Stats Intro and SPSS

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

t-test

determines if there is a difference between groups

closer the number is to 1, the less likely there is a differences

larger it is, more likely there is a true difference

• seen by significance value (sig. 2 tailed)

• ie. .505 (above 0.05) - insufficient evidence to reject the null, while there is a difference in mean scores it is due to chance

interpret this table

t = -.698

• strong negative relationship (number closer to 1)

sig. (2-tailed) = .505

• (above 0.05) cannot reject null hypothesis - difference in mean scores is due to chance

CI 95% and mean difference -3.2

• we are 95% certain where the true mean difference lies

• on average lectures drink 3.2 drinks less than students

  • however we are 95% sure, this average is between 13 less drinks and 7 more drinks than students

    • so we cannot be certain lectures drink more than students

when to use ANOVA

Interested in results between groups and the groups are independent from another

more than 2 samples

homogenity of variance test

equal variance in each of the groups

post-hoc - tukey

tells us where the differences are between the groups

significance value should not be below 0.05

therefore we can conclude the assumption of equal variance has not been violated

interpert this table

significance value .002

• below significance level of 0.05

• yes there is a significant difference between the groups (but where? - multiple comparisons table)

multiple comparisons table

determines where differences lie

row 1- lecturers have 9.4 differences in neurotisism than parents

p = 0.002

statistically significant

0.0 occurs 180 times

% agreement of 88.2% between reviewer 1 and 2

does not account for chance

kappa analysis

evaluates inter-rater reliability or the degree of agreement for categorical (nominal or ordinal) data while correcting for random chance

kappa value = 0.627

• kappa takes into consideration chance

• 62.7% agreement

• above .6 = good agreement