Sample size is when your sample size is increases, it is power of your test. This should make sense because the more you collected information, the larger sample of means for your data which makes it easy to reject the null hypothesis when you should. You have to conduct a power analysis to ensure that your sample size is big enough.
For any power calculation, you need to know
- What type of test you going to use either independent t-test, ANOVA and others.
- The alpha value that you are using. For example, 0.01 or 0.05.
- The expected effect size itself.
- The sample size that going to use.
After the values are already chosen, a power value between 0 and 1 will be generated. If the power less than 0.8, you have to increase your sample size.
What is power?
Power is when you conduct a inferential statistics test, it help to understand what is power. if you are comparing two hypotheses the null and alternative hypothesis. The inferential statistics looks for evidence that you can reject the null or alternative to conclude that you studies had an effect or not. With any statistical test, there always have a possibility to find a difference between group when one does not exist. This is known as Type I error but for Type II error it possible when difference does exist which the test not able to identify.
Power also refers to the probability that your test need to find statistically significant difference when such a difference actually exists. Power is probability you to reject the null hypothesis when you should and accept that the power is greater 0.8
What alpha value that need to use to calculate power?
An alpha level is less than 0.5, it showed a statistically significant and the most common alpha level used in evalutions
What is effect size?
When a difference is significant, it does not necessarily that mean is big. It simply means you that you data had a difference. For example, that you evaluate the effect of activity on student knowledge using pre-test and post-tests. The mean score for the
pre-test was 83 out of 100 while the mean score on the post-test was 84 out of 100. Although
you find that the difference in scores is statistically significant because of
a large sample size, the difference is very slight, suggesting that the
program did not lead to a meaningful increase in student knowledge.
How to calculate the effect size?
There are different ways to calculate the effect size depending on the evaluation that you use. Generally, effect size
is calculated by taking the difference between the two groups such as the mean
of treatment group "minus" the
mean of the control group and "dividing" it by the standard deviation of one of
the groups. For example, in an evaluation with a treatment group and control
group, effect size is the difference in means between the two groups divided by
the standard deviation of the control group.
To interpret the resulting number, most
social scientists use this general guide developed by Cohen:
·
<
0.1 = trivial effect
·
0.1
- 0.3 = small effect
·
0.3
- 0.5 = moderate effect
·
>
0.5 = large difference effect
By: Nur Fariza
References:
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New Jersey: Lawrence Erlbaum.
- Patton, M. Q. (1990). Qualitative research and evaluation methods. London: Sage Publications
- Smith, M. (2004). Is it the sample size of the sample as a fraction of the population that matters? Journal of Statistics Education. 12:2. Retrieved September 14, 2006 from http://www.amstat.org/publications/jse/v12n2/smith.html
- http://www.power-analysis.com/effect_size.htm
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