Making comparisons

Quickly and easily create comparison chart to identify similarities and differences.

Making comparisons

The F-test provides the overall protection against rejecting Ho when it is true. This procedure uses the t statistic for Making comparisons Ho: Why is it called the studentized range? The denominator uses an estimated standard deviation, hence, the statistic is studentized like the student t-test.

The Tukey procedure assumes all ni are equal say to n. The studentized range is the distribution of the difference between the maximum and a minimum over the standard error of the mean. When we calculate a t-test, or when we're using the Bonferroni adjustment where g is the number of comparisons, we are not comparing apples and oranges.

In one case Tukey the statistic has a denominator with the standard error of a single mean and in the other case t-test with the Making comparisons error of the difference between means as seen in the equation for t and q above.

Making comparisons

Example - Tukey vs. Bonferroni approaches Here is an example we can work out. If we look at the studentized range distribution for 5, 30 degrees of freedom, the distribution can be found in Appendix VII, p.

Looking at the t-table found in Appendix II, p. The point that we want to make is that the Bonferroni procedure is slightly more conservative than the Tukey result, since the Tukey procedure is exact in this situation whereas Bonferroni only approximate.

Making comparisons

The Tukey's procedure is exact for equal samples sizes. However, there is an approximate procedure called the Tukey-Kramer test for unequal ni.

Multiple comparisons - Handbook of Biological Statistics

If you are looking at all pairwise comparisons then Tukey's exact procedure is probably the best procedure to use. The Bonferroni, however, is a good general procedure.

Contrasts of Means A pairwise comparison is just one example of a contrast of the means. A general contrast can be written as a set of coefficients of the means that sum to zero. This will often involve more than just a pair of treatments.

In general we can write a contrast to make any comparison we like. We will also consider sets of orthogonal contrasts. Example - Gas Mileage We want to compare the gas mileage on a set of cars: A consumer testing group wants to test each of these cars for gas mileage under certain conditions.

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They take n prescribed test runs and record the mileage for each vehicle. Now they first need to define some contrasts among these means.

Contrasts are the coefficients which provide a comparison that is meaningful. Then they can test and estimate these contrasts. For the first contrast, C1, they could compare the American brand to the foreign brands. We need each contrast to sum to 0, and for convenience only use integers.

How about comparing Toyota to Honda that is C2or hybrid compared to non-hybrid that is C3.Statistical Comparison of Two Groups. A common form of scientific experimentation is the comparison of two groups. This comparison could be of two different treatments, the comparison of a treatment to a control, or a before and after comparison.

Multiple Comparisons with Repeated Measures David C. Howell. For our example, we are making comparisons among 4 means, so r = 4.

I also point out that the Studentized Range Statistic (q) is directly tied to the t statistic. Specifically, q = t√2. Comparison is one of the best ways to make progress. Sometimes, compare with others, and compare your yesterday with today sometimes.

Often times, you need an all-round comparison for more detailed analysis, especially for those large enterprises. An interactive quiz for studying English. It uses the Flash player plug-in.

Switching home loans. Making the switch. Switching home loans could potentially save you thousands of dollars in interest or let you take advantage of features offered by another loan.

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