Lecture 4 (Statistical Significance)

Steps of a Study

1.) Research question and hypotheses

2.) How many people do you need to be able to test this hypothesis?

3.) Write protocol and get approvals to do study

4.) Enroll subjects

5.) Collect data

5.) Get results

7.) Draw conclusions

Before drawing conclusions…

we need to quantify random (sampling) error may occur for the results observed in any individual study (sample)

Statistical Inference

the process of quantifying random (sampling) error

Hypothesis

A predictive statement relationship between independent variables (exposure) and dependent variables (outcomes)

Is there an association between variables in study (hypothesis testing)

• association = statistical relationship between variables

• if the risk of disease is higher or lower in one group compared to the other

• DOES NOT IMPLY SOMETHING CAUSES DISEASE

Null Hypothesis

no relationship between the exposure and outcome variables.

H(0): Risk Rato=1.0

Alternative Hypothesis (H(a))

there IS some relationship between exposure and outcome variables

Two Sided Alternative Hypothesis

occurrence of disease is not the same in the exposed and unexposed

H(a) Risk Ratio does not equal 1.0

One Sided Alternative Hypothesis

occurrence of disease in the exposed group is greater (or less) than the occurrence of disease in the unexposed group

H(a)

Risk Ratio > 1 or

Risk Ratio < 1

2×2 Table 

Disease in column; Exposure in rows

Measures of Association (statistical sig)

assess the strength of the statistical relationship between a given study factor and disease

Relative Risk

compares risk of exposed group relatively to the group of unexposed

The BIG Sentence

The risk of (disease) among the (exposed) is (X) times (higher/lower) than the risk of (disease) among (unexposed) 

Risk Ratio Equation

risk in the exposed / risk in the unexposed

based on 2×2 table

= A/ (A+B) / C/C+D)

Analysis of Risk Ratio

If the null value is less than 1.0 it is PROTECTIVE

If null value is greater than 1.0 it is HAZARDOUS (range is wider numerically but same MAGNITUDE can be presented from both protective and hazardous)

If null value = 1.0 it has NO EFFECT

Interpretation of Risk Ratio, Odds Ratio, Hazardous Ratio

Relative Risk between 1.0 and 2.0

RR-1.0 = % increased risk 

Relative Risk > 2.0

RR number= number of times increased risk

ex. 3 times increased risk of disease if exposed

Relative Risk < 1.0

1.0-RR=% decreased risk

Risk Difference

the number of cases of disease among the exposed that would not occur if the exposure was eliminated 

The role of chance

principle assumption that the measures of disease frequency is what we draw inferences of an entire pop based on evaluation of only a sample.

Quantify Chance

quantify the degree to which chance may account for the results observed

a measure that is reported from all tests of stats sign is the p-value

Interpretation of p-value

The p-value is the probability of obtaining a result at least as extreme as that observed in the study by chance alone. 

p value is based on null hypothesis 

P values are influenced by…

both magnitude/strength of the association AND the sample size

P value- Large Sample Size

a small difference may be statistically significant

P value Small sample size

a large difference may not achieve statistical significance

If p value small

reject null hypothesis ( less than 0.05)

• “statistically significant”

Confidence Intervals

having a range to have a level of certainty for our Risk Ratio

95% of the confidence interval formed containing the TRUE vale (especially when repeating the same procedure)

• how good is our estimate

Confidence Interval Wider Intervals

less precision

Narrower Intervals

more precision

If interval contains null value

the result is NOT statistically significant

If the interval does not contain the null value

the result IS statistically significant

If p-value is < 0.05

the confidence interval will NOT contain the null value

if p-value is > 0.05

the confidence interval WILL contain the null value