The preferred alternative to the approaches discussed above is to make use of statistical tests that compare viability over the duration of the entire experiment, wherein each time point represents a cumulative opportunity to detect differences. For the field, this can be accomplished using a standard version of the . The null hypothesis of the logrank test is that there is no difference in survival (or some other trait of interest) between the two populations under study. Thus, a trend of consistent differences over time would lead to rejection of the null hypothesis and a statistically significant finding. The logrank test is mathematically accomplished in part by combining the survival data from both populations and using this value to calculate the expected number of (such as deaths) that would be predicted to occur in each population at each time point.
You may be surprised to learn that nothing can stop you from running a -test with sample sizes of two. Of course, you may find it difficult to convince anyone of the validity of your conclusion, but run it you may! Another problem is that very low sample sizes will render any test . What this means in practical terms is that to detect a statistically significant difference with small sample sizes, the difference between the two means must be quite large. In cases where the inherent difference is not large enough to compensate for a low sample size, the -value will likely be above the critical threshold. In this event, you might state that there is insufficient evidence to indicate a difference between the populations, although there could be a difference that the experiment failed to detect. Alternatively, it may be tempting to continue gathering samples to push the -value below the traditionally acceptable threshold of 0.05. As to whether this is a scientifically appropriate course of action is a matter of some debate, although in some circumstances it may be acceptable. However, this general tactic does have some grave pitfalls, which are addressed in later sections (e.g., ).
"Hypothesis Testing."From --A Wolfram Web Resource.
Outliers principally affect statistics that are based on , such as means and SDs, but do not generally have much of an impact on or , such as medians. For example, the median of the five values 4, 6, 7, 8, 10 is the same as the median of 4, 6, 7, 8, 235. In contrast, the means and SDs of these two data sets are very different. The resistance of median values to the effects of outliers provides a reasonable argument for using medians over means under certain circumstances. For example, in a subdivision with 100 houses, a mean value of $400,000 may be due to a handful of multi-million dollar properties. A median value of $250,000, however, might better reflect the cost of a home. Some problems with medians are that they are not as widely used in the scientific literature as means and also require a different set of statistical tools for their analysis. Specifically, the statistical analysis of medians is carried out using nonparametric approaches, such as a , or through computational methods, such as bootstrapping (discussed below).
Suppose someone suggests a hypothesis that a certain population is 0
which we get by inserting the hypothesized value of the population mean difference (0) for the population_quantity. If or (that is, ), we say the data are not consistent with a population mean difference of 0 (because does not have the sort of value we expect to see when the population value is 0) or "we reject the hypothesis that the population mean difference is 0". If t were -3.7 or 2.6, we would reject the hypothesis that the population mean difference is 0 because we've observed a value of t that is unusual if the hypothesis were true.
How Do I Write a Statistical Analysis Paper
When you set up a hypothesis test to determine the validity of a statistical claim, you need to define both a null hypothesis and an alternative hypothesis.
Hypothesis testing and p-values (video) | Khan Academy
In statistics terminology, the students in the study are the sample and the larger group they represent (i.e., all statistics students on a graduate management degree) is called the population. Given that the sample of statistics students in the study are representative of a larger population of statistics students, you can use hypothesis testing to understand whether any differences or effects discovered in the study exist in the population. In layman's terms, hypothesis testing is used to establish whether a research hypothesis extends beyond those individuals examined in a single study.