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


Inferential Statistics 


Techniques that allow us to study samples and
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


Uses for Inferential Statistics
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Statistics for determining differences between
experimental and control groups in experimental
research
Statistics used in descriptive research when
comparisons are made between different groups
These statistics enable the researcher to
evaluate the effects of an independent variable
on a dependent variable

Sampling Error


Differences between a sample statistic and a
population parameter because the sample is not
perfectly representative of the population


Hypothesis Testing


The purpose of the statistical test is to evaluate
the null hypothesis (H0) at a specified level of
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


State the hypothesis (H0)



Select the probability level (alpha)

Determine the value needed for significance
Calculate the test statistic
Accept or reject H0

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Statistical Significance


A statement in the research literature that the
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


Parametric Statistics


Techniques which require basic assumptions about
the data, for example:

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normality of distribution
homogeneity of variance
requirement of interval or ratio data

Most prevalent in HHP
Many statistical techniques are considered robust to
violations of the assumptions, meaning that the
outcome of the statistical test should still be
considered valid


t­tests


Characteristics of t-tests

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requires interval or ratio level scores
used to compare two mean scores
easy to compute
pretty good small sample statistic

Types of t­test


One-Group t-test


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Independent Groups t-test


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t-test between a sample and population mean
compares mean scores on two independent samples

Dependent Groups (Correlated) t-test




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


Hypothesis Testing Errors


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Hypothesis testing decisions are made without
direct knowledge of the true circumstance in the
population. As a result, the researcher’s
decision may or may not be correct
Type I Error
Type II Error


Type I Error


. . . 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


Type II 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


Hypothesis Truth Table
NULL HYPOTHESIS
TRUE

FALSE

ACCEPT

CORRECT 
DECISION

TYPE II
ERROR

REJECT

TYPE I
ERROR

CORRECT 
DECISION

DECISION


ANOVA ­ Analysis of Variance


A commonly used family of statistical tests
that may be considered a logical extension of
the t-test
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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


One­way ANOVA


Extension of independent groups t-test, but may
be used for evaluating differences among 2 or
more groups


Repeated Measures ANOVA


Extension of dependent groups t-test, where
each subject is measured on 2 or more
occasions
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a.k.a “within subjects design”

Test of sphericity assumption is recommended


Random Blocks ANOVA



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This is an extension of the matched pairs t-test
when there are three or more groups or the
same as the matched pairs t-test when there are
two groups
Participants similar in terms of a variable are
placed together in a block and then randomly
assigned to treatment groups


Factorial ANOVA


This is an extension of the one-way ANOVA for
testing the effects of 2 or more independent
variables as well as interaction effects
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Two-way ANOVA (e.g., 3 X 2 ANOVA)
Three-way ANOVA (e.g., 3 X 3 X 2 ANOVA)


Assumptions of Statistical Tests


Parametric tests are based on a variety of

assumptions, such as
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Interval or ratio level scores
Random sampling of participants
Scores are normally distributed
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N = 30 considered minimum by some

Homogeneity of variance
Groups are independent of each other
Others

Researchers should try to satisfy assumptions
underlying the statistical test being used


Improving the Probability of Meeting 
Assumptions



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Utilize a sample that is truly representative of
the population of interest
Utilize large sample sizes
Utilize comparison groups that have about the
same number of participants


Two­Group Comparison Tests



a.k.a. Multiple Comparison or Post Hoc Tests
The various ANOVA tests are often referred
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
order to determine which means (groups) are
actually different


Common Post Hoc Tests



Multiple comparison (post hoc) tests are used to
make specific comparisons following a
significant finding from ANOVA in order to
determine the location of the difference
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Duncan
Tukey
Bonferroni
Scheffe
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Note that post hoc tests are only necessary if there are
more than two levels of the independent variable


Analysis of Covariance



ANOVA
ANOVA design which statistically adjusts the
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


Nonparametric Statistics

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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