Department of Psychology
What is it?
The T-test is used to determine whether there’s a significant difference between two group means. It helps to answer the underlying question: do the two groups come from the same population, and only appear different because of chance errors, or is there some significant difference between these two groups, such that we can say that they’re really from two entirely different populations?
Three basic factors help determine whether an apparent difference between two groups is a true difference or just an error due to chance:
1. the larger the sample, the less likely that the difference is due to sampling errors or chance
2. the larger the difference between the two means, the less likely the difference is due to sampling errors
3. The smaller variance among the participants, the less likely that the difference was created by sampling errors
The choice between two types of t-test depends on your groups or samples. If your two groups are independent, or not related in any way, you choose the independent samples t test. For example, if you used a random sampling technique to recruit 40 adults and 40 children into your study, and those 80 people are not related in any way, you would use independent samples. If you recruited 40 adults and then asked their 40 kids to be in the study, those samples are related, so you would use the dependent samples test.
Independent Samples – needs its own page**
Dependent Samples – needs its own page**
Reporting Data
When reporting the results, you should always include the following: whether the t was significant, the observed value of t, the degrees of freedom, alpha, and the type of test used (one- or two-tailed).
Here are some commonly used formats:
When t is significant:
The difference between the means is statistically significant (t= (observed value of t), df= (calculated degrees of freedom), p<(what you set your alpha at), (type of test used: one or two tailed)).
The difference between the means is significant at the (alpha) level (t= (observed value of t), df= (calculated degrees of freedom), (type of test used: one or two tailed)).
The null hypothesis was rejected at the (alpha) level (t= (observed value of t), df= (calculated degrees of freedom), (type of test used: one or two tailed)).
Note that “statistically significant” and “rejected the null hypothesis” are synonymous.
When the t is not significant:
The difference between the means is not statistically significant (t= (observed value of t), df= (calculated degrees of freedom), p>(what you set your alpha at), (type of test used: one or two tailed)).
Note that p is indicated to be greater than the set alpha level.
For the difference between the means, t = (observed value of t) (df = (calculated degrees of freedom), n.s., (type of test used: one- or two-tailed).
Note that this method does not include the alpha level. It is assumed to be .05.
The null hypothesis for the difference between the means was not rejected at the (alpha) level (t= (observed value of t), df = (calculated degrees of freedom), (type of test used: one or two tailed)).
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