Perform a simple power analysis to estimate the sample size you will need for th

Question

Perform a simple power analysis to estimate the sample size you will need for the following experiment. Show your calculation
One wants to determine if age and gender affect discharge time of a patient who is in the emergency room. This is a two way ANOVA. Age and gender are your independent variables and the time is your dependent variable Perform a simple power analysis to estimate the sample size you will need for the following experiment. Show your calculation
One wants to determine if age and gender affect discharge time of a patient who is in the emergency room. This is a two way ANOVA. Age and gender are your independent variables and the time is your dependent variable
One wants to determine if age and gender affect discharge time of a patient who is in the emergency room. This is a two way ANOVA. Age and gender are your independent variables and the time is your dependent variable

Explanation / Answer

Two-Way ANOVA

A two-way ANOVA refers to an ANOVA using 2 independent variable. Expanding the example above, a 2-way ANOVA can examine differences in IQ scores (the dependent variable) by Country (independent variable 1) and Gender (independent variable 2). Two-way ANOVA’s can be used to examine the INTERACTION between the two independent variables. Interactions indicate that differences are not uniform across all categories of the independent variables. For example, females may have higher IQ scores overall compared to males, and are much much greater in European Countries compared to North American Countries.

Two-way ANOVAs are also called factorial ANOVA. Factorial ANOVAs can be balanced (have the same number of participants in each group) or unbalanced (having different number of participants in each group). Not having equal size groups can make it appear that there is an effect when this may not be the case. There are several procedures a researcher can do in order to solve this problem:

The sample size calculation is based a number of assumptions. One of these is the normality assumption for each group. We also assume that the groups have the same common variance. As our power analysis calculation is rooted in these assumptions it is important to remain aware of them.

We have also assumed that we have knowledge of the magnitude of effect we are going to detect which is described in terms of group means. When we are unsure about the groups means, we should use more conservative estimates. For example, we might not have a good idea on the two means for the two middle groups, then setting them to be the grand mean is more conservative than setting them to be something arbitrary.

Here are the sample sizes per group that we have come up with in our power analysis: 17 (best case scenario), 40 (medium effect size), and 350 (almost the worst case scenario). Even though we expect a large effect, we will shoot for a sample size of between 40 and 50. This will help ensure that we have enough power in case some of the assumptions mentioned above are not met or in case we have some incomplete cases .

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