Download Chapter 9: Quantitative Inquiry

Chapter 9
Quantitative Inquiry
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Chapter Overview
• This chapter is presented based upon classical test theory
(pretest–posttest) rather than from the perspective of
clinical epidemiology (case control, cohort, randomizedcontrolled clinical trial) perspective.
• Quantitative inquiry forms the basis for the scientific
method.
• Through the performance of controlled investigation,
researchers can objectively assess clinical and natural
phenomena and develop new knowledge.
• Differences between the types of measurement data.
• Differences between Type I and Type II errors and their
relevance to data analysis.
• Understand the determinants of reliability.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
The Scientific Method
The scientific method is the primary means by which new
knowledge is acquired. Phenomena are tested in objective,
quantitative, and empirical ways.
Basic Steps of the Scientific Method
1. Observation of a natural phenomenon.
2. Ask a research question.
3. Develop a research hypothesis that predicts the answer to
the question.
4. Design and conduct an experiment to test your hypothesis.
5. Answer the research question based on whether the
experiment confirms or refutes the hypothesis.
6. Confirm your results by replicating the experiment.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
The Scientific Method:
Research Question
• A good research question cannot be based on clinical
observation alone.
• It must be developed by framing the observation within the
existing knowledge base of a specific discipline.
• The hypothesis should be based on both clinical observation
and what is known in the existing literature.
• The outcomes measures are referred to as dependent
variables, whereas the interventions are referred to as
independent variables.
• The results of the experiment should provide a clear answer
to the research question.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
The Scientific Method:
Replication
• A very important step in the scientific method is
the replication of an experiment to confirm the
results found in the initial experiment.
• The replication study is performed by a different
group of researchers than the group that
performed the initial study.
• Replication ensures that the findings can be
generalized to a broader population
• Without confirmation, the results of the original
study may not be confidently generalized into the
routine practice of other clinicians.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Measures of Central Tendency
• Hypothesis testing is typically performed to assess:
– Whether there is a difference in the scores of a
dependent variable between two or more groups.
– Whether there is a difference in the scores of a
dependent variable over time within the same group of
studies.
• This requires the comparison of representative scores across
groups or testing sessions.
• This is most often performed by comparing measures of
central tendency.
• The most common measure of central tendency used in
health care research is the mean. The median and the
mode are used less often.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Mean, Median, and Mode
• The mean (x̄) represents the arithmetic average of scores
across all sampled subjects.
• This is expressed mathematically as:
xi is the score of each individual subject
n is the total number of subjects
• The median (Md) represents the individual score that
separates the higher half of scores from the lower half of
scores.
• The median score is determined with the formula:
Md = n+1
2
• The mode (Mo) is the score that occurs most frequently out
of all included observations.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Estimates of Dispersion
• An important characteristic of a data set is the
dispersion, or variability, of observed values.
• The range of scores represents the arithmetic difference
between the highest and lowest scores in a data set.
• A limitation of the range is that outliers can skew this
estimate of dispersion.
• Outliers are individual scores at the low and/or high
extremes of the data set.
• A more robust estimate of dispersion is the standard
deviation.
• The standard deviation estimates how much the scores
of individual subjects tend to deviate from the mean.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Standard Deviation
• The formula to calculate standard deviation is
• The numerator of this equation is termed the “sum
of squares” and is used in a wide variety of statistical
analyses.
• Normal distribution: 68% of data points for the
entire data set will lie within (+) 1 standard
deviation of the mean. Likewise, 95% of data points
will lie within (+) 2 standard deviations of the mean,
and 99% of data points will lie within (+) 3 standard
deviations of the mean.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Tests of Inferential Statistics
• Tests of inferential statistics (t-tests, analysis of
variance) utilize the concepts of the variability in
data sets to compare means.
Application:
• Variance is defined as the standard deviation
squared (s2).
• A comparison of two means with these statistical
tests is based on the probability of overlap in the
normal distribution of the two data sets being
compared.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Hypothesis Testing
• Statistical analysis is performed to test the hypothesis.
• The research hypothesis HA (also called the alternative
hypothesis): The investigator has an idea that the
independent variable is going to cause a change in the
dependent variable.
• The null hypothesis HO : The independent variable will not
cause a change in the dependent variable.
• Inferential statistical analysis is a test of the null hypothesis.
• Most statistical analyses are performed to determine if there is
not a difference between two measures.
