# BTM8106-8 Week 7 Assignment, calculus homework help

**Question description**

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1. Calculate the sample size needed given these factors:

- one-tailed t-test with two independent groups of equal size
- small effect size (see Piasta, S.B., & Justice, L.M., 2010)
- alpha =.05
- beta = .2
- Assume that the result is a sample size beyond what you can obtain. Use the compromise function to compute alpha and beta for a sample half the size. Indicate the resulting alpha and beta. Present an argument that your study is worth doing with the smaller sample.

2. Calculate the sample size needed given these factors:

- ANOVA (fixed effects, omnibus, one-way)
- small effect size
- alpha =.05
- beta = .2
- 3 groups
- Assume that the result is a sample size beyond what you can obtain. Use the compromise function to compute alpha and beta for a sample approximately half the size. Give your rationale for your selected beta/alpha ratio. Indicate the resulting alpha and beta. Give an argument that your study is worth doing with the smaller sample.

## Tutor Answer

Yes you are right, here it's an updated version with the diagram. Let me know if you need other help! Also i would like to know what do you think for my workThanks

Calculation of sample size for t-test

It is considered that, there is a small effective size when Cohen’s d is around 0.2.

So in this case, d is considered equal to 0.2. To calculate the sample sizes for the two groups,

power of analysis, alpha error probability and allocation ratio are needed.

Alpha error probability is 0.05, power of analysis is equal to 1-beta=0.8 and allocation ratio is

1 as the two groups have equal sample sizes.

Using those values for the variables in G*power application, we find that sample size for

each group is 310.

So totally 620 samples are needed. This is a really big number, and in statistical research

sometimes it’s really hard to find so many samples.

G*Power Output

t tests - Means: Difference between two independent means (two groups)

Input: Tail(s)=One

Effect size d=0.2

α err prob=0.05

Power (1-β err prob)=0.8

Allocation ratio N2/N1= 1

Output:Noncentrality parameter δ=2.4899799

Critical t=1.6473230

Df=618

Sample size group 1=310

Sample size group 2=310

Total sample size=620

Actual power=0.8002178

As stated before, sometimes it is really difficult to find samples for a statistical analysis. For

such cases, Erdfelder (1984) developed the concept of compromise power analysis.

Using G*Power, and the compromise selection for t-test, alpha and beta probabilities can be

determinded if we take half of the sample size. That means that the sample size for each

group is now 155. We also have to determine the beta/alpha ratio, which we assume to be

1, as in basic research they are considered equally serious.

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