# ANTC67 exam- stats n on.docx

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University of Toronto Scarborough

Anthropology

ANTC67H3

Larry Sawchuk

Winter

Description

Assessing Etiology
RISK FACTOR (present/absent) association DISEASE (yes /no)
STATISTICAL EVALUATION
Odds Ratio & Chi square
Stratified Odds Ratio
Hypothesis Testing
Indicate whether the observed difference in the two groups can simply be attributed to chance.
The significance test accept or reject?
Common elements are presented in summary form before the actual tests of significance
The expression of the Disease is independent (not associated) of the specified Risk Factor
Compare computed chi square (observed) to expected chi square (critical value)
If chi-square value exceeds the expected, reject the null hypothesis of no association there is an ASSOCIATION
Critical Chi Square Value
Allowing for 5% error in our decision OR 95% confident regarding the null hypothesis
Step 1: State the Hypotheses
Null Hypothesis (Ho):
A probabilistic statement about population parameter that is being tested by sample.
Ho always contains the equality statement
A and B have no relationship
Alternative hypothesis (H1):
Determined by the question implicit in the statement of the problem.
A and B have relationship
Step 2: Select the Level of Statistical Significance
Once the null hypothesis is stated, a decision be:
1. Reject Ho
2. Accept Ho
3. Reserve judgement concerning Ho (the decision is too close to call).
Step 3: Select the Appropriate Test Statistic
Decide which test to use.
Depends on assuptions
Chi-square (Pearson, 1900)
A non-parametric test whose model does not specify conditions about the parameters from which the sample was drawn.
However, non-parametric tests still contain some assumptions
Step 4: Define the Region of Rejection
In general, a significance level of .05 or .01 is used in hypothesis testing.
a = 0.05, there are 5 chance in 100 that Ho will be rejected when it is actually true..
95% confident that we have made the correct decision about Ho.
Chi-square value vs. critical chi-square with 1 df
Df of a test is defined by:
the sample size -1 ( eg., Z test)
Or the number of classes (r-1 * c -1) (Odds ratio test)
Step 5: Compute the test statistic and assess Ho.
If the computed chi square value exceeds that expected at 0.05 level,
Observed relationship between the two factors is not likely to be due to chance factors alone.
95% confident that the association between the two factors is not due to chance.
When one moves to the .01 level, the critical chi square value necessarily becomes larger.
Step 6: Assess the meaning of your finding.
Generate further hypotheses that follow from your assessment of initial Ho.
Chi square
Rules of thumb
Whole numbers only
No zero
In a 2 by 2 if the total is less than 30, use fishers exact
Less than 200 some suggest that you use continuity correction
MH chi-square
Chi square = {(|ad-bc|-N/2)^2 * N} / (C1*C2*R1*R2)
Assumptions
Random sample data
A sufficiently large sample size Type I error: a true null hypothesis is incorrectly rejected
Type II error: one fails to reject a false null hypothesis
No accepted cutoff.
Adequate cell sizes.
All cells of a 2-by-2 table, and 5 or more in 80% of cells in larger tables, but no cells with zero.
When this assumption is not met, Yates' correction is applied.
Independent observations.
Same observation can only appear in one cell.
Chi-square cannot be used to test correlated data (ex., before-after, matched pairs, panel data).
All observation has the same underlying distribution.
Distribution is known in advance
Non-directional hypotheses
Chi-square tests the hypothesis that two variables are related only by chance.
Finite values
Normal distribution of deviations (observed minus expected values)
Chi-square is a non-parametric test in the sense that is does not assume the parameter of normal distribution for the data - only for the
deviations.
Data level
Odds Ratio = (a*d) / (b*c)
Yes No Total
Yes A B A+b
No C D C+d
Total A+c B+d A+B+C+D
If OR is not equal to 1, there is an association.
The further away OR is, the stronger the association.
General Guidelines for Interpreting Values of OR
Value Effect of Exposure
0-0.3 Strong negative
0.4-0.5 Moderate negative
0.6-0.8 Weak
0.9-1.1 No effect
1.2-1.6 Weak
1.7-2.5 Moderate positive
= or >2.6 Strong positive
One Risk Factor
Step 1
Simple comparisons between the Disease and various Risk Variables
Get ORs
Get levels of significance
Possible Risk Computed chi-squares
Factors Judged to be
A sex Not significant
Disease
B smoke Not significant
C diet Significant
D drug Not significant
Step 2
Data are then stratified for heterogeneity
Compute OR with disease and Risk Factor C and then stratified by other Risk Factor (A)
Examine the two ORs (are they the same?)
Evaluate interactive chi-square value is greater than critical value, assume interaction is present and there are differences in Disease
and C depending on the level of strata STRATIFIED
Level A
sex Level B
BASIC
Level A
Disease diet smoke Level B
drug Level A
Level B
Step 3
If interaction is present, report the strata-specific measures of association
If interaction is not present, report the crude (unadjusted for the strata) estimates of association
Step 4
Report your Results
Confounding the masking effect
A situation in which a measure of association or effect and outcome is distorted by the presence of another variable
An extraneous variable that wholly or partially accounts for the observed effect of a risk factor on disease status
Positive the observed association is biased away from the null
Negative when the observed association is biased toward the null
To be a confounder: 3 conditions
It is risk factor for the disease, no relationship with the putative risk factor - testable
It is associated with putative risk factor - testable
It is not in the causal pathway between exposure and disease - conceptual
How to identify confounders?
Your acquired knowledge
Prior experience with data
The three criteria for confounders cited earlier
Example
Diabetes No diabetes
CHD 2249 91 2340
No CHD 190 26 216
2439 117 2556
OR = 3.38
The odds of having diabetes among those with coronary heart disease is 3.3 times as high as the odds of having diabetes among those who do not have
coronary heart disease
In this case, since OR = 3.38 is greater than 1, there is some kind of association.
Would diabete mean elevated CHD?
Potential confounder: Hypertension (elevated blood pressure/no elevated blood pressure)
Diabetes & CHD among non- Hypertensives
Diabetes No diabetes
CHD 6 77 83
No CHD 51 1572 1623
57 1649 1706
OR = 2.40
Diabetes & CHD among hypertensives
Diabetes No diabetes
CHD 20 113 133
No CHD

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