# Double check sample calculation from pilot study

#### lph2005

##### New Member
I am really a neophyte to statistics but am in the middle of a research project and would appreciate someone checking my calculations.

I ran a pilot study, an 89-item survey instrument in which the last 6 are summed into an intent-to-stay index. The mean and standard deviation of the index is useful for calculating a sample size (Is this assumption correct?).

n = (s)^2 * (t)^2 / (d)^2, where s is standard deviation, t is critical value of 1.96, and d is (.1*mean)

From pilot study
standard deviation of index = 5.839
Mean = 20.33

n = (5.839)^2 * (1.96)^2 / (.1 * 20.33)^2

n = 32

My questions are:

1. Do I only use the dependent variable (intent to stay) index to calculate the mean or do I do the same calculations for the independent variables too (emotional, appraisal, informational, and instrumental support)?

Thank you for your help and guidance.

#### TheAnalysisFactor

##### New Member
1. Do I only use the dependent variable (intent to stay) index to calculate the mean or do I do the same calculations for the independent variables too (emotional, appraisal, informational, and instrumental support)?

Thank you for your help and guidance.
If the only point of your study is to estimate the mean of the dependent variable, then the calculations you've done are appropriate.

But since you have independent variables, I assume the relationship between them and the dependent variable is the point of the study. If you want to check what is an adequate sample to detect that relationship, you need to base your sample size estimate on the test of the relationship. Are you planning on using a multiple linear regression?

Karen

#### lph2005

##### New Member
Thank you for the reply. I think I better back up. These are the four research questions.

1. What perceptions do beginning secondary science teachers have of administrator support?
2. What is the relationship between perceived administrator support and a beginning science teacher’s intent to stay?
3. Which perceptions of administrator support influence a teachers’ intent to stay?
4. Do physical science and life science teachers’ perceptions of administrative support differ from each other?

Number 1 is descriptive statistics.
Number 2 & 3 are correlations (using SPSS Pearson r, p<.05) for each of 4 independent variables relative to intent to stay index.
Number 4 is ANOVA comparing 2 groups.

Does this make sense ?

#### TheAnalysisFactor

##### New Member
Thank you for the reply. I think I better back up. These are the four research questions.

1. What perceptions do beginning secondary science teachers have of administrator support?
2. What is the relationship between perceived administrator support and a beginning science teacher’s intent to stay?
3. Which perceptions of administrator support influence a teachers’ intent to stay?
4. Do physical science and life science teachers’ perceptions of administrative support differ from each other?

Number 1 is descriptive statistics.
Number 2 & 3 are correlations (using SPSS Pearson r, p<.05) for each of 4 independent variables relative to intent to stay index.
Number 4 is ANOVA comparing 2 groups.

Does this make sense ?
Yes, very clear.

You can base your sample size estimates on any of these tests--a description of the mean, correlations, ANOVA. The ANOVA will be a little trickier.

I would suggest using sample size software to run the calculations. The one I use is called Study Size 2.0. They have a 30-day trial period if you want to try it out. It can do a lot of designs (you do not want to calculate sample sizes for an ANOVA by hand), but is very intuitive.

There are a lot of web sites with free sample size applications. It looks like this one will do what you need, and the author knows what he's doing. He has some articles on sample size estimation as well. http://www.cs.uiowa.edu/~rlenth/Power/

Karen