chapter 12 a primer for inferential statistics what does statistically significant mean? it’s the...
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Chapter 12Chapter 12
A Primer for Inferential Statistics
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What Does Statistically What Does Statistically Significant Mean?Significant Mean?
• It’s the probability that an observed difference or association is a result of sampling fluctuations, and not reflective of a “true” difference in the population from which the sample was selected
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Example 1:Example 1:
• Suppose we test differences between high school men and women in the hours they study: females spend 12 minutes more per night than males and the result is analyzed and shown to be statistically significant
• It means that less than 5% of the time could the difference be due to chance sampling factors
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Example 2:Example 2:
• Suppose we measure the difference in self-esteem between 12 year old males and females and get a statistically significant difference, with males having higher self-esteem
• This means that the difference probably reflects a “true” difference in the self-esteem levels. Wrong: < 5% of the time.
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Example 3:Example 3:
• You test the relation between gender and self-esteem: a test of significance indicates that the null hypothesis should be accepted. What does this mean?
• It means that more than 5% of the time the difference you are getting could be the result of sample fluctuations
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Clinically Significance
• Clinical significance means the findings must have meaning for patient care in the presence or absence of statistical significance
• Statistical significance indicates that the findings are unlikely to result from chance, clinical significance requires the nurse to interpret the findings in terms of their value to nursing
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Sample FluctuationSample Fluctuation
• Sample fluctuation is the idea that each time we select a sample we will get somewhat different results
• If we selected repeated samples, and plotted the means, they would be normally distributed; but each one would be different
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A Test of Significance
• A test of significance reports the probability that an observed difference is the result of sampling fluctuations and not reflective of a “real” difference in the population from which the sample has been taken
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Research & Null HypothesisResearch & Null Hypothesis
• Research Hypothesis: reference is to your predicted outcome.
• Null Hypothesis: the prediction that there is no relation between the variables.
• It is the null hypothesis that is tested
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Testing the Null HypothesisTesting the Null Hypothesis
• In a test, you either accept the null hypothesis or you reject it.
– To accept the null hypothesis is to conclude that there is no difference between the variables
– To reject the null is to conclude that there probably is a difference between the variables.
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One- and Two-Tailed TestsOne- and Two-Tailed Tests
If you predict the direction of a relationship,
you do a one-tailed test; if you do not predict
the direction, you do a two-tailed test.
• Example: females are less approving of violence than are males (one-tailed)
• Example: there is a gender difference in the acceptance of violence (two-tailed)
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Type I & II Errors
• TYPE 1. Reject a null hypothesis (that states no relationship between variables) when it should be accepted
• TYPE 2. Accept a null hypothesis when it should be rejected
• RAAR -Reject when you should accept: Accept when you should reject-the first 2 letters give you type 1, the second two letters, type 2
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Chi-Square: Red & White BallsChi-Square: Red & White Balls
• The Chi-square (X2) involves a comparison of expected frequencies with observed frequencies. The formula is:
X2 = (fo - fe)2
fe
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One Sample Chi-Square TestOne Sample Chi-Square Test
Suppose the following incomes:
INCOME STUDENT GENERAL
SAMPLE POPULATION
Over $100,000 30 15.0 7.8
$40,000 - $99,999 160 80.0 68.9
Under $40,000 10 5.0 23.3
TOTAL 200 100.0 100.0
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The Computation
• Remember, Chi-squares compare expected frequencies (assuming the null hypothesis is correct) to the observed frequencies.
• To calculate the expected frequencies simply multiply the proportion in each category of the general population times the total no. of students (200).
• Why do you do this?
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Why?
• If the student sample is drawn equally from all segments of society then they should have the same income distribution (this is assuming the null hypothesis is correct).
• So what are the expected frequencies in this case?
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Expected Frequencies fe
Frequency Frequency
Observed Expected
• 30 15.6 (200 x .078)
• 160 137.8 (200 x .689)
• 10 46.6 (200 x .233)
• Degrees of Freedom = 2
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Decision:Decision:
• Look up Chi square value in Appendix p. 399• 2 degrees of freedom• 1 tailed test (use column with value .10)• Critical Value is 4.61• Chi-Square calculated 45.61• Decision: (Calculated exceeds Critical) Reject
null hypothesis
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Standard Chi-Square Test
• Drug use by Gender
• 3 categories of drug use (no experience, once or twice, three or more times)
• row marginal times column marginal divided by total N of cases yields expected frequencies
• degrees of freedom = (row - 1)(columns - 1) = 2.
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DecisionDecision
• With 2 degrees of freedom, 2-tailed test, the Critical Value is 5.99
• Calculated Chi-Square is 5.689
• Does not equal or exceed the Critical Value
• So, your decision is what?
• Accept the null hypothesis
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T-TestsT-Tests
• Sample sizes < 30
• Dependent variable measured at ratio level
• Independent assignment to treatments
• Treatment has two levels only
• Population normally distributed
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Two T-Tests: Between & Within
• Between-Subjects T-Test: used in an experimental design, with an experimental and a control group, where the groups have been independently established.
• Within-Subjects: In these designs the same person is subjected to different treatments and a comparison is made between the two treatments.