63 - Scientific Inference

What are the Three Steps of the Scientific Process?

1. Observation

2. Hypothesis testing

3. Inference

What is Scientific Inference?

Drawing conclusions about unobserved phenomena using observed evidence

Why do we use Statistics in Scientific Inference?

To estimate unknown population parameters and quantify uncertainty

What is a Population Parameter?

The true, usually unknown value of a characteristic in the population

What is the Difference between an Estimate and a Parameter?

• Estimate comes from sample data

• Parameter is the true population value

How are Scientific Inference and Statistical Inference Related?

Statistical inference is a subset of scientific inference

• Hypothesis testing is part of statistical inference

Why must we Quantify Uncertainty in Hypothesis Testing?

Because sample estimates may differ from the true population values

What is the Null Hypothesis (H₀)?

An assumption of no difference or association between groups

What is the Purpose of Hypothesis Testing?

To assess how plausible the observed data are if H₀ is true

What are the Two Possible Decisions Regarding H₀?

Reject H₀ or fail to reject H₀

Why do we Not Accept H₀ when results are Nonsignificant?

Failing to reject H₀ does not prove it is true

What is a P-value?

The probability of obtaining the observed result or a more extreme result, assuming H₀ is true

What does a Low P-value indicate?

The observed data are unlikely under H₀ → providing evidence against it

What does P ≤ 0.05 typically indicate?

A statistically significant result at α = 0.05

• Reject H₀

What does P > 0.05 typically indicate?

A statistically nonsignificant result

• Fail to reject H₀

What does Statistical Significance Mean?

The evidence against H₀ meets the predetermined significance threshold

What was the Observed Difference in the NSAID Study?

Among 40 arthritic dogs, the NSAID group improved 8 pain-score points more than placebo

What does P = 0.03 mean in the NSAID Study?

If the drug had no effect, a result at least this extreme would occur in about 3% of comparable studies

It does not mean:

• A 3% chance the drug is useless

• A 97% chance the drug works

• The effect is big enough to matter

Why is the Null Distribution Centered at Zero?

Because H₀ assumes no difference between treatment groups

Does P = 0.03 mean there is a 3% Chance the Drug is Ineffective?

No

• A p-value does not tell us the probability that H₀ is true

Does a Small P-value Demonstrate a Clinically Important Effect?

No

• Statistical significance does not establish clinical importance

What is the Significance Level (α)?

A predetermined cutoff used to decide whether to reject H₀

What does α = 0.05 represent?

A 5% probability of a Type I error when H₀ is true

What does α = 0.001 represent?

A 0.1% probability of a Type I error when H₀ is true

What is a Type I Error?

A false positive: rejecting H₀ when H₀ is true

What is the Difference between Statistical and Clinical Significance?

• Statistical significance concerns evidence against H₀

• Clinical significance concerns practical importance

What Two Questions should we ask about a Study Result?

1. Is it statistically significant?

2. Is the effect clinically meaningful?

How can Sample Size Affect Statistical Significance?

• Large samples may detect very small effects

• Small samples may miss real effects

Why is 'No Difference' Incorrect for P = 0.15?

A nonsignificant result does not prove that the groups are equivalent

How should a Study Result with P = 0.15 be Reported?

No statistically significant difference was found between the groups

What is a Confidence Interval (CI)?

An interval estimate expressing uncertainty about a population parameter

What does a 95% Confidence Interval Mean?

Across repeated samples, 95% of intervals made using this method would contain the true parameter

What is the Relationship between Confidence Level and α?

Confidence level = 1 − α; α = 0.05 corresponds to 95% confidence

What Changes with Repeated Sampling: the CI or the True Parameter?

The confidence interval changes

• The true population parameter remains fixed

What does a Wider Confidence Interval indicate?

Greater uncertainty and lower precision in the estimate

What does a Narrower Confidence Interval indicate?

Less uncertainty and greater precision in the estimate

What is a Type II Error?

A false negative: failing to reject H₀ when a real effect exists

What is Statistical Power?

The probability of detecting a true effect

• Power = 1 − β

What are the Main Steps of Statistical Inference?

1. Estimate the effect

2. Quantify uncertainty

3. Test H₀

4. Interpret p-values and CIs

5. Consider errors

What is a Cohort Study?

FOLLOWING exposed AND unexposed animals over time to measure new disease occurrence

What is a Case-Control Study?

SELECTING diseased cases AND nondiseased controls, then comparing previous exposure

What does a Cohort Study Directly Estimate?

Disease incidence or risk in exposed and unexposed groups

What does a Case-Control Study Compare?

The odds of exposure in cases versus controls

What is the Risk Ratio (RR) Formula?

RR =

Risk in exposed animals

÷

Risk in unexposed animals

What is the Odds Ratio (OR) Formula?

