Question

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 ENK ENK 30 16 10 18 20 14 34 S3 24 38 26 30 30 SOURCE ENK Subjects Residual Total df MS

Answer 1

(a) since p-value of ENK is less than typical value of level of significance alpha=0.05, so we conclude that adminitsration of ENK alter the sensory threshold in mice

(b) here we use fisher LSD to find the pair-wise multiple comparison for significantly different from one another

LSD=t(alpha/2, error df)*sqrt(2*MSE/r)=t(0.05/2, 12)*SQRT(2*9.4/5)=2.179*1.939=4.225

so any difference greater than 4.225 will be signficant

ENK	difference	LSD	Remarks
0-2	0.8	4.225	not significant
0-5	10.8	4.225	singifiant
0-20	5.6	4.225	singifiant
2--5	10	4.225	singifiant
2-20	6.4	4.225	singifiant
5-20	16.4	4.225	singifiant

Bar diagram 35 30 25 2 20 2 15 A 10 ENK2 ENK5 ENK20 ENKO Enk

following information has been generated using ms-excel

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
Row 1	4	108	27	60
Row 2	4	64	16	26.667
Row 3	4	92	23	28
Row 4	4	136	34	104
Row 5	4	98	24.5	51.667
Column 1	5	132	26.4	76.8
Column 2	5	128	25.6	42.8
Column 3	5	78	15.6	14.8
Column 4	5	160	32	64
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Enk	698.2	3	232.733	24.759	0.000	3.490
Subject	680.8	4	170.200	18.106	0.000	3.259
Error	112.8	12	9.4
Total	1491.8	19