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One of the main goals of statistical hypothesis testing is to estimate the *P* value, which is the probability of obtaining the observed results, or something more extreme, if the null hypothesis were true. If the observed results are unlikely under the null hypothesis, your reject the null hypothesis. Alternatives to this "frequentist" approach to statistics include Bayesian statistics and estimation of effect sizes and confidence intervals.

If your P value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample gives reasonable evidence to support the alternative hypothesis. It does NOT imply a "meaningful" or "important" difference; that is for you to decide when considering the real-world relevance of your result.

I have a linear model generated using . I use the function in the package go test a hypothesis with my desired from the package. The default null hypothesis is . What if I want to test , for example. I know I can simply take the estimated coefficient, subtract 1 and divide by the provided standard error to get the t-stat for my hypothesis. However, there must be functionality for this already in R. What is the right way to do this?

A rule of the thumb from a good advisor of mine was to set the Null-Hypothesis to the outcome you do not want to be true i.e. the outcome whose direct opposite you want to show.

This because in the course of a statistical test you either reject the Null-Hypothesis (and favor the Alternative Hypothesis) or you cannot reject it. Since your "goal" is to reject the Null-Hypothesis you set it to the outcome you do not want to be true.

Note that if the alternative hypothesis is the less-than alternative, you reject H_{0} only if the test statistic falls in the left tail of the distribution (below –2). Similarly, if H_{a} is the greater-than alternative, you reject H_{0} only if the test statistic falls in the right tail (above 2).

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You need descriptive statistics for three reasons. First, if you don’t have enough variance on the variables of interest, you can’t test your null hypothesis. If everyone is white or no one is obese, you don’t have the right dataset for your study. Second, you are going to need to include a table of sample statistics in your paper. This should include standard demographic variables – age, sex, education, income and race are the main ones. Last, and not necessarily least, descriptive statistics will give you some insight into how your data are coded and distributed.

The null hypothesis is a statement that you want to test. In general, the null hypothesis is that things are the same as each other, or the same as a theoretical expectation. For example, if you measure the size of the feet of male and female chickens, the null hypothesis could be that the average foot size in male chickens is the same as the average foot size in female chickens. If you count the number of male and female chickens born to a set of hens, the null hypothesis could be that the ratio of males to females is equal to a theoretical expectation of a 1:1 ratio.

The alternative hypothesis is that things are different from each other, or different from a theoretical expectation. For example, one alternative hypothesis would be that male chickens have a different average foot size than female chickens; another would be that the sex ratio is different from 1:1.

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.

There are different ways of doing statistics. The technique used by the vast majority of biologists, and the technique that most of this handbook describes, is sometimes called "frequentist" or "classical" statistics. It involves testing a null hypothesis by comparing the data you observe in your experiment with the predictions of a null hypothesis. You estimate what the probability would be of obtaining the observed results, or something more extreme, if the null hypothesis were true. If this estimated probability (the *P* value) is small enough (below the significance value), then you conclude that it is unlikely that the null hypothesis is true; you reject the null hypothesis and accept an alternative hypothesis.

The null hypothesis, H_{0} is the commonly accepted fact; it is the opposite of the . Researchers work to reject, nullify or disprove the null hypothesis. Researchers come up with an alternate hypothesis, one that they think explains a phenomenon, and then work to .

At this point, a word about error. **Type I error** is the false rejection of the null hypothesis and **type II error** is the false acceptance of the null hypothesis. As an aid memoir: think that our cynical society rejects before it accepts.

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