﻿ What a p-Value Tells You about Statistical Data

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## Customarily, the alternative hypothesis is

A small -value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

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# For example, the alternative hypothesis is

involves the careful construction of two statements: the null hypothesis and the alternative hypothesis. These hypotheses can look very similar, but are actually different.

The null hypothesis for an experiment to investigate this is “The mean adult body temperature for healthy individuals is 98.6 degrees Fahrenheit.” If we fail to reject the null hypothesis, then our working hypothesis remains that the average adult who is healthy has temperature of 98.6 degrees. We do not prove that this is true.

## Draw the conclusion: Reject or fail to reject the null hypothesis,

The final conclusion is made by comparing the test statistic (which is a summary of the information observed in the sample) to the decision rule. The final conclusion will be either to reject the null hypothesis (because the sample data are very unlikely if the null hypothesis is true) or not to reject the null hypothesis (because the sample data are not very unlikely).

If the null hypothesis is rejected, then an exact significance level is computed to describe the likelihood of observing the sample data assuming that the null hypothesis is true. The exact level of significance is called the p-value and it will be less than the chosen level of significance if we reject H0.

## Here, the null hypothesis is that the person is innocent, and the

You should also indicate the used to analyze your results, including the probability level at which you determined significance (usually at 0.05 probability).

It is not necessary (or even desirable) to use the words "hypothesis" or "null hypothesis", since these are usually implicit if you clearly state your purpose and expectations.

• ### In statistical testing, the significance level

A large -value ( 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

• ### State the alternative hypothesis,

Often, the non-significant p-value is assumed to indicate that the treatment has been proven ineffective.

• ### Decide on a level of significance

Significance Tests / Hypothesis Testing

## If , reject H0: x = y at the 0.05 level of significance.

Due to naturally occuring variablilty, two seperate measurements (even of the same phenomenon) will almost always give different results. For example, assume I measure my happiness after a run on Monday, and I measure it again after a run on Wednesday. It would not be surprising if the results are different each time, since there are many factors that impact mood. Therefore, the goal of hypothesis testing is not to see if there is any difference between sets of measurements (there almost always will be), but rather to see if the differences are unlikely to be due to random variation. If so, we can say that our result is statistically significant. The general procedure is as follows:

## It is also called the significance level

The goal of hypothesis testing is to select either the null hypothesis or the alternative hypothesis. However, no matter how careful you are with your experimental design, there is always a non-zero probability that you will come to the incorrect conclusion. There are two possible errors, depending on which hypothesis is actually true:

## When the null hypothesis is rejected, the ..

If we are studying a new treatment, then the alternative hypothesis is that our treatment does in fact change our subjects in a meaningful and measurable way.

## Understanding Hypothesis Tests: Significance Levels …

For example, suppose a pizza place claims their delivery times are 30 minutes or less on average but you think it’s more than that. You conduct a hypothesis test because you believe the null hypothesis, Ho, that the mean delivery time is 30 minutes max, is incorrect. Your alternative hypothesis (Ha) is that the mean time is greater than 30 minutes. You randomly sample some delivery times and run the data through the hypothesis test, and your -value turns out to be 0.001, which is much less than 0.05. In real terms, there is a probability of 0.001 that you will mistakenly reject the pizza place’s claim that their delivery time is less than or equal to 30 minutes. Since typically we are willing to reject the null hypothesis when this probability is less than 0.05, you conclude that the pizza place is wrong; their delivery times are in fact more than 30 minutes on average, and you want to know what they’re gonna do about it! (Of course, you could be wrong by having sampled an unusually high number of late pizza deliveries just by chance.)

## What do significance levels and P values mean in hypothesis tests

The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic (e.g., reject H0 if Z > 1.645). The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. Each is discussed below.

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