## Hypothesis Tests - Statistics and Probability

### Statistical Hypothesis Testing Overview - Statistics By Jim

The intent of these sections will be to provide researchers with a practical guide to the application of statistics using examples that are relevant to our field. Namely, which common situations require statistical approaches and what are some of the appropriate methods (i.e., tests or estimation procedures) to carry out? Our intent is therefore to aid worm researchers in applying statistics to their own work, including considerations that may inform experimental design. In addition, we hope to provide reviewers and critical readers of the worm scientific literature with some criteria by which to interpret and evaluate statistical analyses carried out by others. At various points we suggest some general guidelines, which may lead to somewhat more uniformity in how our field conducts and presents statistical findings. Finally, we provide some suggestions for additional readings for those interested in a more systematic and in-depth coverage of the topics introduced ().

### Statistical concepts > Hypothesis testing - StatsRef

Notice something about the code above – the WHERE statement. My hypothesis only mentioned three groups – Caucasians, African-Americans and Latinos. Those were the only three groups that had a value for the race variable. (*This example uses a modified subset of the CHIS , if you are really into that sort of thing and want to know.*) Since that is the population I will be analyzing, I do not want to include people who don’t fall into one of those three groups in my computation of the frequency distributions and means.

Often we can never really know the true mean or SD of a population because we cannot usually observe the entire population. Instead, we must use a sample to make an educated guess. In the case of experimental laboratory science, there is often no limit to the number of animals that we could theoretically test or the number of experimental repeats that we could perform. Admittedly, use of the term “populations” in this context can sound rather forced. It's awkward for us to think of a theoretical collection of bands on a western blot or a series of cycle numbers from a qRT-PCR experiment as a population, but from the standpoint of statistics, that's exactly what they are. Thus, our populations tend to be mythical in nature as well as infinite. Moreover, even the most sadistic advisor can only expect a finite number of biological or technical repeats to be carried out. The data that we ultimately analyze are therefore always just a tiny proportion of the population, real or theoretical, from whence they came.

## the results of statistical analysis

Getting back to -values, let's imagine that in an experiment with mutants, 40% of cross-progeny are observed to be males, whereas 60% are hermaphrodites. A statistical significance test then informs us that for this experiment, = 0.25. We interpret this to mean that even if there was no actual difference between the mutant and wild type with respect to their sex ratios, we would still expect to see deviations as great, or greater than, a 6:4 ratio in 25% of our experiments. Put another way, if we were to replicate this experiment 100 times, random chance would lead to ratios at least as extreme as 6:4 in 25 of those experiments. Of course, you may well wonder how it is possible to extrapolate from one experiment to make conclusions about what (approximately) the next 99 experiments will look like. (Short answer: There is well-established statistical theory behind this extrapolation that is similar in nature to our discussion on the SEM.) In any case, a large -value, such as 0.25, is a red flag and leaves us unconvinced of a difference. It is, however, possible that a true difference exists but that our experiment failed to detect it (because of a small sample size, for instance). In contrast, suppose we found a sex ratio of 6:4, but with a corresponding -value of 0.001 (this experiment likely had a much larger sample size than did the first). In this case, the likelihood that pure chance has conspired to produce a deviation from the 1:1 ratio as great or greater than 6:4 is very small, 1 in 1,000 to be exact. Because this is very unlikely, we would conclude that the null hypothesis is not supported and that mutants really do differ in their sex ratio from wild type. Such a finding would therefore be described as statistically significant on the basis of the associated low -value.

## Statistical Analysis Hypothesis Help - BrainMass

To aid in understanding the logic behind the -test, as well as the basic requirements for the -test to be valid, we need to introduce a few more statistical concepts. We will do this through an example. Imagine that we are interested in knowing whether or not the expression of gene is altered in comma-stage embryos when gene has been inactivated by a mutation. To look for an effect, we take total fluorescence intensity measurements^{} of an integrated ::GFP reporter in comma-stage embryos in both wild-type (Control, ) and mutant (Test, ) strains. For each condition, we analyze 55 embryos. Expression of gene appears to be greater in the control setting; the difference between the two sample means is 11.3 billion fluorescence units (henceforth simply referred to as “11.3 units”).

## Statistical Analysis Hypothesis Help

The Central Limit Theorem having come to our rescue, we can now set aside the caveat that the populations shown in are non-normal and proceed with our analysis. From we can see that the center of the theoretical distribution (black line) is 11.29, which is the actual difference we observed in our experiment. Furthermore, we can see that on either side of this center point, there is a decreasing likelihood that substantially higher or lower values will be observed. The vertical blue lines show the positions of one and two SDs from the apex of the curve, which in this case could also be referred to as SEDMs. As with other SDs, roughly 95% of the area under the curve is contained within two SDs. This means that in 95 out of 100 experiments, we would expect to obtain differences of means that were between “8.5” and “14.0” fluorescence units. In fact, this statement amounts to a 95% CI for the difference between the means, which is a useful measure and amenable to straightforward interpretation. Moreover, because the 95% CI of the difference in means does not include zero, this implies that the -value for the difference must be less than 0.05 (i.e., that the null hypothesis of no difference in means is not true). Conversely, had the 95% CI included zero, then we would already know that the -value will not support conclusions of a difference based on the conventional cutoff (assuming application of the two-tailed -test; see below).