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## Significance Tests / Hypothesis Testing

When we make this decision about a population based upon a sample, this is statistical inference.

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# In statistics, the data are the evidence.

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I'll confess that I don't really understand Bayesian statistics, and I apologize for not explaining it well. In particular, I don't understand how people are supposed to come up with a prior distribution for the kinds of experiments that most biologists do. With the exception of systematics, where Bayesian estimation of phylogenies is quite popular and seems to make sense, I haven't seen many research biologists using Bayesian statistics for routine data analysis of simple laboratory experiments. This means that even if the cult-like adherents of Bayesian statistics convinced you that they were right, you would have a difficult time explaining your results to your biologist peers. Statistics is a method of conveying information, and if you're speaking a different language than the people you're talking to, you won't convey much information. So I'll stick with traditional frequentist statistics for this handbook.

## Type II error: The null hypothesis is not rejected when it is false.

The significance level you choose should also depend on how likely you think it is that your alternative hypothesis will be true, a prediction that you make before you do the experiment. This is the foundation of Bayesian statistics, as explained below.

The significance level (also known as the "critical value" or "alpha") you should use depends on the costs of different kinds of errors. With a significance level of 0.05, you have a 5% chance of rejecting the null hypothesis, even if it is true. If you try 100 different treatments on your chickens, and none of them really change the sex ratio, 5% of your experiments will give you data that are significantly different from a 1:1 sex ratio, just by chance. In other words, 5% of your experiments will give you a false positive. If you use a higher significance level than the conventional 0.05, such as 0.10, you will increase your chance of a false positive to 0.10 (therefore increasing your chance of an embarrassingly wrong conclusion), but you will also decrease your chance of a false negative (increasing your chance of detecting a subtle effect). If you use a lower significance level than the conventional 0.05, such as 0.01, you decrease your chance of an embarrassing false positive, but you also make it less likely that you'll detect a real deviation from the null hypothesis if there is one.

## the null hypothesis is not rejected when it is false c.

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The fact that a hypothesis is consistent with a set of data does not mean that it is correct; whereas, if it is not consistent with the data set it may be incorrect.

• ### the research hypothesis is not rejected when it is false722-1

Every hypothesis test — regardless of the population parameter involved — requires the above three steps.

• ### the null hypothesis is probably wrong b.

Descriptive statistics

• ### the null hypothesis is probably true d.

2. GENERATE A HYPOTHESIS

## the sampling distribution of the statistic assuming H(A).

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 sampling distribution of the statistic assuming H(O).

Recall that it is either likely or unlikely that we would observe the evidence we did given our initial assumption. If it is likely, we do not reject the null hypothesis. If it is unlikely, then we reject the null hypothesis in favor of the alternative hypothesis. Effectively, then, making the decision reduces to determining "likely" or "unlikely."

## The sample statistics are XBAR = 6.4, s = 10.

To address these common problems, Stats Engine was created to test more in less time. By helping you make statistically sound decisions in real time, Stats Engine adjusts values as needed and shares trustworthy results quickly and accurately.

## It is equal to the calculated statistic from the observed data.

Many statisticians harshly criticize frequentist statistics, but their criticisms haven't had much effect on the way most biologists do statistics. Here I will outline some of the key concepts used in frequentist statistics, then briefly describe some of the alternatives.

## Suppose that you are unable to reject the hypothesis.

Stats Engine operates by combining sequential testing and false discovery rate control signs to deliver statistically significant results regardless of sample size. Updating in real time, Stats Engine will ensure a 95% significance level results every time, boosting your confidence in making the right decision for your company and to along the way.

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