Paired sample t-test is done when an experiment contains matched pair of subjects, like patients before and after some drug is administered to them. Some kind of treatment is given to the subjects and the effects are measured before and after the treatment. The outcomes are thereafter analyzed pair-wise. It’s a parametric test. Here each subject is used as their own control. This way, the correct rejection of the null hypothesis (that there was no effect of the treatment) is much easier, and the statistical power of the test is increased as the random intra-patient variation have now been removed.
In the study reviewed the authors have investigated whether there are any sexual differences in body size preferences in the poeciliid fish, Brachyrhaphis rhabdophora. One aspect of the study was to look at whether males preferred larger females to smaller ones for mating. Fishes were separated when they became mature and kept in separate tank sex wise. Then an experimental setup was made where another tank had three compartments. The test male subject was kept in the central compartment and two females, different in size, were kept in the left and right compartments. Observations were made as to how much time the male spent in the centre, left and right side of the tank. A paired t-test was used to analyze the time spent by males with larger and smaller females. The paired t statistic came out to be t14= 0. 85 with a P value of 0. 41 at 0. 05 level of confidence. This establish that there was no significant interaction of males with larger females. The power of the test was 0. 61 (61%; how surely we can reject the null hypothesis) and the effect size (measure of the strength of a phenomenon) was 0. 62. It was also noticed that larger males preferred larger females and smaller males preferred smaller females. This was tested using correlation and the test statistic was r13= 0. 62 with a significance value of 0. 01.
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Basolo, A. L. (2004). Variation between and within the sexes in body size preferences. Animal Behaviour, 68(1), 75-82.