Discussion Question

profileyury12082
Chapter18.pptx

Chapter 18 Inferential Statistics

Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

1

Question #1

Tell whether the following statement is true or false:

Inferential statistics are based on laws of probability.

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

Answer to Question #1

True

Inferential statistics, which are based on laws of probability, allow researchers to make inferences about a population based on data from a sample; they offer a framework for deciding whether the sampling error that results from sampling fluctuations is too high to provide reliable population estimates.

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

Inferential Statistics

A means of drawing conclusions about a population, given data from a sample

Based on laws of probability

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

4

Sampling Distribution of the Mean

A theoretical distribution of means for an infinite number of samples drawn from the same population

Is always normally distributed

Has a mean that equals the population mean

Has a standard deviation (SD) called the standard error of the mean (SEM)

SEM is estimated from a sample SD and the sample size

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

5

Sampling Distribution

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

6

Question #2

Tell whether the following statement is true or false:

Point estimation through statistical procedures enables researchers to make objective decisions about the validity of their hypotheses.

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

Answer to Question #2

False

Hypothesis testing through statistical procedures enables researchers to make objective decisions about the validity of their hypotheses. Point estimation provides a single descriptive value of the population estimate.

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

Estimation of Parameters

Statistical inference—Two forms

Estimation of parameters

Hypothesis testing (more common)

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

9

Confidence Intervals

Used to estimate a single parameter

Two forms of estimation

Point estimation

Calculating a single statistic to estimate the population

Interval estimation

Calculating a range of values within which the parameter has a specified probability of lying

A confidence interval (CI) is constructed around the point estimate.

The upper and lower limits are confidence limits.

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

10

Hypothesis Testing #1

Based on rules of negative inference: Research hypotheses are supported if null hypotheses can be rejected.

Involves statistical decision-making to either

Accept the null hypothesis, or

Reject the null hypothesis

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

11

Hypothesis Testing #2

Researchers compute a test statistic with their data and then determine whether the statistic falls beyond the critical region in the relevant theoretical distribution.

If the value of the test statistic indicates that the null hypothesis is “improbable,” the result is statistically significant.

A nonsignificant result means that any observed difference or relationship could have resulted from chance fluctuations.

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

12

Question #3

Tell whether the following statement is true or false:

Type II error occurs when a null hypothesis is incorrectly rejected (a false positive).

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

Answer to Question #3

False

A Type I error occurs when a null hypothesis is incorrectly rejected (a false positive). A Type II error occurs when a null hypothesis is wrongly accepted (a false negative).

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

Statistical Decisions Are Either Correct or Incorrect

Two types of incorrect decisions

Type I error: a null hypothesis is rejected when it should not be rejected

Risk of a Type I error is controlled by the level of significance (alpha), that is,  = .05 or .01.

Type II error: failure to reject a null hypothesis when it should be rejected

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

15

Hypotheses Testing

Test statistic

Critical region

Statistically significant

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

One-Tailed and Two-Tailed Tests

Two-tailed tests

Hypothesis testing in which both ends of the sampling distribution are used to define the region of improbable values.

One-tailed tests

Critical region of improbable values is entirely in one tail of the distribution—the tail corresponding to the direction of the hypothesis.

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

17

Parametric Statistics

Involve the estimation of a parameter

Require measurements on at least an interval scale

Involve several assumptions (e.g., that variables are normally distributed in the population)

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

18

Nonparametric Statistics (Distribution-Free Statistics)

Do not estimate parameters

Involve variables measured on a nominal or ordinal scale

Have less restrictive assumptions about the shape of the variables’ distribution than parametric tests

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

19

Overview of Hypothesis-Testing Procedures #1

Select an appropriate test statistic.

Establish the level of significance (e.g.,  = .05).

Select a one-tailed or a two-tailed test.

Compute test statistic with actual data.

Calculate degrees of freedom (df) for the test statistic.

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

20

Overview of Hypothesis-Testing Procedures #2

Obtain a tabled value for the statistical test.

Compare the test statistic to the tabled value.

Make decision to accept or reject null hypothesis.

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

21

Groups

Independent groups compare separate groups of people.

Dependent groups compare the same group of people over time or conditions.

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

Commonly Used Bivariate Statistical Tests

t-test

Analysis of variance (ANOVA)

Pearson’s r

Chi-square test

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

23

t-Test

Tests the difference between two means

t-test for independent groups (between subjects)

t-test for dependent groups (within subjects)

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

24

Analysis of Variance (ANOVA)

Tests the difference between three or more means

One-way ANOVA

Multifactor (e.g., two-way) ANOVA

Repeated-measures ANOVA (within subjects)

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

25

Correlation

Pearson’s r, a parametric test

Tests that the relationship between two variables is not zero

Used when measures are on an interval or ratio scale

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

26

Chi-Square Test

Tests the difference in proportions in categories within a contingency table

A nonparametric test

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

27

Power Analysis #1

A method of reducing the risk of Type II errors and estimating their occurrence

With power = .80, the risk of a Type II error () is 20%

Method is frequently used to estimate how large a sample is needed to reliably test hypotheses

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

28

Power Analysis #2

Four components in a power analysis

Significance criterion ()

Sample size (N)

Population effect size—the magnitude of the relationship between research variables (γ)

Power—the probability of obtaining a significant result (1 − β)

Copyright © 2021 Wolters Kluwer Health | Lippincott Williams & Wilkins

29