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Basic Stats, QuaNTitative variables (Analysis of matched pairs (difference…
Basic Stats
QuaNTitative variables
numerical
graph
grouped frequency table
cumulative relative frequency table
histogram
cumulative relative frequency table
symmetric distribution
mean
standard deviation
non-symmetric distribution
median (Q50)
lower quartile (Q25)
upper quartile (Q75)
cumulative relative frequency plot
box plot
positive (right skew)
geometric mean
mode
Sampling Variability of a
Mean
Standard Error
SE = s / root[ n ]
95% CI
n > 20
95% CI: mean +/- 1.96*SE
n < 20
95% CI = mean +/- t* SE
df = n-1
look for t in table
Significance Test
Z = (mean - "population mean")/ SE (mean)
n < 20
df = n-1
look in table the crossing of Z and df
P value is btw two values (e.g. 0.002 and 0.001)
Analysis of
matched pairs
difference d= p1 - p2
calculate mean (d-bar) of all d
SE (d-bar) = s / root[ n ]
look for t at df= n-1
95% CI = d-bar +/- t*SE
T-test: (d-bar - 0)/SE(d-bar)
look for P in table at df and T
Comparing Two Means (unpaired data)
Significance Test
n > 20
95% Confidence Interval
(mean 1- mean 2) +/- 1.96 * SE (mean1 - mean2)
Standard Error
SE (mean1 - mean1)= root[ s1^2/n1 + s2^2/n2)
Significance Test
Z = (mean1 - mean2)/ SE (mean1-mean2)
n < 20
pooled standard deviation
s(p) = root [ ((n1-1)s1^2 + (n2-1)s^2) / (n1-1) + (n2-1) ]
Standard Error
SE (mean 1-mean2) = s(p) * root[ 1/n1 + 1/n2 ]
95% CI
(mean1 - mean2) +/- t*SE
Significance Test
T = (mean1 - mean2) / SE (mean1-mean2)
P Value
Calculation
Z test (for n>20)
T test (for n<20)
if 95% CI included 0 (proportion) or 1 (risk ratio), then P> 0.05
p> 0.1: no evidence against H0 (H0 might be correct)
P< 0.05: null hypothesis rejected due to evidence against it
0.05 < P < 0.01: weak / suggestive evidence against H0
0.01 < P < 0.05: quite strong evidence against H0
0.001 < P < 0.01: strong evidence against H0
P<0.001: very strong evidence against H0
Stat Table gives one-sided P-value (so multiply with 2! for two-sided P-Value)
QuaLItative variables
Proportions
Comparison of Two Proportions
Standard error
SE= root[ p-bar(100-p-bar)/n1 + p-bar (100- p-bar)/n2 ]
p-bar = overall percentage of cases
95% CI for difference
= (p1 - p2) +/- root[ p1(100-p1)/n1 + p2(100-p2)]
sample n>20
2 X P = two-sided P-value
with Z value: look for one-sided P
Z test= (p1 - p2)/SE(p1-p2)
Confidence Interval
n >20
95% CI: p +/- 1.96* SE
n < 20
95% CI= p +/- t*SE
Standard error = root[ p*(100-p)/n ]
Graph
bar chart
frequency table
ordered categorical
categorical
binary