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Hi I need help interpreting one sample t test power analysis and independent samples t test power analysis results.

  • 1.  Hi I need help interpreting one sample t test power analysis and independent samples t test power analysis results.

    Posted Thu July 22, 2021 06:59 PM
    My power analysis for the one sample t test was done for estimating the power (because I aimed for a sample size > 30 for two groups, one of my groups only managed to get < 30 however). My data consists of a survey that was administered and was converted to a score/100 and then compared to an established mean value. For the purposes of my data, I did a one sample t test twice (two samples and wanted to compare the respective samples to an established mean value) and found that the means of both groups were statistically different from the established mean. I did a power analysis to estimate the power which I gave the calculated mean of the sample size, the sample sizes' respective standard deviation, the sample size, a null value which I understood was supposed to be the value I am comparing it to (i.e. the established mean), and then done again for the second sample group. (these one sample t tests were done in separate data sets in order to get the results for the two sample sizes before doing the power analysis)

    My first output was:
    My second was: 
    I also did one for independent samples t test to compare if the means were significantly different from each other and the independent samples t test for that said they were not different from each other. This is the power analysis for independent samples t test:
    how do I interpret the power analysis results?

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    Emanuel Mejia
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  • 2.  RE: Hi I need help interpreting one sample t test power analysis and independent samples t test power analysis results.

    Posted Fri July 23, 2021 11:41 AM
    Edited by Rick Marcantonio Fri July 23, 2021 11:43 AM
    Hi.

    The first test tells you that the difference of (about) 10 points between the sample and population average, with a std. deviation of about 18.4 and p-value of .05 (2-tailed), results in a very small chance of failing to reject the null when you should (beta error = 1-.941, or about .06). In other words, you have a very good probability (.94) of correctly rejecting the null hypothesis that there is no difference between the sample and population averages. Same for the second test. In fact, in that case the effect size is 1, so the difference between the sample and population means is about equal to the (known) std. deviation. That's a pretty big difference, which is why you only need 11 cases to get more than adequate power (.85).

    These were both one-sample t-tests, designed to compare a sample mean to a known population mean with a known variability.

    The last table is totally different. It's for a two-sample test, which looks at the difference between the means of two groups using a measure of the variability of the two groups (not only one group, like the previous test). This test, as you see, is under-powered; the effect is too small, meaning that the difference between the two sample means is only a fraction of the combined samples' variability.



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    Rick Marcantonio
    Quality Assurance
    IBM
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  • 3.  RE: Hi I need help interpreting one sample t test power analysis and independent samples t test power analysis results.

    Posted Wed July 28, 2021 10:08 AM

    hi Rick,

    Apologies for my late reply. Thank you so much for your help! I was having a lot of difficulty understanding this and you helped me. 

    thank you so much for all your help!

    Stay safe!

    Best,

    Emanuel



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    Emanuel Mejia
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