OMG T-tests

Welcome to this years enthusiastic blog about stats and other things.

Going to go ahead and jump straight into explaining what exctly a t-test is. What’s that you say? No introduction?

That’s right, no interesting and witty introduction or colourful fonts for you reader. I don’t get any extra points for making this fun. So how about some extra points for dragging out this post? Well, let’s find out shall we!

THE T-TEST is used for assessesing whether the means of two groups are statistically different from each other. This analysis is appropriate whenever you want to compare the means of two groups.

In the picture above are three distributions. We can see that in all three, the difference between the means is the same. But the three distributions do not look the same. The most striking of the three distributions is the low variability, where there is little overlap between the curves. The high variability distribution is least striking as the curves overlap a great deal. So it’s important to understand that when comparing groups, we must take into account variability/spread as well as the difference in means. That is what the t-test does for us.

In the diagram above, we can see a simplified version of the t-test. The top part of the forumla is simply calculated by finding the difference between the group means. The bottom part of the forumla is calculated by dividing the variance of each group by the number of people in the group. Then we add them together and find thee square root. Simples. Don’t panic if you can’t remember how to work this out, it seems pretty unlikely that you’ll have to do this by hand anyway thanks to the wonders of SPSS.

The standard alpha level (which is like a risk level really) is 0.5 for most social and psychology research. If the p value is less than 0.5 then you can say it’s a significant result and reject the null hypothesis.

So to finish off this exciting post about t-tests, I’m going to cover how to work this out via SPSS and how to report the findings:

How to work out on SPSS: Analyse –> Compare Means —> Independant T-test —> Select the dependant variable you wish to test and put it in test variable box —> Select the independant variable and put it in the grouping variable box —> Define groups (the number which determines the groups) —> press OK!

So now you know how to do that, this is how you would report a t-test:


That concludes this weeks posts, I hope it was helpful in reminding you what the t-test is for. It’s mainly a reference for my own sake seeing as writing a blog about statistics does nothing to aid my learning and it saves me googling this when I have to actually carry out the tests! Tune in next week for some enlightening posts about ANOVAs. I know, I can’t wait either!

Diolch for reading.



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6 responses to “OMG T-tests

  1. Hey great blog. It was very in-dept on what t-tests are used for and the picture examples aided the information well! Although very well written more examples of when a t-test is to be used would have more benefits. Like can you use it for anything or is it just for the means of two groups that are statistically different like you states in the first paragraph. Also when explaining the visual aides it would add more if you explained them in more detail and gave more reasons why, if there is low variability, that that holds any particular information!

  2. Great blog! Your general lack of jargon along with the good use of pictures made it very easy to read and understand. The only constructive criticism I could make is that your definition of an alpha level is a little vague. Though you’re right in saying that it is risk level, it would be more informative to say that it’s risk of committing a Type I error. A type I error is when you say that there is a difference between the groups, when there actually isn’t. Therefore with an alpha level of 0.05 there is 5% chance of making a type I error. Though people describe it as the risk of a type I error, it’s important to remember that there is a risk of making a Type II when the alpha level is too small. A type II error is when you report that there isn’t a difference when there actually is.

    You could have then expanded upon this, stating that one of the major weaknesses of a T-test is that it’s alpha level inflates when performing multiple comparisons. For example if you ran 20 T-tests using an alpha level of 0.05(5% chance).There would be a 100% chance that you made a Type I on one of those comparisons, This is known as experiment wise/family wise error.

    All in all, this is just me being picky. Great blog.

  3. Pumpkin Queen

    I really enjoyed your blog on t-tests and thought it was an enjoyable read (as far as it can be for t -tests).
    the only thing I can say about your blog is maybe the different types of t-test could have been mentioned and when it is best to use each of them. For example the independent samples t-test and the paired samples t-test. The paired samples t-test is when there are two means that are repeated measures for the same participants, where as the independent t-test compares two means from completely different groups.

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  5. Pingback: this weeks blog comments :) « the pumpkin queen and statistics

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