Download Statistics

Statistics &
Evidence-Based Practice
THE PENNSYLVANIA STATE UNIVERSITY
COLLEGE OF NURSING
NURSING 200W
Objectives
Identify the purposes of statistical analyses.
 Describe the process of data analysis.
 Describe probability theory and decision theory
that guide statistical data analysis.
 Describe the process of inferring from a sample
to a population.
 Discuss the distribution of the normal curve.

Objectives





Identify descriptive analyses.
Describe the results obtained from inferential statistical
analyses.
Describe the five types of results obtained from quasiexperimental and experimental study designs.
Compare and contrast statistical significance and
clinical importance of results.
Critically appraise statistical results, findings, limitations,
conclusions, and generalization of findings.
A Statistical
Primer
Statistics in Nursing Practice





Reading or critiquing published research
Examining outcomes of nursing practice by
analyzing data collected in a clinical site
Developing administrative reports with support data
Analyzing research done by nursing staff and other
health professionals at a clinical site
Demonstrating a problem or need and conducting
a study
Critically Appraising Statistics

Identify statistical procedures used

Determine whether statistics used were
appropriate or not

Evaluate researchers interpretation of statistics
Stages in Data Analysis
1.
2.
3.
4.
5.
Prepare data for analysis.
Describe the sample.
Test reliability of measurement methods.
Conduct exploratory analysis.
Conduct confirmatory analysis guided by
hypotheses, questions, or objectives.
6. Conduct posthoc analyses.
Major Statistics in Nursing Studies
Descriptive
Inferential
Descriptive Statistics

Describe and summarize the sample and
variables
 Also
referred to as summary statistics
Inferential Statistics

Infer or address the objectives, questions, and
hypotheses
Descriptive Statistics

If a research study collects numerical data,
data analysis begins with descriptive statistics
 Not
limited to quantitative research!
 May
be the only statistical analysis conducted in a
descriptive study
Types of Descriptive Statistics

Frequency distributions

Measures of central tendency

Measures of dispersion
Two-Tailedness
Ungrouped Frequency Distribution

Data in raw form:
 1:
☺
 2:
☺☺☺☺☺☺☺
 3:
☺☺
 4:
☺☺☺☺
 5:
☺
Grouped Frequency Distribution

Data are grouped into categories:
 Ages
15 to 20: 12
 Ages
20 to 25: 14
 Ages
25 to 30: 19….
Example of a Percentage Distribution

Housing: 41.7%

Textbooks: 8.3%

Clothing: 16.7%

Food: 8.3%

Additional Supplies: 25%
How Frequency Distributions are
Presented in Research Articles
Measures of Central Tendency
Mean
Median
Mode
Normal Curve
Normal Curve

A theoretical frequency distribution of all
possible values in a population

Levels of significance and probability are based
on the logic of the normal curve
Mean

Is the sum of values divided by the number of
values being summed
Median

Is the value in exact center of ungrouped
frequency distribution

Is obtained by rank ordering the values
Mode

Is the numerical value or score that occurs with
greatest frequency

Is expressed graphically
Bimodal Distribution
Measures of Dispersion
Range
Variance
Standard deviation
Standardized scores
Scatterplots
Range

Is obtained by subtracting lowest score from
highest score
Difference Scores

Are obtained by subtracting the mean from
each score

Sometimes referred to as a deviation score
because it indicates the extent to which a
score deviates from the mean
Standard Deviation
Is the square root of the variance
 Just as the mean is the “average” value, the
standard deviation is the “average” difference
score

Standardized Scores

Raw scores that cannot be compared and are
transformed into standardized scores

Common standardized score is a Z-score

Provides a way to compare scores in a similar
process
Scatterplots
Probability
Theory
Probability Theory

Used to explain:
 Extent
of a relationship
 Probability
of an event occurring
 Probability
that an event can be accurately
predicted
Probability

If probability is 0.23, then p = 0.23

There is a 23% probability that a particular event
will occur
Inferences

A conclusion or judgment based on evidence

Judgments are made based on statistical results
Decision Theory
Decision Theory

Assumes that all the groups in a study used to
test a hypothesis are components of the same
population relative to the variables under study

It is up to the researcher to provide evidence
that there really is a difference

To test the assumption of no difference, a cutoff
point is selected before analysis
Statistics
JUDGING THE
APPROPRIATENESS OF THE
STATISTICAL TESTS USED
Critical Appraisal

Factors that must be considered include:
 Study
purpose
 Hypotheses,
questions, or objectives
 Design
 Level
of measurement
Critical Appraisal

You must judge whether the procedure was
performed appropriately and the results were
interpreted correctly.
Information Needed
1.
Decide whether the research question focuses
on differences or associations/relationships.
Information Needed
1.
Decide whether the research question focuses
on differences or associations/relationships.
2.
Determine level of measurement.
Data Types

Nominal

Ordinal

Interval/Ratio
Information Needed
1.
Decide whether the research question focuses
on differences or associations/relationships.
2.
Determine level of measurement.
3.
Select the study design that most closely fits
the one you are looking at.
Information Needed
Decide whether the research question focuses
on differences or associations/relationships.
2. Determine level of measurement.
3. Select the study design that most closely fits
the one you are looking at.
4. Determine whether the study samples are
independent, dependent, or mixed.
1.
Statistical Tests
SOME COMMON STATISTICAL
TESTS IN RESEARCH
Chi-Square

Nominal or ordinal data

Tests for differences between expected
frequencies if groups are alike and frequencies
actually observed in the data
Chi-Square
Regular
Exercise
Male
35
No Regular
Exercise
15
Total
50
Female
10
40
50
Total
45
55
100
Chi-Square

Indicate that there is a significant difference
between some of the cells in the table

The difference may be between only two of the
cells, or there may be differences among all of
the cells.

