Lecture Conducting and reading research in health and human performance (4/e): Chapter 14 - Ted A. Baumgartner, Larry D. Hensley

Chapter 14 - Inferential data analysis. This chapter includes contents: Inferential statistics, uses for inferential statistics, sampling error, hypothesis testing, hypothesis testing procedures, statistical significance, parametric statistics, t-tests, types of t-test,...

Chapter 14 Inferential Data Analysis

then make generalizations about the population Inferential statistics are a very crucial part of

scientific research in that these techniques are used to test hypotheses

experimental and control groups in experimental research

comparisons are made between different groups

evaluate the effects of an independent variable

on a dependent variable

population parameter because the sample is not perfectly representative of the population

significance (e.g., p < 05)

 In other words, do the treatment effects differ

significantly so that these differences would be

attributable to chance occurrence less than 5 times in 100?

Hypothesis Testing Procedures

statistical test was significant indicates that the value of the calculated statistic warranted

rejection of the null hypothesis

 For a difference question, this suggests a real

difference and not one due to sampling error

 requires interval or ratio level scores

 used to compare two mean scores

 easy to compute

 pretty good small sample statistic

 t-test between a sample and population mean

 compares mean scores on two independent samples

 compares two mean scores from a repeated

measures or matched pairs design

 most common situation is for comparison of pretest with posttest scores from the same sample

direct knowledge of the true circumstance in the population As a result, the researcher’s

decision may or may not be correct

 is made when the researcher rejects the null

hypothesis when in fact the null hypothesis is true

 probability of committing Type I error is equal to the significance (alpha) level set by the researcher

 thus, the smaller the alpha level the lower the chance

of committing a Type I error

 occurs when the researcher accepts the null

hypothesis, when in fact it should have been rejected

 probability is equal to beta (B) which is influenced by several factors

 inversely related to alpha level

 increasing sample size will reduce B

 Statistical Power – the probability of rejecting a false null hypothesis

 Power = 1 – beta

 Decreasing probability of making a Type II error increases statistical power

CORRECT  DECISION

CORRECT  DECISION

TYPE II ERROR

TYPE I ERROR

NULL HYPOTHESIS

ACCEPT

REJECT DECISION

that may be considered a logical extension of the t-test

 requires interval or ratio level scores

 used for comparing 2 or more mean scores

 maintains designated alpha level as compared to experimentwise inflation of alpha level with multiple t-tests

 may also test more than 1 independent variable as well as interaction effect

be used for evaluating differences among 2 or more groups

each subject is measured on 2 or more

occasions

 a.k.a “within subjects design”

when there are three or more groups or the

same as the matched pairs t-test when there are two groups

placed together in a block and then randomly

assigned to treatment groups

testing the effects of 2 or more independent

variables as well as interaction effects

 Two-way ANOVA (e.g., 3 X 2 ANOVA)

 Three-way ANOVA (e.g., 3 X 3 X 2 ANOVA)

assumptions, such as

 Interval or ratio level scores

 Random sampling of participants

 Scores are normally distributed

 N = 30 considered minimum by some

 Homogeneity of variance

 Groups are independent of each other

 Others

Assumptions

the population of interest

same number of participants

to as “omnibus” tests because they are used

to determine if the means are different but

they do not specify the location of the

difference

 if the null hypothesis is rejected, meaning that

there is a difference among the mean scores, then the researcher needs to perform additional tests in

make specific comparisons following a

significant finding from ANOVA in order to

determine the location of the difference

difference among group means to allow for the fact that the groups differ on some other

variable

 frequently used to adjust for inequality of groups at the start of a research study

 Considered assumption free statistics

 Appropriate for nominal and ordinal data or in

situations where very small sample sizes (n < 10) would probably not yield a normal distribution of scores

 Less statistical power than parametric statistics

data which are common with survey research

 The statistic is used when the researcher is

interested in the number of responses, objects, or

people that fall in two or more categories

chi-square

data (observed scores) fits an expected

distribution

 i.e are the observed frequencies and expected

frequencies for a questionnaire item in agreement with each other?

chi-square

(association) between two nominally scaled

variables

patterns of frequencies to see if they are

independent from each other

multiple dependent variables

dependent variable and 2 or more predictor variables

from another

 Y’ = b1 X 1 + b2 X 2 + c

accuracy of the prediction

correctly reject a false null hypothesis

 it is effectively the probability of finding

significance, that the experimental treatment actually does have an effect

 a researcher would like to have a high level of power

 rejecting a true null hypothesis

 this is your significance level

 failing to reject a false null hypothesis

01) will reduce the power of a statistical test

This makes it harder to reject the null hypothesis

greater the power This is because the standard error of the mean decreases as the sample size increases

one-tailed test than a two-tailed test because the critical region is larger

effect, its meaningfulness

differences and statistical power will be high

difficult to detect differences and power will be low

estimate the magnitude of differences between groups as well as to report the significance of the effects

effect, or meaningfulness of the findings, is the computation of “effect size” (ES)

ES =  M1 ­ M2

SD

advised to provide post hoc estimates of ES for any significant findings as a way to evaluate the meaningfulness

certain effect (ES) given a specific alpha and power

 may require an estimation of ES from previous published studies or from a pilot study