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The tests are used to test for differences between two conditions. The statistic is t . This statistic, t , must be greater than or equal to the critical value to be statistically significant. The information you need to provide to enable someone to check t is the degrees of freedom. Different versions of this test are used with an unrelated measures IV (the independent t test) and with a related measures IV (the related t test). (See Section 10.2 of the book if you are unfamiliar with the terms unrelated or related measures IVs.) You must therefore state clearly which version you used. There are also two versions of the independent t test, one for when the two samples have equal variances and one for when they have unequal variances, so you need to know which one to use for your data.
In an experiment to test whether the 15 students who received a positive comment from their tutor once in every class performed differently in the end of course examination from those in the control group, also of 15 students, who did not receive the positive comment. Degrees of freedom = total number of participants (30) minus 2. There was no evidence of differences in the variances of the two samples, so analysis used the independent t test for equal (or pooled) variances. With degrees of freedom = 28, the obtained value of t = 2.70 has an associated probability = .01 (two-tailed test).
These findings are reported succinctly in Section 4.6.8 of the book.
This experiment tested whether the 15 students who received a positive comment from their tutor once in every class performed differently on the examination at the end of this course than they did in the examination of an equivalent course in which they did not receive the positive comment. Degrees of freedom for the related t test = total number of participants (15) minus 1 = 14. With degrees of freedom = 14, the obtained value of t = 2.49 with an associated probability = .03 (two-tailed test).
These findings are reported succinctly in Section 4.6.9 of the book.
Make sure that you use the appropriate version for related and unrelated measures IVs. If you used an independent t test make sure that you state whether you used the version for equal or unequal variances. If you used an independent t test and the result is not statistically significant, did you run enough participants? (See sections 5.2 and 13.1.1 of the book for more about this issue.)
Analysis of variance is a family of related analyses that can be used to test for differences between two or more conditions. The design can include any number and any combination of related or unrelated measures IVs. (See Section 10.2 of the book if you are unfamiliar with the terms unrelated or related measures IVs.) You must therefore describe precisely which version you used. Advice on this can be found in Section 13.3 of the book. (See also Section 4.6.10.)
The statistic is F. This statistic, F , must be greater than or equal to the critical value to be statistically significant. The information you need to provide to enable someone to check F is two (NB two ) sets of degrees of freedom: the degrees of freedom for the numerator of the F ratio and the degrees of freedom for the denominator of the F ratio. The numerator is the source under test, such as the main effect of an IV or the interaction between two or more IVs. (See Sections 13.4 and 13.5 of the book if you are not familiar with these terms.) The denominator (the bit that divides into the numerator) is called the error term. The F ratio is thus formed by dividing the error term (the denominator) into the source under test (the numerator).
The sample RESULTS section reported for the mnemonic experiment in Section 4.6.10 of the book contains several examples of how to report analysis of variance. You can also find an example RESULTS section for more advanced students that also contains F ratios in Section H6 of this Web site.
Make sure that your F ratios contain both degrees of freedom described above. Make sure that you punctuate the F ratios properly, using commas, spaces and italics exactly as in the examples in the book. Unless you are told explicitly to the contrary, make sure that you report all of the main effects and interactions, making it clear in each case which is which and whether the effect is or is not statistically significant. (You can find in Section C7 of this Web site a table containing a list of all the possible effects in designs with two, three, or four IVs.) When interpreting, make sure that you remember that statistically significant interactions qualify main effects involving that IV. (You can find a discussion of this issue in Section C4 of this Web site.) With effects involving more than 1 degree of freedom, further comparisons are usually required to locate the differences. (You can find more about this in Section B7 of this Web site.) Some statistical software packages (e.g., certain versions of SPSS) produce output with several options for the degrees of freedom and probability of F for related measures IVs and their interactions. Don't panic! Most of the time you can happily report the version labelled "sphericity assumed". Only concern yourself about this in the rare event that the sphericity assumed version is statistically significant and the other versions are not. If so, check the outcome of Mauchly's Sphericity Test - if this is significant (the value of χ² has an associated probability of .05 or less) then report the corrected (nonsignificant) versions of F .
A number of common and basic mistakes to avoid when reporting analysis of variance can be found in Section 4.6.11 of the book. See also Section B7 of this Web site. |
