Once again Professor Schmedlap has brought forward his reading program and requested it be compared with the new and old basal reading programs. Given this information, we will create the hypothesis: that there is at least one pair of means that is statistically significant. That is to say that Schmedlap's reading program will be significantly better than at least one of the other two programs. Our null hypothesis is that there is no significant difference among the means.
In order to compare the three reading groups, we will need to do an overall test of multiple means. This will test whether or not the group mean of Schmedlap's program is statistically significant when compared to the other two groups means. In the case where there are more than two levels of the independent variable, the analysis goes through two steps; first, we will carry out an overall f-test to determine if there is any significant differences existing among any of the means. If we find that the f-score is statistically significant, then we will move on to step two of the analysis. In this second step we will compare two sets of means simultaneously in order to determine specifically where the significant difference likes. This is known as a multiple comparison t-test.
An ANOVA provides a statistical test of whether or not the means of several groups are all equal, and therefore generalize t-tests to more than two groups. Doing multiple two sample t-tests would result in an increased chance of resulting in a Type I error. For this reason, ANOVAs are useful in comparing two, three, or means.
Some assumptions should be considered in this analysis:
Each sample is independent and randomly selected we can assume that this criteria was met given the information that Schmedlap provided us with. However it would be important to make sure this criteria was met before conducting a reliable study with valid results. It...
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