Biostats (3)

Range

max-min

not affected by skew

affected by outliers and sample size

appropriate for sample, not population

IQR

75th percentile-25th percentile

not affected by skew or outliers

affected by sample size

appropriate for sample, not population 

Variance

measure of heterogeneity (how much one thing varies from another)

s² = sum (x-x)² /n-1

affected by outliers and sample size

appropriate for predicting heterogeneity of population

units squared is not a useful measure

Standard Deviation

average distance from each data point to the sample mean

s=√s²

affected by sample size and outliers

appropriate for predicting spread of population

units are the same as measurement

Normal Curve SD

-3 → 2.5%

-2 → 13.5%

-1 → 34%

1 → 34%

2 → 13.5%

3 → 2.5%

Z-score

z=(xi-x)/2

stander deviations away from mean

T-score

T=50+10z

Standard Error of Mean

how “confident” are we that the sample mean can represent population mean

-an estimate if the SD of the resampling distribution

-not strictly a measure of spread

S/√n

x+-SEM

When to Use What Type of Spread Measurement

Nominal→ no measure of spread

Ordinal → range or IQR

Metric → IQR(median) or SD(mean)

Confidence Intervals

measure how precisely our sample statistic estimates our population parameter

T-Distribution

resampling distributions w/ constant

-smaller n=wider variability

-bigger n= narrow variability

95% Confidence Interval

CI=x +- critical t (SEM)

how confident we are that (x) matches population (μ)

Degrees of freedom

(n-1)

Critical T

df + % on T-distribution table

(95% means 2.5% on T-distribution table)

One Sample t-test

Ho=null hypothesis, no relationship or difference, we try to “prove” this

Ha= alternative hypothesis

George Box

“All models are wrong but some are useful”

Simple Probability

P(A)=# of A/ total # of possible outcomes

Combining Probabilities when Independent

prob. of 1st event doesn’t affect the 2nd event

and = times

or = add

2 Sample t-test

examine the difference between the spread between 2 groups to the amount of spread within each group

Find t-score=x2-x1/SEx1-x2

find critical t (df=(n1-1+n2-1)

If t-score≥critical t then we fail to reject Ho(p>0.05)