# You have conducted an experiment looking at the impact of encephalin (ENK) on sensory thresholds ...

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

(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

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
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