Stats Intro

relevant statistical tests

associations

• Pearson’s correlation

• chi-square test of association (2 × 2)

• relative risk (2 × 2)

• odds ratio (2 × 2)

diagnostic accuracy

• sensitivity and specificity

• positive and negative predictive value

• positive and negative liklihood ratios

reliability

• Cohen’s kappa

difference between groups

• independent-samples t-test

• paired-samples t-test

• one-way repeated measures ANOVA

• mixed ANOVA

odds

how likely an event is to happen

risk

probability of having a specific event

intervention vs control odds

the odds of experiencing the outcome in the intervention group is 0.37 times the odds in the control group

for every 37 persons who experience the event in the intervention, 100 persons will experience the event in the control group

odds > 1

increased

more likely to happen than not

odds = 1

just as likely to happen than not

odds < 1

decreased

less likely to happen than not

intervention vs control risk

the risk of the outcome in the intervention group is 0.5 times the risk of the outcome in the control group

the risk of the outcome is reduced by 50% among participants in the intervention group compared to control group

risk difference

sensitivity

measures a tests ability to correctly find people who have a condition (true positive)

high sensitivity catches “sick people” and avoids missing cases

specificity

measures a tests ability to correctly find people who do not have the condition (true negative rate)

high specificity avoids false alarms

likelihood ratio (LR)

probability of finding patients with a disease / probability of same findings in patients without the disease

LR +

indicates that a positive test result is more likely to occur in a person WITH the condition than in a person without the condition

LR -

the test is less likely to be negative in someone with the condition than in someone without it

lower value indicates better performance of the test in ruling out the condition

1 variable can be

sensitivity calculation

true positive (TP) / true positive (TP) + false negative (FN)

high sensitivity

high true positive (TP)

low false negative (FN)

sensitivity calculation example

true positive (TP) = 79

false negative (FN) = 21

false positive (FP) = 9

true negative (TN) = 891

79 / 79 + 21

= 0.79

SNOUT

Highly sensitive test is positive in almost everyone with the disease, but it would hardly ever be negative in a person with the disease…

sensitive … negative … OUT

high specificity

high true negatives

low false positives

low specificity

low true negatives

high false positives

specificity calculation

true negative (TN) / true negative (TN) + false positive (FP)

specificity calculation example

TP = 79

FN = 21

FP = 280

TN = 620

620 / 620 + 280

=0.69

SPIN

specific

positive

in

LR+

LR-

paired samples t-test

differences within group

same group being measured pre and post intervention

paired samples t-test example question

H0 = There is no difference between quadriceps strength prior to and post an exercise intervention

independent samples t-test

differences between groups

ie. quad tendon graft vs hamstring tendon graft

2 separate groups independent from each other

ANOVA

differences between multiple groups

ie. quad graft, hamstring graft, cross-bracing protocol

f-value

one-way repeated measures ANOVA

differences within groups

ie. quad tendon graft group strength measured 2x immediately post surgery and 4-weeks post

one-way repeated measures ANOVA example hypothesis

H0 = There is no difference between quadriceps strength prior to, immediately post, and 4-weeks post an exercise intervention

two-way mixed design ANOVA

differences between and within groups

ie. quad graft, hamstring graft, cross-bracing strength post exercise program