## Descriptive and Inferential Statistics - B W Griffin

### 13/09/2016 · How to Write a Hypothesis

One aspect of the -test that tends to agitate users is the obligation to choose either the one or two-tailed versions of the test. That the term “tails” is not particularly informative only exacerbates the matter. The key difference between the one- and two-tailed versions comes down to the formal statistical question being posed. Namely, the difference lies in the wording of the research question. To illustrate this point, we will start by applying a two-tailed -test to our example of embryonic GFP expression. In this situation, our typical goal as scientists would be to detect a difference between the two means. This aspiration can be more formally stated in the form of a or . Namely, that the average expression levels of ::GFP in wild type and in mutant are different. The must convey the opposite sentiment. For the two-tailed -test, the null hypothesis is simply that the expression of ::GFP in wild type and mutant backgrounds is the same. Alternatively, one could state that the difference in expression levels between wild type and mutant is zero.

### INTRODUCTORY STATISTICS: CONCEPTS, MODELS, AND APPLICATIONS

Hello, in a scenario where the hypothesis is “there will be no differences in X between the three groups” is it more appropriate to use a post-hoc than run a one-way anova with contrasts? (there will obviously be three contrasts in that case, 1 -1 0, 0 -1 1, 1 0 -1). And would you ever choose to do a post-hoc in a planned comparison when you have hypothesised a difference (directional or not)? Thank you so much in advance!

proportions or distributions refer to data sets where outcomes are divided into three or more discrete categories. A common textbook example involves the analysis of genetic crosses where either genotypic or phenotypic results are compared to what would be expected based on Mendel's laws. The standard prescribed statistical procedure in these situations is the test, an approximation method that is analogous to the normal approximation test for binomials. The basic requirements for multinomial tests are similar to those described for binomial tests. Namely, the data must be acquired through random sampling and the outcome of any given trial must be independent of the outcome of other trials. In addition, a minimum of five outcomes is required for each category for the Chi-square goodness-of-fit test to be valid. To run the Chi-square goodness-of-fit test, one can use standard software programs or websites. These will require that you enter the number of expected or control outcomes for each category along with the number of experimental outcomes in each category. This procedure tests the null hypothesis that the experimental data were derived from the same population as the control or theoretical population and that any differences in the proportion of data within individual categories are due to chance sampling.

## Research Methods and Statistics Flashcards | Quizlet

Interestingly, there is considerable debate, even among statisticians, regarding the appropriate use of one- versus two-tailed -tests. Some argue that because in reality no two population means are ever identical, that all tests should be one tailed, as one mean must in fact be larger (or smaller) than the other (). Put another way, the null hypothesis of a two-tailed test is always a false premise. Others encourage standard use of the two-tailed test largely on the basis of its being more conservative. Namely, the -value will always be higher, and therefore fewer false-positive results will be reported. In addition, two-tailed tests impose no preconceived bias as to the direction of the change, which in some cases could be arbitrary or based on a misconception. A universally held rule is that one should never make the choice of a one-tailed -test ^{} after determining which direction is suggested by your data In other words, if you are hoping to see a difference and your two-tailed -value is 0.06, don't then decide that you really intended to do a one-tailed test to reduce the -value to 0.03. Alternatively, if you were hoping for no significant difference, choosing the one-tailed test that happens to give you the highest -value is an equally unacceptable practice.

## One Sample Hotelling's T-square | Real Statistics Using …

Regardless of the method used, the -value derived from a test for differences between proportions will answer the following question: What is the probability that the two experimental samples were derived from the same population? Put another way, the null hypothesis would state that both samples are derived from a single population and that any differences between the sample proportions are due to chance sampling. Much like statistical tests for differences between means, proportions tests can be one- or two-tailed, depending on the nature of the question. For the purpose of most experiments in basic research, however, two-tailed tests are more conservative and tend to be the norm. In addition, analogous to tests with means, one can compare an experimentally derived proportion against a historically accepted standard, although this is rarely done in our field and comes with the possible caveats discussed in . Finally, some software programs will report a 95% CI for the difference between two proportions. In cases where no statistically significant difference is present, the 95% CI for the difference will always include zero.