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# Making Sense of Statistics

## Fred Pyrczak, Deborah M. Oh

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eBook - ePub

# Making Sense of Statistics

## Fred Pyrczak, Deborah M. Oh

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Making Sense of Statistics is the ideal introduction to the concepts of descriptive and inferential statistics for students undertaking their first research project. It presents each statistical concept in a series of short steps, then uses worked examples and exercises to enable students to apply their own learning.

It focuses on presenting the why as well as the how of statistical concepts, rather than computations and formulae, so is suitable for students from all disciplines regardless of mathematical background. Only statistical techniques that are almost universally included in introductory statistics courses, and widely reported in journals, have been included. Once students understand and feel comfortable with the statistics that meet these criteria, they should find it easy to master additional statistical concepts.

New to the Seventh Edition

Retaining the key features and organization that have made this book an indispensable text for teaching and learning the basic concepts of statistical analysis, this new edition features:

• discussion of the use of observation in quantitative and qualitative research

• the inclusion of introductions to the book, and each Part.

• section objectives listed at the beginning of each section to guide the reader.

• new material on key topics such as z-scores, probability, Central Limit Theorem, Standard Deviation and simple and multiple regression

• Expanded discussion on t test with separate sections for independent and dependent samples t tests, as well as one-sample t test

• progressive analysis of bivariate vs multivariate statistics (starts with the basic concepts and moves to more complex analysis as the student progresses)

• updated and extended pedagogical material such as Chapter Objectives, exercises and worked examples to test and enhance student's understanding of the material presented in the chapter

• Bolded key terms, with definitions and Glossary for quick referral

• expanded Appendices include a brief reference list of some common computational formulas and examples.

• a Glossary of key terms has been added at the end of the book, with references to sections in parenthesis.

• New online instructor resources for classroom use consisting of test bank questions and Powerpoint slides, plus material on basic math review
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Publisher
Routledge
Year
2018
ISBN
9781351717458
Edition
7

# PART FMeans Comparison

Having introduced hypothesis testing, null hypothesis and how we make decisions about the null hypothesis in the previous part, the remaining two parts, F and G, take a closer look at hypothesis testing in terms of various types of means comparisons. In particular, Part F introduces the t Test, followed by three types of t Tests to compare two means: Independent Samples t Test, Paired Samples t Test, and One Sample t Test, as well as reports of t Test results. Part F discusses One- and Two-Way ANOVAs.

# CHAPTER 21Introduction to the t Test

## Chapter Objectives

The reader will be able to:
â Understand the concept of t test as a test of the difference between two sample means to determine statistical difference
â Understand the factors affecting the probability level that the null hypothesis is true
â Understand the difference among independent samples, paired samples, and one sample t tests
Researchers frequently need to determine the statistical significance of the difference between two sample means. Consider Example 1, which illustrates the need for making such a comparison.
This chapter deals with how to compare two sample means for statistical significance.
About a hundred years ago, a statistician named William Gosset developed the t test for exactly the situation described in Example 1 (i.e., to test the difference between two sample means to determine whether there is a significant difference between them or statistical significance).1 As a test of the null hypothesis, the t test yields a probability that a given null hypothesis is correct. As indicated in Chapter 20, when there is a low probability that it is correctâsay, as low as .05 (5%) or lessâresearchers usually reject the null hypothesis.
The t test tests the difference between two sample means to determine significant difference.
When the t test yields a low probability that a null hypothesis is correct, researchers usually reject the null hypothesis.
The computational procedures for conducting t tests are beyond the scope of this book.2 However, the following material describes what makes the t test work. In other words, what leads the t test to yield a low probability that the null hypothesis is correct for a given pair of means? Here are the three basic factors, which interact with each other in determining the probability level:
Example 1 illustrates Independent Samples t Test

## Example 1

A researcher wanted to determine whether there are differences between men and women voters in their attitudes toward welfare. Separate samples of men and women were drawn at random and administered an attitude scale. Women had a mean of 38.00 (on a scale from 0 to 50, where 50 was the most favorable attitude). Men had a mean of 35.00. The researcher wanted to determine whether there is a significant difference between the two means. What accounts for the 3-point difference between a mean of 38 and a mean of 35? One possible explanation is that the population of women has a more favorable attitude than the population of men and that the two samples correctly reflect this difference between the two populations. Another possible explanation is raised by the null hypothesis, which states that there is no true difference between men and womenâthat the observed difference is due to sampling errors created by random sampling.
The larger the sample, the more likely the null hypothesis will be rejected.
The larger the observed difference between two means, the more likely the null hypothesis will be rejected.
1. The larger the samples, the less likely that the difference between two means was created by sampling errors. This is because larger samples have less sampling error than smaller samples. Other things being equal, when large samples are used, the t test is more likely to yield a probability low enough to allow rejection of the null hypothesis than when small samples are used. Put another way: when there is less sampling error, there is less chance that the null hypothesis (an assertion that sampling error created the difference) is correct. In other words, when there is great precision because large samples are used, researchers can be more confident that their sample results reflect the underlying difference in a population than when small samples are used.
2. The larger the observed difference between the two means, the less likely that the difference was created by sampling errors. Random sampling tends to create many small d...