OR =

Odds of exposure in cases

÷

Odds of exposure in controls

What is the 2 × 2 Table Formula for an Odds Ratio?

OR = (A × D)/(B × C)

• A/B are exposed/unexposed cases

• C/D are exposed/unexposed controls.

Why can't Case-Control Studies Directly Calculate Disease Risk?

Researchers predetermine case and control numbers → so population incidence cannot be calculated directly

When can the Odds Ratio Approximate the Risk Ratio?

When the disease is rare

• Incidence below 5% as a rule of thumb

How is the Leptospirosis Odds Ratio Calculated?

OR = (60 × 70)/(40 × 30)

= 3.5

What does OR = 3.5 Mean in the Leptospirosis Study?

The odds of puddle exposure were 3.5 times higher among leptospirosis cases than controls

Why is '3.5 Times the Risk' Incorrect for This Study?

Case-control sampling provides an odds ratio, not a direct risk ratio

What is the Main Purpose of Case-Control Studies for Rare Diseases?

To efficiently examine exposure associations without following a large population over time

How do Case-Control Studies Select Participants?

Researchers predetermine cases and controls based on disease status

What can Cohort Studies Estimate Besides Risk Ratios?

Incidence odds ratios, using the disease odds in exposed and unexposed groups

Why must the Null Hypothesis be Carefully Constructed?

It must clearly specify the exposure, outcome, and association being tested

What is an Appropriate Null Hypothesis for the Puddle Study?

“Rainwater puddle exposure does not increase the odds of leptospirosis in dogs”

Why is a P-value Not an Effect Measure?

It measures compatibility with H₀ → not the magnitude of an effect or association

Why should Cases and Controls be Comparable?

To reduce differences unrelated to the exposure being investigated

What are the Key Practical Limitations of Case-Control Studies?

• They cannot directly estimate absolute risk

• Odds differ from probabilities

• Adequate statistical power is important

Hypothesis Testing and P-value Interpretation SUMMARY

Concept	Meaning	Interpretation
Null hypothesis (H₀)	No difference or association	Assumed true during testing
P-value	Probability of observed or more extreme results if H₀ is true	Measures evidence against H₀
P ≤ 0.05	Statistically significant	Reject H₀
P > 0.05	Not statistically significant	Fail to reject H₀
α (alpha)	Significance threshold	Commonly 0.05
Statistical significance	Evidence against H₀	Does not guarantee clinical importance
Clinical significance	Effect matters clinically	Consider effect size and practical relevance

Remember: Failing to reject H₀ does not mean H₀ is true

Type I vs. Type II Errors SUMMARY

Feature	Type I Error	Type II Error
Meaning	False positive	False negative
Mistake	Reject a true H₀	Fail to reject a false H₀
Reality	No real effect	Real effect exists
Symbol	α	β
Example	Conclude treatment works when it doesn't	Fail to detect an effective treatment
Related concept	Significance level	Power = 1 − β

Remember: 

• Type I = False alarm

• Type II = Missed effect

P-values vs. Confidence Intervals SUMMARY

Feature	P-value	Confidence Interval (CI)
Purpose	Tests evidence against H₀	Quantifies uncertainty
Main question	How surprising are the data if H₀ is true?	What range of values is compatible with the data?
Example	P = 0.03	95% CI
Interpretation	Smaller p-value = stronger evidence against H₀	Narrower CI = greater precision
Measures effect size?	No	Provides a range for the effect size
Important point	Does not prove clinical importance	Reflects uncertainty around an estimate

Remember: 

• P-value = evidence against H₀

• CI = estimate precision and uncertainty

Cohort vs. Case-Control Studies SUMMARY

Feature	Cohort Study	Case-Control Study
Groups selected by	Exposure status	Disease status
Groups	Exposed vs. unexposed	Cases vs. controls
Measures	Disease incidence/risk	Odds of exposure
Main ratio	Risk ratio (RR)	Odds ratio (OR)
Directly calculates disease risk?	Yes	No
Useful for rare diseases?	Less practical	Yes
Direction	Exposure → disease	Disease → previous exposure

Remember:

• Cohort = RR

• Case-control = OR

Odds Ratio Formulas and Interpretation SUMMARY

Concept	Formula / Interpretation
Risk ratio (RR)	Risk in exposed ÷ Risk in unexposed
Odds ratio (OR)	Odds of exposure in cases ÷ Odds of exposure in controls
OR calculation	(A × D) ÷ (B × C)
OR = 1	No association
OR > 1	Positive association
OR < 1	Negative association
OR ≈ RR	When disease is rare (lecture rule: incidence below 5%)

Leptospirosis example: How to Calculate Odds Ratio SUMMARY

Correct interpretation: “Dogs with leptospirosis had 3.5 times the odds of rainwater puddle exposure compared with controls.”

Incorrect: “Dogs exposed to puddles had 3.5 times the risk of leptospirosis.”