)

Of course, the amphetamine caused a difference in balancing time. We can clearly see from the sample mean values that the mean of group C is much larger than that of A and B.

So, we can say that it increased the balancing time.

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E)

No. we have enough evidence to reject the null hypothesis. And as the sample mean of group C is much larger than other two, so its certainly different from other two.