Inferences Concerning Two Means
Inferences Concerning Two Means
If researchers want to compare two samples in terms of the mean scores using inferential statistics, they can utilize a confidence interval approach to the data or an approach that involves setting up and testing a null hypothesis. Whether two samples are considered to be independent or correlated is tied to the issue of the nature of the groups before data are collected on the study’s dependent variable. If the two groups have been assembled in such a way that a logical relationship exists between each member of the first sample and one and only one member of the second sample, then the two samples are correlated samples. However, if no such relationship exists, the two samples are independent samples.
Correlated samples come into existence in one of three ways. If a single group of people is measured twice (e.g., to provide pretest and posttest data), then a relationship exists in the data because each of the pretest scores goes with one and only one of the posttest scores, because both come from measuring the same research participant. A second situation that produces correlated samples is matching. Here, each person in the second group is recruited for the study because he or she is a good match for a particular individual in the first group. The matching could be done in terms of height, IQ, running speed, or any of a multitude of possible matching variables.
The matching variable, however, is never the same as the dependent variable to be measured and then used to compare the two samples. The third situation that produces correlated samples occurs when biological twins are split up, with one member of each pair going into the first sample and the other member going into the second group. Here, the obvious connection that ties together the two samples is genetic similarity.
When people, animals, or things are measured twice or when twin pairs are split-up, it is fairly easy to sense which scores are paired together
If researchers want to compare two samples in terms of the mean scores using inferential statistics, they can utilize a confidence interval approach to the data or an approach that involves setting up and testing a null hypothesis. Whether two samples are considered to be independent or correlated is tied to the issue of the nature of the groups before data are collected on the study’s dependent variable. If the two groups have been assembled in such a way that a logical relationship exists between each member of the first sample and one and only one member of the second sample, then the two samples are correlated samples. However, if no such relationship exists, the two samples are independent samples.
Correlated samples come into existence in one of three ways. If a single group of people is measured twice (e.g., to provide pretest and posttest data), then a relationship exists in the data because each of the pretest scores goes with one and only one of the posttest scores, because both come from measuring the same research participant. A second situation that produces correlated samples is matching. Here, each person in the second group is recruited for the study because he or she is a good match for a particular individual in the first group. The matching could be done in terms of height, IQ, running speed, or any of a multitude of possible matching variables.
The matching variable, however, is never the same as the dependent variable to be measured and then used to compare the two samples. The third situation that produces correlated samples occurs when biological twins are split up, with one member of each pair going into the first sample and the other member going into the second group. Here, the obvious connection that ties together the two samples is genetic similarity.
When people, animals, or things are measured twice or when twin pairs are split-up, it is fairly easy to sense which scores are paired together