# Independent or single sample t-test, also a question about chi squared tests on percentage data

#### Aaraa

##### New Member
Hi everyone,
Have a bit of a question for some stats I need to run for my research. Have already asked around the lab and no one's 100% sure.

1. I have the data for a single population of individuals including the mean and SD. I need to compare this to a paper that only lists the mean, SD and number of individuals. Is this a single sample or independent t-test (and can anyone suggest an accurate online calculator if it's an independant t-test as I think SPSS needs the background data for both to run.) Looking at the previous paper's analysis (where they've done a comparison against a previous year) I think it seems to be a single sample, but wouldn't you run an independent t-test if you know the mean, SD and n of each group? (Both lots of n are larger than 30 and are definitely independant.)

2. I have a separate lot of data I need to compare to the same paper, but this time they've only given me percentage values. (Example 73.2% light, 21.3% medium and 4.9% dark materials.) Again, the previous paper ran a chi squared test on their data, comparing to another location. If I need to compare my own data to these values, I'm guessing the best way would be to round the percentages into whole numbers then run a chi-square? (ie 73% light, 21% medium, 5% dark?) Also does it matter if the rounding does not add to 100 (ie due to rounding it causes the total to = 101 say?)

Thank you very much in advance.

#### Karabiner

##### TS Contributor
If you have got sample data with n, mean and SD, and data from literature with n, mean and sd, then you should perform an independent samples t-test. I guess there are online calclators which can do this for you.

For a Chi², you need the frequencies, not just the percentages.

With kind regards

Karabiner

#### obh

##### Active Member
Hi everyone,
Have a bit of a question for some stats I need to run for my research. Have already asked around the lab and no one's 100% sure.

1. I have the data for a single population of individuals including the mean and SD. I need to compare this to a paper that only lists the mean, SD and number of individuals. Is this a single sample or independent t-test (and can anyone suggest an accurate online calculator if it's an independant t-test as I think SPSS needs the background data for both to run.) Looking at the previous paper's analysis (where they've done a comparison against a previous year) I think it seems to be a single sample, but wouldn't you run an independent t-test if you know the mean, SD and n of each group? (Both lots of n are larger than 30 and are definitely independant.)

2. I have a separate lot of data I need to compare to the same paper, but this time they've only given me percentage values. (Example 73.2% light, 21.3% medium and 4.9% dark materials.) Again, the previous paper ran a chi squared test on their data, comparing to another location. If I need to compare my own data to these values, I'm guessing the best way would be to round the percentages into whole numbers then run a chi-square? (ie 73% light, 21% medium, 5% dark?) Also does it matter if the rounding does not add to 100 (ie due to rounding it causes the total to = 101 say?)

Thank you very much in advance.
Hi Aaraa,
following online calculator (equal standard deviation assumption or unequal)

http://www.statskingdom.com/150MeanT2uneq.html
or
http://www.statskingdom.com/140MeanT2eq.html

#### Aaraa

##### New Member
Thank you very much for the advice obh and Karabiner
Any suggestions for how to compare percentages is a Chi square is not appropriate? I'm at a bit of a loss with what to use for that one as I was suggested to just follow the tests used by the paper I'm comparing (which may have done the wrong thing from the sounds of it if a chi square shouldn't have been used to compare percentage data.) There's two groups to compare, each with multiple categories (at least 3 depending on the test as there's a few of them).
Just as an example, you might have the percentage of pieces in light, dark and medium colour shades for this year, compared to last year.

Thank you again! This advice has been a life saver, have been trying to work this out on my own for ages.

#### Karabiner

##### TS Contributor
If you have got the sample sizes and the percentages,
then you can calculate the frequencies and perform
a Chi² test.

Or maybe there's an online calculator or some software
where you can just put in the percentages and the total n's .

With kind regards

Karabiner

#### obh

##### Active Member
Per my understanding, the chi-square goodness of fit compares your sample (observed) to a population. (expected)
In this case you (or the calculator) multiple the proportion by your sample size to get the expected value.

If the other research is a sample (not population), I'm not sure if it is correct to use the chi-square goodness of fit test.
(I assume other research with very big sample size or a mixture of several researches can be treated as population, what do you mean by "separate lot of data")

Karabiner, what do you think?

#### Aaraa

##### New Member
Hi obh. The paper I need to use for comparison is the same study I'm doing but was about 10 years ago. So it's a comparison to see if changes have taken place. Both would be samples I think, as they cannot represent the entire population. I just assumed that the chi squared test would be the correct one to use as that's what they had done to compare their work with a different sampled population and had the paper published, but maybe it's not correct (or they somehow had access to raw data that I don't know about to run it )

Edit: Actually I do have the total number of samples for the prior study, so would it be appropriate just to multiply it out?
So for example, if I know they had 500 samples and 10% were light, 70% were medium and 20% were dark, could I just enter them into the table as 50, 350, 100 as the expected values, and then add my data into the results obtained? I think that's what you mean Karabiner?

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