Transcript Chatburn_CH11_PP statistics for nominal

Handbook for Health Care Research, Second Edition
Chapter 11
CHAPTER 11
Statistical Methods for Nominal Measures
© 2010 Jones and Bartlett Publishers, LLC
Handbook for Health Care Research, Second Edition
Chapter 11
Describing the Data
• Contingency table - used to display counts or
frequencies of two or more nominal variables.
• Proportion- the number of objects of a particular type
divided by the total number of objects in the group
• Percentage- proportion multiplied by 100%
• Ratio- number of objects in a group with a particular
characteristic of interest divided by the number of
objects in the same group without the characteristic
• Odds- A ratio of the probabilities of the two possible
states of a binary event.
• Rate-number of objects occurring per unit of time
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Handbook for Health Care Research, Second Edition
Chapter 11
Characteristics of a Diagnostic Test
• One of the most common sources of nominal data is
diagnostic testing
• True- and False-Positive Rates (sensitivity)probability that a test will be positive when the
condition of interest is present
• True- and False-Negative Rates (specificity)probability that the test will be negative when the
condition of interest is absent
• Sensitivity is the ability of a test to correctly identify
patients with the condition of interest
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Handbook for Health Care Research, Second Edition
Chapter 11
Characteristics of a Diagnostic Test
• Specificity is the ability of a test to correctly identify
patients who do not have the condition of interest
• Positive predictive value of a test is the probability
that the condition of interest is present when the
test is positive
• Negative predictive value of a test (or predictive
value of a negative test) is the probability that the
condition of interest is absent when the test is
negative
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Handbook for Health Care Research, Second Edition
Chapter 11
Characteristics of a Diagnostic Test
• Diagnostic Accuracy- proportion of correct results
out of all results
• Likelihood ratio-combines sensitivity and
specificity into a single number expressing the
odds that the test result occurs in patients with
the condition versus those without the condition:
likelihood ratio = sensitivity/false positive rate
• Receiver Operating Characteristic (ROC) Curvehelps compare two diagnostic tests to see which
would be most useful
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Chapter 11
ROC
Receiver operating characteristic curves for two weaning tests, the RSBI and
the CROP index.
0.00.20.40.60.81.0
False Positive Rate
The CROP is a better test because there is more area under its curve compared with the RSBI curve.
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Handbook for Health Care Research, Second Edition
Chapter 11
Characteristics of a Diagnostic Test
• Intrarater reliability index-person measures the
same variable twice and the measurements are
compared
• Inter-rater reliability index- two or more people
measure the same variable and their measurements are compared
• Kappa- allows evaluation of the inter-rater
reliability: =observed agreement-�chance agreement
K
1-chance agreement
• Phi -is an index of agreement independent of
chance: Φ=
ad-bc
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Handbook for Health Care Research, Second Edition
Chapter 11
Comparing a Single Sample with a Population
• Binomial Test- the plotted probability of each
outcome from an experiment
Binomial distribution showing the probability of getting various numbers of heads in 10 coin tosses.
X, Number of Heads
This assumes the probability of getting heads on a single toss is 0.50.
• Z test: z= p-po
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Handbook for Health Care Research, Second Edition
Chapter 11
Comparing Two Samples, Unmatched Data
• Unpaired data-data from two independent
groups
• Fisher Exact Test-used for 2 × 2 contingency
tables (which have exactly two rows and two
columns)
– Null Hypothesis: There is no significant difference
between the proportion of patients that lived (or
died) in ICU A compared with ICU B.
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Handbook for Health Care Research, Second Edition
Chapter 11
Comparing Two or More Samples, Matched
Data
• Paired data-patients act as their own controls
• McNemar test- is an analysis of contingency
tables that have repeated observations of the
same individuals. Conditions for use:
• determining whether or not individuals responded to
treatment
• comparing results of two different treatments on the same
people
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Handbook for Health Care Research, Second Edition
Chapter 11
Comparing Three or More Samples, Unmatched
Data
• Chi-squared test- can be used for analyzing
contingency tables that are larger than 2 × 2.
-Suppose we wanted to test the effectiveness of three
different drugs
-Null Hypothesis-The proportions are all equal
Contingency Table for a Chi-Squared Test
Outcome
Effective
Not effective
Drug A
Drug B
Drug C
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Report from Statistics Program
Power of performed test with alpha = 0.05: 0.671.
The power of the performed test (0.671) is below the desired power of 0.800.
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