Collect Data
type of variable |
categorical vs quantitative (continuous vs discrete) |
type of descriptive methods |
tabular, graphic, Numberical |
Tabular |
n, f, rf, 100rf,cf, rcf, 100rcf |
graphical |
relations: bar, pie, dot, stem leave, histogram, cumulative freq |
numberic |
precise/inference, dull, complicated |
graph the data
qualitative |
bar pie |
quantitative |
dot plot,stemplot; histogram,cumulatice freq charts, boxplot |
Examining graph |
center(mean,median,mode), spread (range, std, variance), shape (symmetric, skewed) |
pattern/deviations |
cluster/gap, outliers |
dotplot |
spread,shape,approx center |
stemplot |
shaped,spread, center |
histograph |
f vs rf, shape/center, large dataset, error bar for spread |
cumulative freq charts |
S shaped, T(skewed) shape, meaningful order |
Central tendency - mean, median, mode
summering distribution |
population/sample, center/spread/sape |
mean |
mu=population mean,X bar=sample mean |
median |
for skewed data, odd/even sample size |
mode |
number with highest freq |
symmetrical |
mean=median=mode |
left skewed |
mode>median>mean |
right skewed |
mode>mean>media |
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variance/spread - range, IQR, STD
variance |
spread from mean |
range |
largest-smallest measurement, outliers affect |
IQR |
interquartile range, eg Q3-Q1, not affected by outliers, median / IQR |
STD |
standard deviation, square root of variance, outlier affect, >=0 |
variance |
average the square of deviation from mean |
population variance |
N, sigma, mu |
sample variance |
n-1, x bar, s |
Position - quartile,percentile,standarded score
percentile |
order, divide into 100 equal parts, count kth perncentile Pk |
quartile |
order, divide into 4 equal parts (median calc), count kth quartile Qk, P25=Q1, P50=Q2.. |
z score |
standardized score, (x-mean)/std, compare datasets with different scales, eg temperature in north vs south city |
Graphing uni variant data
graphical summaries |
Y scale:misleading manipulation |
box plots |
box(Q2-Q3) and whiskers(lower Q1,upper Q4), whiskers <1.5IQR (Q3-Q1), L=Q1-1.5IQR, U=Q3+1.5IQR. point >U or <L are outliers |
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based on position, identify outlier and general shape(skewed or not) |
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calc: Q1, Median, Q3, IQR, L, U |
shift unit +a |
(variance/spread) range, std,IQR not affected |
enlarge or shrink unit,*b |
all stat enlarged or shrinked |
Compare distributions |
center, spread, shape |
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outerlier or unusual values,cluster/gap |
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context of the question |
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dot plot, stemplot, histogram, freq polygram |
Avoid simple list the stat ( center,std and shape), instead, make a clear comparative statement.
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Bivariant data
Scatter plot |
shape: linear, non-linear, no relation |
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direction: positive or negative linear relation |
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strength of linear relation: close to the line |
Numeric methods |
correlation coefficient |
degree and direction of linear relation of two quantitative variables (x,y) |
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rho and r, [-1,+1] |
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0, 0.1, 0.5,0.85,1 |
least squares regression line |
formular |
Y = a+ bX +e |
Y |
dependent/response variable |
x |
independent/explanatory variable |
a |
y intercept of line |
b |
slope of the line |
e |
random error, residual error |
predicted vaue |
y hat |
residual error |
e |
least square regression |
minimize the sum of squares of residual error |
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line of best fit (X bar, Y bar), slope=r(Sy/Sx) |
coefficient of determination |
R squared, percent of variance of Y determined by variance X |
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[-1,+1] |
influential point |
point that affect the correlation efficient |
Outlier |
maybe influential point |
residual plot |
should be random, or else, fit is not the best |
transformation to fit linear |
log, sqrt,reciprocal,square,power |
1 calc slope, intercept, write formula, plot the linear line
2 make a prediction, calc residual error
3 calc coefficient of determination r = SSxy/sqrt(SSxx * SSyy)
stat and interpretation
categorical data
marginal and joint freq of two way tables |
contingency(joint) table |
r*c |
marginal |
row col grant total |
conditional relative frequency |
association |
compare with row total * col total /grand total |
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