Chi-square results will not tell you which cells are
different.
Example
Pearson Product-Moment Correlation

Tests for the presence of a relationship between
two variables

Works with all types of data
Correlation

Performed on data collected from a single
sample

Measures of the two variables to be examined
must be available for each subject in the data
set.
Correlation

Results
 Nature
of the relationship (positive or negative)
 Magnitude
 Testing
of the relationship (–1 to +1)
the significance of a correlation coefficient
Response Question

Which are the following are significant?
 A.
r = 0.56 (p = 0.03)
 B.
r = –0.13 (p = 0.2)
 C.
r = 0.65 (p < 0.002)
Example
Factor Analysis
Examines relationships among large numbers of
variables
 Disentangles those relationships to identify
clusters of variables most closely linked
 Sorts variables according to how closely related
they are to the other variables
 Closely related variables grouped into a factor

Factor Analysis

Several factors may be identified within a data set

The researcher must explain why the analysis
grouped the variables in a specific way

Statistical results indicate the amount of variance in
the data set that can be explained by each factor
and the amount of variance in each factor that
can be explained by a particular variable
Regression Analysis

Used when one wishes to predict the value of
one variable based on the value of one or
more other variables
Regression Analysis

The outcome of analysis is the regression
coefficient R

When R is squared, it indicates the amount of
variance in the data that is explained by the
equation
 R2
= 0.63
Example
T-test

Requires interval level measures

Tests for significant differences between two
samples

Most commonly used test of differences
Example
Analysis of Variance

ANOVA

Tests for differences between means

Allows for comparison of groups
Example
Results
A SUMMARY OF THE TYPES OF
RESULTS YOU WILL FIND IN
EXPERIMENTAL AND
QUASI-EXPERIMENTAL
RESEARCH STUDIES
Types of Results
Significant and predicted
Nonsignificant
Significant and not predicted
Mixed
Unexpected
Significant and Predicted

Support logical associations between variables

As expected by the researcher
Nonsignificant

Negative or inconclusive results

No significant differences or relationships
Significant and Unpredicted

Opposite of what was expected

Indicate potential flawed logic of researcher
Mixed

Most common outcome of studies

One variable may uphold predicted
characteristics, whereas another does not

Or two dependent measures of the same
variable may show opposite results.
Unexpected

Relationships between variables that were not
hypothesized and not predicted from the
framework being used
Findings,
Conclusions, &
Implications
Findings

Results of a research study that have been
translated and interpreted
Statistically Significant Findings

Significant p-values
Clinically Significant Findings

Practical application of findings

Somewhat based on opinion
Conclusions

A synthesis of findings

Researchers should not go beyond what the
findings state or interpret too much!
Implications

The meaning for nursing practice, research,
and/or education

Specific suggestions for implementing the
findings
Critical
Appraisal
QUESTIONS TO ASK
Critical Appraisal
1.
2.
3.
4.
5.
What statistics were used to described the
characteristics of the sample?
Are the data analysis procedures clearly described?
Did statistics address the purpose of the study?
Did the statistics address the objectives, questions or
hypotheses of the study?
Were the statistics appropriate for the level of
measurement of each variable?
Critical Appraisal
1.
2.
3.
4.
5.
What statistics were used to described the
characteristics of the sample?
Are the data analysis procedures clearly described?
Did statistics address the purpose of the study?
Did the statistics address the objectives, questions or
hypotheses of the study?
Were the statistics appropriate for the level of
measurement of each variable?
Critical Appraisal
1.
2.
3.
4.
5.
What statistics were used to described the
characteristics of the sample?
Are the data analysis procedures clearly described?
Did statistics address the purpose of the study?
Did the statistics address the objectives, questions or
hypotheses of the study?
Were the statistics appropriate for the level of
measurement of each variable?
Critical Appraisal
1.
2.
3.
4.
5.
What statistics were used to described the
characteristics of the sample?
Are the data analysis procedures clearly described?
Did statistics address the purpose of the study?
Did the statistics address the objectives, questions or
hypotheses of the study?
Were the statistics appropriate for the level of
measurement of each variable?
Critical Appraisal
1.
2.
3.
4.
5.
What statistics were used to described the
characteristics of the sample?
Are the data analysis procedures clearly described?
Did statistics address the purpose of the study?
Did the statistics address the objectives, questions or
hypotheses of the study?
Were the statistics appropriate for the level of
measurement of each variable?
Critical Appraisal
1.
2.
3.
4.
5.
What statistics were used to described the
characteristics of the sample?
Are the data analysis procedures clearly described?
Did statistics address the purpose of the study?
Did the statistics address the objectives, questions or
hypotheses of the study?
Were the statistics appropriate for the level of
measurement of each variable?
The End!
QUESTION?
COMMENTS?