• Hypothesis testing will yield a yes or no answer as to whether
there is a statistically significant difference between measures
in the study sample.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Contingency Table of Hypothesis
Testing Results
If the results of the tested sample do not match what is true in the
population at large, either a Type I or a Type II error has occurred.
Population Result
Sample Result
HA True
(difference between
measures does exist)
HO True
(difference between
measures does not
exist)
HA True
(difference
between measures
does exist)
HO True
(difference between
measures does not
exist)
Correct
Incorrect
(Type I error)
Incorrect
(Type II error)
Correct
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Sampling
• Experiments are performed on a representative sample of
subjects rather than on the entire population of
individuals.
• The sampling frame represents the group of individuals
who have a real chance of being selected for the sample.
• Investigators need to establish specific inclusion and
exclusion criteria for the subjects in studies.
• Without such criteria, there are limits to the generalizability
of the study results. This concept is referred to as “external
validity.”
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Type I and Type II Errors
• Type II error: Occurs when a difference exists in
the population at large but the study results reveal
no difference in the study sample.
• The most common reason for a Type II error is
inadequate sample size. This is also referred to as
having low “statistical power” for the study.
• Estimation of an appropriate sample size for a study
is done by performing an a priori power analysis.
• Type I Error: Occurs when a difference is found in
the study sample but there is in fact no difference
present in the population at large.
• Investigators are willing to accept a 5% risk of
incurring a Type I error (α = .05) and a 20% risk of
incurring a Type II error (1-β = .80). These values
are a bit arbitrary.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Types of Sampling
• Probability sampling involves the use of randomization to select
individual potential subjects from the sampling frame.
• Nonprobability sampling is a method of sampling in which selected
subjects are not drawn randomly from the sampling frame.
• Random sampling is method of sampling in which every potential
individual in the sampling frame has an equal chance of being selected
for study participation (uses computerized random number generators).
• Systematic random sampling is a method of sampling in which every
xth individual out of the entire list of potential subjects is selected for
participation.
• Stratified random sampling provides a method for dividing the
individual members of the sampling frame into groups, or strata, based
on specific subject characteristics.
• Cluster random sampling is a process of dividing the sampling frame
into groups based on some common characteristics and then randomly
selecting specific clusters to participate in the study out of all possible
clusters.
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Convenience vs. Purposive Sampling
• Random sampling is considered superior to
nonrandom sampling because the results of the
study are more likely to be representative of the
population at large.
• Convenience sampling is a type of sampling in
which potential subjects are selected based on the
ease of subject recruitment.
• Purposive sampling is a type of nonrandom
sampling. It entails potential subjects from a
predetermined group to be sought out and
sampled.
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Basic Experimental Research Methods
Pre-Experimental Designs
One shot posttest design
• Consists of a single measurement completed after a group of subjects has already
received the treatment of interest (case series). Lacks pretest and a control group.
Threats to internal validity.
One group pretest–posttest design
• Adds a pretest to the previous design.
Static group posttest design
• Has two groups, one that receives the intervention and one that does not. Both
groups are assessed only once. There is no pretest for either group.
Nonrandomized pretest–posttest design
• Compares two groups before and after intervention. The two groups receive
different interventions. The assignment of subjects to groups is based on
convenience rather than on randomization.
Time series design
• Compares a single group at multiple, but regular, time intervals before and after
intervention.
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Basic Experimental Research Methods
True Experimental Designs
• Randomized assignment of subjects to groups. This
improves the internal validity of the study design.
Randomized posttest design
• Subjects are randomly assigned to treatment groups.
• There is no pretest taken before the administration of
treatment.
Randomized pretest–posttest design
• Subjects are pretested, and then they are randomized to
assigned groups. They are posttested after they receive
their assigned intervention.
• This prevents any potential bias on the part of the research
team member.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins
Chapter Summary and Key Points
• Clinician observations can be translated into hypotheses
that can be evaluated via experimental study by following
the steps of the scientific method.
• The concepts of central tendency are the foundation for
inferential statistics.
• Hypothesis testing allows for the research hypothesis to be
confirmed or refuted.
• Sampling of potential study volunteers is important to the
generalizability of the study results.
• Experimental design of a study forms the infrastructure for
the project.
• Quantitative inquiry is central to advancing the health
sciences.
Copyright © 2011 Wolters Kluwer Health | Lippincott Williams & Wilkins