## Difference between revisions of "Tests of differences of means and proportions"

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− | If testing for differences beyond a simple "pre-test, post-test" design (for example, for multiple stages of interventions), an appropriate technique would be [[ | + | If testing for differences beyond a simple "pre-test, post-test" design (for example, for multiple stages of interventions), an appropriate technique would be [[Analysis of variance#Repeated measures|Repeated measures ANOVA]]. |

= The difference of proportions test = | = The difference of proportions test = |

## Revision as of 05:51, 20 April 2012

## Contents

# Objectives

# Introduction

One of the primary goals research is to examine the relationships between variables, usually with the goal of determining causal relationships. Often, a first step is to determine whether two groups have statistically different means across some variable of interest. **Note:** just because the sample means for two groups are *literally* different does not mean that they are *statistically* different in the population as a whole. The numerical difference may be an artifact of sampling, which is why a difference of means test is required.

The possible outcomes for difference of means tests is that the means of two groups *are* statistically different or *are not* statistically different.

The **Research (or Alternative) Hypothesis** posits that there **is** a statistically significant difference between the means of the two groups. The **Null Hypothesis** posits that there **is not** a statistically significant difference between the means of the two groups.

If there *is* a statistical difference, then we say that we **reject** the *null hypothesis* and **accept** the *alternative hypothesis.* Conversely, if there *is not* a statistical difference, then we say that we **accept** the *null hypothesis* and **reject** the *alternative hypothesis.*

## Type I and Type II Errors

XXX Consider fearless deletion in favor of the Testing Hypotheses discussion (which should be a separate page).

Two types of error are possible when conducting statistical tests such as difference of means tests.

- A
**Type I Error**is__rejecting__the*null hypothesis*when it is, in fact, true and__accepting__the*alternative hypothesis*when it is, in fact, false. This is also known as a**false positive**; that is, incorrectly finding a difference of means when there really is not one.

- A
**Type II Error**is__accepting__the*null hypothesis*when it is, in fact, false and__rejecting__the*alternative hypothesis*when it is, in fact, true. This is also known as a**false negative**; that is, failing to find a statistical difference in means when there really is one.

**See also:**Testing Hypotheses

# Independent samples (unpaired) t test

## Extension to more than two groups

For comparisons across more than two groups (or categories of the independent variable), you can use either ANOVA or linear regression.

# Paired samples t test

## Beyond two waves

If testing for differences beyond a simple "pre-test, post-test" design (for example, for multiple stages of interventions), an appropriate technique would be Repeated measures ANOVA.

# The difference of proportions test

## Alternatives to the difference of proportions test

Nominal and ordinal differences of proportions can also be tested using the chi-square test.

# Heading

## Sub-heading

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### Example

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# Conclusion

# References

# Discussion questions

# Problems

# Glossary

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