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FOUNDATIONS OF
NURSING RESEARCH
Sixth Edition
CHAPTER
15
Inferential Statistics
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objectives
1. Recall The Two Purposes Of Inferential
Statistics
2. Discuss The Sampling Distribution Of
The Mean
3. Define Terms Used In Inferential
Statistics
4. Distinguish Between A One-tailed And A
Two-Tailed Test
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objectives
5. Describe Type I And Type II Errors
6. Differentiate Between Parametric And
Nonparametric Statistical Tests
7. Discuss The Power Of A Statistical Test
8. List Criteria For Selecting A Statistical
Test
9. Identify Statistical Tests Commonly
Reported In Nursing Studies
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objectives
10. Critique The Inferential Statistics Section
Of Research Reports
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objective One
Recall The Two Purposes Of Inferential
Statistics
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Broad Purposes of Inferential
Statistics
• Estimating population parameters from
sample data (after data collection)
• Testing hypotheses (before data
collection)
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objective Two
Discuss The Sampling Distribution Of The
Mean
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Sampling Distribution of the Mean
• Approximates the normal curve
• Larger samples are more adequate.
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Standard Error of the Mean
• Standard deviation of the sampling
distribution of the mean
• Symbolized xˆ
– Smaller xˆ value means it is more likely the
sample is an accurate reflection of the
population mean.
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objective Three
Define Terms Used In Inferential Statistics
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Inferential Statistics
• Central limit theorem
– Tendency of sample values to be normally
distributed around population value
• Sampling distribution
– Theoretical frequency distribution based on
infinite samples
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Confidence Interval
• CI
• Range thought to contain the population
value
• Includes lower and upper limit, with
specified degree of probability
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Hypotheses
• Directional research hypothesis
– Predicts results of study
• Null hypothesis
– No difference exists between populations or
no correlation exists between variables in the
population.
– (H0)
– Subjected to statistical analysis
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Hypotheses (cont’d)
• Null
– Rejected or retained
• Research
– Supported or not supported
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Level of Significance
• Probability level of rejecting a null
hypothesis when it is true
• Symbolized by letter p and Greek letter
alpha (α)
• The most common probability level in
nursing research is p = .05.
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Inferential Statistics
• Critical value
– Value in a theoretical distribution at which all
obtained sample values that are equal to or
beyond that point in the distribution are said to
be statistically significant
• Critical region or region of rejection—all
values beyond the critical value
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Degrees of Freedom
• Symbolized (df)
• Concerns the number of values that are
free to vary
• Interpretation of statistical tests dependent
on the degrees of freedom
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objective Four
Distinguish Between A One-tailed And A
Two-Tailed Test
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
One-Tailed Versus
Two-Tailed Tests
• One-tailed tests
– Appropriate for directional research
hypotheses
– Degree of difference or type of correlation
predicted
– Easier to reject the null hypothesis
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
One-Tailed Versus
Two-Tailed Tests
• Two-tailed tests
– Appropriate for nondirectional research
hypotheses
– Difference or correlation predicted, but the
degree is not indicated
– More difficult to reject the null hypothesis
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objective Five
Describe Type I And Type II Errors
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Errors
• Type I error
– Null hypothesis is actually true, but is
rejected.
• Type II error
– Null hypothesis is actually false and it is
retained.
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objective Six
Differentiate Between Parametric And
Nonparametric Statistical Tests
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Parametric Tests
• Population parameters
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Parametric Tests
• Make assumptions about the population
from which a sample was drawn
– The level of measurement of the data is
interval or ratio.
– Data taken from populations that are normally
distributed on the variable that is being
measured
– Data taken from populations that have equal
variances on the variable that is being
measured
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Nonparametric Tests
• Distribution-free statistics
– Makes no assumptions about the distribution
of the population
• May be used with nominal and ordinal
data
• Sample sizes may be small.
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objective Seven
Discuss The Power Of A Statistical Test
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Power of a Statistical Test
• Ability of the test to reject a null hypothesis
when it is false
• Dependent on the sample size and the
level of significance that is chosen
• The larger the sample size chosen, the
more power the statistical test has.
• The higher the level of significance
selected, the more power the statistical
test has.
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Power of a Statistical Test (cont’d)
• A one-tailed test is more powerful than a
two-tailed test.
• If the assumptions of parametric tests are
met they are more powerful than
nonparametric tests.
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objective Eight
List Criteria For Selecting A Statistical Test
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
The T Test
• Parametric test assumptions
• Compares the difference between mean
values of some variable in two groups
• Particularly useful for small sample sizes
• Interval or ratio data required
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Analysis of Variance (ANOVA)
• Parametric statistical test
• Compares differences among more than
two means at one time
• Based on assumptions that data
– Are interval or ratio level
– Have been selected from populations that are
normally distributed
– Have equal variances on the variable that is
being measured
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Chi-Square (χ2)
• Nonparametric inferential technique
• Used for comparing nominal sets of data
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objective Nine
Identify Statistical Tests Commonly
Reported In Nursing Studies
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
t Tests
• Parametric test that examines differences
between the means of two groups of
values
• Independent t test or unrelated samples t
test
– Test for samples with no association or
connection
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
t Tests (cont’d)
• Dependent t test or paired t test
– Used when scores or values are associated
or have some connection
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Analysis of Variance (ANOVA)
• Examines the two types of variances in
data obtained
– “Mean square between” (MSB) groups
explore variation between the means of the
groups.
– “Mean square within” (MSW) groups examine
variation of individual scores within each of
the groups.
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Chi-Square (χ2)
• Observed frequencies are compared to
expected frequencies.
• Null hypothesis is rejected if the observed
frequencies are quite different from the
expected frequencies at a specified level
of significance.
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Advanced Statistical Tests
•
•
•
•
Multiple regression
Analysis of covariance (ANCOVA)
Canonical correlation
Multivariate analysis of variance
(MANOVA)
• Meta-analysis
• Metasynthesis
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Learning Objective Ten
Critique The Inferential Statistics Section
Of Research Reports
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Critique of Research Reports
• Minimal understanding of inferential
statistics is sufficient.
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Critique of Research Reports
(cont’d)
• Reader should
– Search the report for any inferential statistics
that were used in data analysis
– Determine if there is enough information to
make a decision about the appropriateness of
each test that was used
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Critique of Research Reports
(cont’d)
• Reader should
– Be provided with the value of the statistical
test that was obtained, the degrees of
freedom, and the significance level that was
reached when each hypothesis was tested
– Be able to determine if each of the
researcher’s hypotheses was supported or
not
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.
Critique of Research Reports
(cont’d)
• Every research report should clearly
present the results of hypothesis testing in
both the text of the report and in the
tables.
Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Copyright ©2012 by Pearson Education, Inc.
All rights reserved.