PPT Chapter 04

Airgas templateStatistical Methods for Health Care Research
Chapter 4
Copyright © 2013 Wolters Kluwer Health | Lippincott Williams & Wilkins
Answers two types of questions
Parameter Estimation
Hypothesis Testing
Statistical Inference
Point Estimate
Confidence Interval
A range into which the estimated value is estimated to fall within
Parameter Testing
Example:
What is the prevalence of sexually transmitted diseases (STDs) in young women in the United States?
Point estimate: 24.1% of women age 14 to 19 have at least one STD.
Confidence interval: between 18.4% and 30.9% of women age 14 to 19 have at least one STD.
Parameter Testing (cont.)
Hypotheses articulate the expected relationships between variables.
Stem directly from the research questions
Grounded in theory or conceptual models
Tested using data and inferential statistics
Testable hypotheses define
The variables on which the groups are being compared
The expected relationship
Types of relationships
Causal
The independent variable is said to cause changes in the dependent variable.
Hypotheses (cont.)
Null hypothesis (H0) states that there will be no relationship between the two variables.
Alternative hypothesis (Ha) states that there will be a relationship between the two variables.
Directional
Nondirectional
Null hypothesis (H0)
There will be no relationship between height and weight in adolescent boys.
Alternative hypothesis (Ha)
Directional: Height will be positively related to weight in adolescent boys (e.g., taller boys will weigh more).
Nondirectional: There will be a relationship between height and weight in adolescent boys.
Types of Hypotheses: Example
Hypotheses are tested with inferential statistics.
The null hypothesis (H0) is always the hypothesis that is being tested.
Rejecting the null: This means that the researchers believe the variables are statistically associated with one another.
Accepting the null hypothesis (failing to reject the null): This means that the researchers do not believe that the variables are statistically associated with one another.
Hypothesis Testing
The decision to reject or accept the null hypothesis is based upon two things:
The p-value (probability value): This is the probability that the results of the statistical test were obtained by chance alone. This is computed from the data and is not known until the statistical test is completed.
The α-level (alpha-level): This is p-value that is defined by the researcher as “statistically significant.” This is defined before any statistical tests are conducted. Common α-levels are “0.10”, “0.05”, and “0.01”.
Hypothesis Testing (cont.)
Which type of hypothesis is the following statement?
People who are immunized against the flu will be less likely to contract the flu than those who are not immunized.
Null hypothesis
Directional hypothesis
Nondirectional hypothesis
B. Directional hypothesis
Rationale: This hypothesis states that a relationship between immunization and contracting the flu is expected and also states the direction of that hypothesis.
Answer
When we test hypotheses with statistics, one of the four things can happen:
Outcome of Testing Hypotheses
Type I Error
Reject the null when it is true
In other words, we say that there is a relationship between the variables when one really does not exist.
Type II Error
Accept the null when it is false
In other words, we say that there is no relationship between the variables when one really does exist.
In any given study, we will never know if we have committed either one of these errors.
Types of Errors
Type I Error: reject the null when it is true
The probability of making a type I error is defined by the α-level of the study.
Given an α-level of 0.10, we will make a type I error 10% of the time.
Type II Error: not rejecting the null when it is false.
This is referred to as “β” (beta).
Errors
The power of a test is its ability to detect statistically significant differences.
Mathematically, this is defined as 1-β.
Power is a function of the α-level, the sample size, and the population effect size.
There are numerous statistical packages that will compute the power of a study.
Power of a Test
If there is, in fact, a relationship between immunization and contracting the flu and the researcher concludes there is no relationship, what type of error have they committed?
Insufficient power in the study
Logical error
Type I
Type II
D. Type II Error
Rationale: A type II error is when we say that there is no relationship between the variables, but one really does exist.
Answer
State the hypothesis (in both the null and the alternative form).
Define the α-level and choose the appropriate statistic.
Make sure the data meet the assumptions of the statistic that you are using.
Compute the parameters (e.g., means, percents) that are being compared.
Compute the test statistic and obtain the p-value of the statistic.
Compare the p-value to the α-level and state a conclusion.
Six-Steps for Hypothesis Testing
We will use the six-step process to conduct a one-sample z-test. A one-sample z-test is used to compare a sample mean to a population mean.
In this example, we will ask the question: do women who attend a local church health fair have a significantly different mean BMI than women in the general U.S. population?
Our data come from a sample of women attending a health fair at a local church.
Example of Six-Step Process
Step 1: State the hypothesis
H0: The mean BMI of the women attending the health fair will not be significantly different than that of the U.S. population.
Ha (nondirectional): The mean BMI of the women attending the church health fair will be significantly different than that of the U.S. population.
State the Hypothesis
Step 2: Define the α-level
The α-level for this study is 0.05.
This means that if the value of the computed statistic occurs by chance 5% of the time or less, the null hypothesis will be rejected.
We will use a one-sample z-test.
This is the appropriate test to use when comparing a sample mean to a population mean.
Define the α-Level and Choose the Appropriate Statistic
*
This following figure shows the “rejection region” for the one-sample z-test with a nondirectional hypothesis. This is also referred to as a “two-tailed” test.
Those test results that fall in the bottom or top 2.5% (e.g., the outer 5%) are considered statistically significant. This is our “rejection region”; if the value of the computed one-sample z-test falls in this region, we reject the null hypothesis.
Note: The current standard is to use two-tailed tests even with directional hypotheses, although it is more technically correct to use a one-tailed test with these.
The Rejection Region
The Rejection Region (cont.)
Step 3: Make sure the data meet the assumptions of the statistic that you are using
The one-sample z-test assumes that
The data are normally distributed (the BMI data meet this assumption).
The population mean and standard deviation are known (the population mean BMI is 27.9 [sd=5.4]).
The assumptions are met so we can proceed with the test.
Assumptions
Step 4: Compute the Parameters (e.g., means, percents) that are being compared
The mean BMI of the 48 women in the sample was 29.2, with a standard deviation of 3.4.
Compute the Parameters
Step 5: Compute the test statistic, and obtain the p-value of the statistic
The equation for the one-sample z-test is
The computed statistic is
Compute the Test Statistic
Step 6: Compare the p-value to the α-level and state a conclusion
The computed statistic is 1.67. Since it does not fall into the “rejection region” (it would need to be either less than −1.96 or greater than +1.96), the associated p-value is greater than 0.05.
We conclude that there is no statistically significant difference in the mean BMI between the women in our sample and the U.S. population mean.
State a Conclusion
True or False
If the difference between two groups is large, we can say that it is statistically significant even if our computed p-value is not less than the α-level that we set for the study.
Question
False
Rationale: Statistical significance is defined by our computed p-value and our preset α-level.
Answer
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PPT Chapter 04

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