Null and Alternative Hypothesis | Real Statistics Using …

One of the most common tests in statistics is the t-test, used to determine whether the means of two groups are equal to each other. The assumption for the test is that both groups are sampled from normal distributions with equal variances. The null hypothesis is that the two means are equal, and the alternative is that they are not. It is known that under the null hypothesis, we can calculate a t-statistic that will follow a t-distribution with n1 + n2 - 2 degrees of freedom. There is also a widely used modification of the t-test, known as Welch's t-test that adjusts the number of degrees of freedom when the variances are thought not to be equal to each other. Before we can explore the test much further, we need to find an easy way to calculate the t-statistic.

The 20% Statistician: One-sided tests: Efficient and …

This is the first of three modules that will addresses the second area of statistical inference, which is hypothesis testing, in which a specific statement or hypothesis is generated about a population parameter, and sample statistics are used to assess the likelihood that the hypothesis is true. The hypothesis is based on available information and the investigator's belief about the population parameters. The process of hypothesis testing involves setting up two competing hypotheses, the null hypothesis and the alternate hypothesis. One selects a random sample (or multiple samples when there are more comparison groups), computes summary statistics and then assesses the likelihood that the sample data support the research or alternative hypothesis. Similar to estimation, the process of hypothesis testing is based on probability theory and the Central Limit Theorem.

You can only use the paired t–test when there is just one observation for each combination of the nominal values. If you have more than one observation for each combination, you have to use with replication. For example, if you had multiple counts of horseshoe crabs at each beach in each year, you'd have to do the two-way anova.

One and Two Tailed Tests - Mathematics A-Level Revision

Since the statistic is the same in both cases, it doesn't matter whether we use the correction or not; either way we'll see identical results when we compare the two methods using the techniques we've already described. Since the degree of freedom correction changes depending on the data, we can't simply perform the simulation and compare it to a different number of degrees of freedom. The other thing that changes when we apply the correction is the p-value that we would use to decide if there's enough evidence to reject the null hypothesis. What is the behaviour of the p-values? While not necessarily immediately obvious, under the null hypothesis, the p-values for any statistical test should form a uniform distribution between 0 and 1; that is, any value in the interval 0 to 1 is just as likely to occur as any other value. For a uniform distribution, the quantile function is just the identity function. A value of .5 is greater than 50% of the data; a value of .95 is greater than 95% of the data. As a quick check of this notion, let's look at the density of probability values when the null hypothesis is true: