Question

Please show work and explain. Thanks

You have conducted an experiment looking at the impact of encephalin (ENK) on sensory thresholds in male mice. You decide to use a within subjects design rather than a between subjects design for a number of reasons: (1) based on your previous data, you know that sensory thresholds tend to be quite variable across mice; (2) using different mice for each dose will require at least 20 mice for n-5 per dose and these mice are quite expensive; and (3) you always want to minimize the number of animals used in research and choose to re-test subjects whenever possible. Mice were tested once a week and the dose order of ENK was counterbalanced (what does this mean?) Changes in sensory thresholds were assessed by measuring the amount of time (in secs) it took for a mouse to lick its paw in response to a heated stimulus (hot plate latency; HPL) Below are the data. 1. 2. 3. Did administration of ENK alter sensory thresholds in these mice? Construct a bar graph of the means. Indicate which ones are significantly different from one another. Write a brief (1 paragraph) description of your results ENK 2.0 28 18 20 34 28 ENK 5.0 16 10 18 20 ENK 0.0 30 ENK 20.0 34 30 24 38 26 30 df SOURCE ENK Subjects Residual Total MS

Answer 1

s

Source	DF	SS	MS	F	P
ENK	3	698.2	232.733	24.76	0.000
Subjects	4	680.8	170.2	18.11	0.000
Residuals	12	112.8	9.4
Total	19	1491.8

a) The estimated p-value of ENK is 0.000. Hence, the administration of ENK alters sensory thresholds in these mice at the 0.05 significance level.

b)

Interval Plot of Sensory Thresholds 95% CI for the Mean 45 - 40 g 35 U 30 25 G 20 15 10 1 20 ENK

From this graph of means and their corresponding confidence interval, we may say that the mean sensory thresholds of ENK 5 are different from the 0, 2 and 20.

Interval Plot of Sensory Thresholds 95% CI for the Mean 50 40 E 30 D 20 10 4 Subject

From this graph of means and their corresponding confidence interval, we may say that the mean sensory thresholds of Subject 2 are different from the 1, 3, 4 and 5.

c) From the ANOVA table, we can conclude that at least one ENK has a significant mean difference of sensory thresholds from the remaining ENK at 0.05 significance level.

Again from the same ANOVA table, we can conclude that at least one Subject has a significant mean difference of sensory thresholds from the remaining Subject at 0.05 significance level.