Suppose a study is being planned that will investigate whether female Beagles wi

Question

Suppose a study is being planned that will investigate whether female Beagles with severe periodontitis (gum and mouth disease) give birth to sma?er litters of puppies, on average, than Beagles without periodontitis. Based on previous research, the standard deviation of litter size is estimated to be 2.1 puppies Suppose we suspect that Beagles with perlodontitis will give birth to on average 6 puppies whereas Beagles without periodontitis will give birth to on average 5 puppies. a. Using the assumed values above, calculate Cohen's d. If you get a negative value, report it as positive. d 0 47619 b. This value (Cohen's d) can be thought of as... (select all that apply) The effect size O The probability we will fail to reject the null hypothesis. The assumed difference in standard deviations of litter size for Beagles with and without periodontitis, in terms of the means The assumed difference between mean litter sizes for Beagles with and without periodontitis, in terms of number of standard deviations The standard error of the effect size The probability we will reject the null hypothesis. c. Let's assume that population effect size is Cohen's d-0.5 (in practice the population effect size is unknown, so we just have to assume a value). For each value of desired power, find the total sample size (i.e. the sample size for both groups combined) required to detect this effect. Use the-sample size and Power" tool in JMP, found under the DOE / Design Diagnostics menu, if you have trouble, take a look at the class example on power. i. For power - 0.65, required n 194.8338x i. For power - 0.7, required n 216986112x iii. For power-0.95, required n- 458499762 ]× d. Now let's see what happens to these calculations if we assume the effect size is a little bit larger. Using d- 0.6, re-do the calculations from part c. above: l. For power-0.65, required n-113530125 ii. For power = 0.7, required n " ili. For power- 0.95, required n | X

Explanation / Answer

(C)

Given that d=0.5

The power function will be

P{Z> Z??/2 or Z< -Z??/2}=1-[Z??/2-d*n]+[-Z?/2-d*n]

At, two tail =0.05

Power=1-[1.96-0.5*n]+[-1.96+0.5*n]

Thus, for power=0.65 n= 45

  for power=0.70 n= 50

  for power=0.95 n= 105

(D)

Given that d=0.6

The power function will be

P{Z> Z??/2 or Z< -Z??/2}=1-[Z??/2-d*n]+[-Z??/2-d*n]

At, two tail =0.05

Power=1-[1.96-0.6*n]+[-1.96+0.6*n]

Thus, for power=0.65 n= 31

  for power=0.70 n= 35

  for power=0.95 n= 73

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