Transcript Chapter 12 Gillis & Jackson Inferential Statistics PP

Chapter 12
A Primer for Inferential
Statistics
What Does Statistically
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
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
Example 2:
• Suppose we measure the difference in selfesteem between 12 year old males and
females and get a statistically significant
difference, with males having higher selfesteem
• This means that the difference probably
reflects a “true” difference in the selfesteem levels. Wrong: < 5% of the time.
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
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
Sample 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
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
Research & 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
Testing 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.
One- 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)
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
Chi-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
One 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
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?
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?
Expected Frequencies fe
Frequency
Observed
•
30
•
160
•
10
Frequency
Expected
15.6 (200 x .078)
137.8 (200 x .689)
46.6 (200 x .233)
• Degrees of Freedom = 2
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
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.
Decision
• 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
T-Tests
•
•
•
•
•
Sample sizes < 30
Dependent variable measured at ratio level
Independent assignment to treatments
Treatment has two levels only
Population normally distributed
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.