# Statistical methods and testing of hypothesis pdf

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## Introduction

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### Hypothesis Testing

When you are evaluating a hypothesis, you need to account for both the variability in your sample and how large your sample is. Hypothesis testing is generally used when you are comparing two or more groups. For example , you might implement protocols for performing intubation on pediatric patients in the pre-hospital setting. To evaluate whether these protocols were successful in improving intubation rates, you could measure the intubation rate over time in one group randomly assigned to training in the new protocols, and compare this to the intubation rate over time in another control group that did not receive training in the new protocols.

Based on this information, you'd like to make an assessment of whether any differences you see are meaningful, or if they are likely just due to chance. This is formally done through a process called hypothesis testing.

The null hypothesis H 0 is a statement of no effect, relationship, or difference between two or more groups or factors. In research studies, a researcher is usually interested in disproving the null hypothesis.

The alternative hypothesis H 1 is the statement that there is an effect or difference. This is usually the hypothesis the researcher is interested in proving.

The alternative hypothesis can be one-sided only provides one direction, e. We often use two-sided tests even when our true hypothesis is one-sided because it requires more evidence against the null hypothesis to accept the alternative hypothesis. The significance level denoted by the Greek letter alpha— a is generally set at 0. The smaller the significance level, the greater the burden of proof needed to reject the null hypothesis, or in other words, to support the alternative hypothesis.

In another section we present some basic test statistics to evaluate a hypothesis. Hypothesis testing generally uses a test statistic that compares groups or examines associations between variables. The p-value describes the probability of obtaining a sample statistic as or more extreme by chance alone if your null hypothesis is true. This p-value is determined based on the result of your test statistic.

Your conclusions about the hypothesis are based on your p-value and your significance level. Cautions About P-Values Your sample size directly impacts your p-value. Large sample sizes produce small p-values even when differences between groups are not meaningful. You should always verify the practical relevance of your results. On the other hand, a sample size that is too small can result in a failure to identify a difference when one truly exists.

Plan your sample size ahead of time so that you have enough information from your sample to show a meaningful relationship or difference if one exists. See calculating a sample size for more information. If you do a large number of tests to evaluate a hypothesis called multiple testing , then you need to control for this in your designation of the significance level or calculation of the p-value. For example, if three outcomes measure the effectiveness of a drug or other intervention, you will have to adjust for these three analyses.

Hypothesis testing is not set up so that you can absolutely prove a null hypothesis. Therefore, when you do not find evidence against the null hypothesis, you fail to reject the null hypothesis. When you do find strong enough evidence against the null hypothesis, you reject the null hypothesis. Your conclusions also translate into a statement about your alternative hypothesis.

When presenting the results of a hypothesis test, include the descriptive statistics in your conclusions as well. Report exact p-values rather than a certain range. Search Campus:. Hypothesis Testing When you are evaluating a hypothesis, you need to account for both the variability in your sample and how large your sample is. Introduction Hypothesis testing is generally used when you are comparing two or more groups.

Examples: There is no difference in intubation rates across ages 0 to 5 years. The intervention and control groups have the same survival rate or, the intervention does not improve survival rate. There is no association between injury type and whether or not the patient received an IV in the prehospital setting.

Step 2: Specify the Alternative Hypothesis The alternative hypothesis H 1 is the statement that there is an effect or difference. Examples: The intubation success rate differs with the age of the patient being treated two-sided. There is an association between injury type and whether or not the patient received an IV in the prehospital setting two sided. Step 3: Set the Significance Level a The significance level denoted by the Greek letter alpha— a is generally set at 0. Step 4: Calculate the Test Statistic and Corresponding P-Value In another section we present some basic test statistics to evaluate a hypothesis.

Not likely to happen strictly by chance. Very likely to occur strictly by chance. Example: Average ages were significantly different between the two groups Is this an important difference? Probably not, but the large sample size has resulted in a small p-value. Example: Average ages were not significantly different between the two groups It could be, but because the sample size is small, we can't determine for sure if this is a true difference or just happened due to the natural variability in age within these two groups.

Your result is statistically significant. Your result is not statistically significant. Example: H 0 : There is no difference in survival between the intervention and control group.

H 1 : There is a difference in survival between the intervention and control group. The difference in survival between the intervention and control group was statistically significant. The difference in survival between the intervention and control group was not statistically significant. Link 1. Link 1 Description of link.

## Testing Statistical Hypotheses

The third edition of Testing Statistical Hypotheses updates and expands upon the classic graduate text, emphasizing optimality theory for hypothesis testing and confidence sets. The principal additions include a rigorous treatment of large sample optimality, together with the requisite tools. In addition, an introduction to the theory of resampling methods such as the bootstrap is developed. The sections on multiple testing and goodness of fit testing are expanded. The text is suitable for Ph. Joseph P.

The null hypothesis can be thought of as the opposite of the "guess" the research made in this example the biologist thinks the plant height will be different for the fertilizers. So the null would be that there will be no difference among the groups of plants. We state the Null hypothesis as:. The reason we state the alternative hypothesis this way is that if the Null is rejected, there are many possibilities.

When you are evaluating a hypothesis, you need to account for both the variability in your sample and how large your sample is. Hypothesis testing is generally used when you are comparing two or more groups. For example , you might implement protocols for performing intubation on pediatric patients in the pre-hospital setting. To evaluate whether these protocols were successful in improving intubation rates, you could measure the intubation rate over time in one group randomly assigned to training in the new protocols, and compare this to the intubation rate over time in another control group that did not receive training in the new protocols.

A statistical hypothesis is a hypothesis that is testable on the basis of observed data modelled as the realised values taken by a collection of random variables. The hypothesis being tested is exactly that set of possible probability distributions. A statistical hypothesis test is a method of statistical inference.

### Introduction

Published on November 8, by Rebecca Bevans. Revised on February 15, Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics.

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