Hi,
I am looking for a solution how to compare three means in jamovi.
We plan to collect two samples of people in a study we run and have them perform a standardized test. Mean scores from the standardized test may differ in the two samples, but apart from this comparison, I want to compare the two samples against norm data for the test.
Suppose the test score can go from 0 to 50, and we know the Norm mean=35 with SD=5, based on a sample of 3000.
I would collect two groups, each N=50.
How can I compare the two groups against each other and also against the Norm?
The first that comes to mind is comparing the two samples using independent samples t-test and then comparing these samples individually with the norm running Independent Mean Difference tests in the ESCI module.
This calculation depends on N, and the N for Norm samples is larger in orders of magnitude and thus with tiny CIs.
Or would it be OK to generate a sample data N=50 based on know mean and SD of the Norm? I guess a seed would be needed for reproducible generated data.
Comparing three means - two from samples, one from norm
Re: Comparing three means - two from samples, one from norm
After doing an independent samples t test to assess the the differences between the means of the two samples you collected, you could then conduct a one-sample t test, separately for each of the two collected samples. Each one-sample t test would be configured to asses whether the mean is significantly different not from 0.00, but from 35.00. (Your example used 35.00.)
Re: Comparing three means - two from samples, one from norm
Hey reason180,
I was thinking about this too. But, I am not comparing against a point estimate of only 35; the mean score is 35 with a known SD of 5. So it is more comparing against the distribution of values than a single point.
I was thinking about this too. But, I am not comparing against a point estimate of only 35; the mean score is 35 with a known SD of 5. So it is more comparing against the distribution of values than a single point.
Re: Comparing three means - two from samples, one from norm
Hi Vit.
I'm not sure if you're conceptualizing the problem as on of comparing three sample means (with the norm sample considered as just another sample), or if the label, "norm" is indicating that your treating the M = 35 and SD = 5 values as population parameters. If the norm sample is just another sample then as you indicated initially, you could just use the esci module to do three planned t tests on 'summary data.' (Or if you have the raw data for the norm sample, you don't need to rely on summary-data analysis.)
On the other hand of the norm mean and norm SD are considered to be population values, then I think things become more complicated. The standard way of doing things would be to estimate the population SD from the sample rather than rely on a "know" SD. This would amount to doing a standard one-sample t test comparing the sample mean to 35 and not utilizing the 'SD = 5' value. I suppose, however, that you could substitute the "known population 'SD = 5' ratter than estimate SD from the sample, but I don't think the esci module lets you use summary data input when it's a simple sample as opposed to a two-sample t test.
I'm not sure if you're conceptualizing the problem as on of comparing three sample means (with the norm sample considered as just another sample), or if the label, "norm" is indicating that your treating the M = 35 and SD = 5 values as population parameters. If the norm sample is just another sample then as you indicated initially, you could just use the esci module to do three planned t tests on 'summary data.' (Or if you have the raw data for the norm sample, you don't need to rely on summary-data analysis.)
On the other hand of the norm mean and norm SD are considered to be population values, then I think things become more complicated. The standard way of doing things would be to estimate the population SD from the sample rather than rely on a "know" SD. This would amount to doing a standard one-sample t test comparing the sample mean to 35 and not utilizing the 'SD = 5' value. I suppose, however, that you could substitute the "known population 'SD = 5' ratter than estimate SD from the sample, but I don't think the esci module lets you use summary data input when it's a simple sample as opposed to a two-sample t test.