Comparing Means and Proportions

Question 1

Define Hypothesis test.

Answer 1

estimate the probability of obtaining the observed result, or one more extreme, f there is no true difference (P-value) –> use this informaiton to make decisions about the population

Question 2

Paired vs. Unpaired data

Answer 2

• paired examples
  
  • pre-post comparison
  • cross-over trial (patients randomized to sequence of interventions; ex. race car drivers)
  • matched case-control study
  • twin study
• unpaired examples
  
  • “traditional” randomized controlled trial
  • epi study without matching

Question 3

When to compare means, medians, or proportions?

Answer 3

• Compare Means: continuous, normally distrubuted data
• Compare Medians:
  
  • continuous, not normally distributed data
  • ordinal data
• Compare Proportions:
  
  • ordinal data
  • nominal data

Question 4

What test do you use to compare means of normally distrubuted continuous UNPAIRED data?

Answer 4

unpaired t test

Question 5

Unpaired T Test

Answer 5

• two-sided test, alpha = 0.05 (used to determine if p value is low enough for significance)
• H₀: mean_experimental - mean_placebo = 0
• H_A: meanexperimental - meanplacebo does not = 0
• find test statistic (difference in means/ SE of means), look up P-value in t table

Question 6

What test do you use to compare medians (of non-normally distributed continuous UNPAIRED data OR of ordinal UNPAIRED data)?

Answer 6

Mann-Whitney U/ Wilcoxon rank-sum

Question 7

Mann-Whitney/ Wilcoxon Test

Answer 7

• nonparametric test
• H₀: Median_experimental - Median_placebo = 0
• same procedure as unpaired T test, but uses medians and a different table

Question 8

Why use a nonparametric test?

Answer 8

• less sensitive to outliers
• don’t require a normal distribution
• good for ordinal data as well as interval/ratio data
• less powerful when using normally distrbuted data or complex hypotheses

Question 9

What test do you use to compare means of normally distrubuted continuous PAIRED data?

Answer 9

Paired t test

Question 10

Paired T test

Question 11

What test do you use to compare medians (of non-normally distributed continuous PAIRED data OR of ordinal PAIRED data)?

Answer 11

Wilcoxon signifed rank test or Sign test

Question 12

Wilcoxon Signed Rank Test

Answer 12

• H₀ : median differences = 0
• nonparametric test

Question 13

What test do you use to compare medians (of ordinal OR of nominal UNPAIRED data)?

Answer 13

Z test, Chi square, or Fisher’s exact

Question 14

Z Test

Answer 14

Question 15

Chi Square Test

Answer 15

• can be used to compare many different proportions (very vertasile for study design, not possible with T test)
• not useful for small sample size

1. calculate expected frequencies as if the null hypothesis is true
   
   • take overall percentages and apply to the experimental/ control groups
2. calculate (observed-expected)² / expected for each cell, sum resulkt across all cells
3. look us results in chi square table

Question 16

Chi Square & Epidemiological Studies (define null hypothesies)

Answer 16

• H₀: p1 = p2; Ha: p1 ≠ p2
• Cohort study
  
  • Odds ratio = p1/p2
    
    • H₀: If p1 = p2, p1/p2 = 1
  • Risk difference = p1 – p2
    
    • H₀: If p1 = p2, p1 – p2 = 0
• Relative risk = p1/p2
  
  • H₀: If p1 = p2, p1/p2 = 1

Question 17

Fisher Test

Answer 17

• good for small sample in one of the categories
• consider all possible 2x2 tables with the same row and column totals as your table
• how many of these are at least as extreme as your table?

Question 18

What test do you use to compare proportions of ordinal or nomial PAIRED data?

Answer 18

McNemar’s Test

Question 19

McNemar’s Chi Square Test

Answer 19

• chi square test, but use binomial categories
  
  • ex. kids who have symptoms/ no symptoms at 12 and 14
  • Does prevalence change with age?
    • H0: P_age 12 = P_age14
    • HA: P_age 12 ≠ P_age14
    • ​α = 0.05, 2-sided test
• ex. If no change in prevalence, expect the same number of kids to switch from “no symptoms” to “symptoms” as vice versa
  • use difference between kids who switched from symtoms to none from 12 to 14 and from none to symptoms from 12 to 14 to calcualte X² value

Question 20

ANOVA

Answer 20

• used to compare means in 3 or more groups of unpaired data
• Example:
  
  • H_0: no difference (rousuvastatin - atorvastatin = simvastatin)
  • H₀: rosuvastatin = atorvastatin
  • H_0: rosuvastatin = simvastatin
  • H₀: simvastatin = atorvastatin
• multiple comparisons can result in a higher chance of a result coming back significant even if it is not –> can use special adjustments, but this lowers power of statistical test (increases type II error)

Question 21

Statistical vs. Clinical Significance

Answer 21

Question 22

What does a P-value below 0.05 mean?

Answer 22

• we are unlikely to get this result purely by chance
• however, this result could occur w/ biased study
• gives no information about clinical significance

Question 23

Absence of evidence is not evidence of absence!!!

Answer 23

• Just because you can’t reject the null hypothesis does not make it true