Statistic formulas - STATISTICS FORMULAS DESCRIPTIVE...

Reference: Moore DS, McCabe GP & Craig BA. Introduction to the Basic Practice of Statistics . New York: W.H. Freeman & Co, 5
th
edition.
STATISTICS FORMULAS
DESCRIPTIVE STATISTICS:
MEAN:
VARIANCE:
STANDARD DEVIATION:
STANDARD ERROR:
Z-SCORE:
REGRESSION LINES:
For a data set , where ( ) are the centroids (means)
of the data set, and is the correlation coefficient:
LEAST-SQUARES REGRESSION LINE: +
RESIDUALS:
SSM SSE SST = SSM+SSE
COEFFICIENT OF DETERMINATION: r
2
=
CORRELATION COEFFICIENT: r =
SLOPE:
INTERCEPT:
VARIANCE: ST DEV:
STANDARD ERROR b
1
: SE
b1
=
STANDARD ERROR b
o
: SE
b0
=
CONFIDENCE LEVEL FOR THE INTERCEPT : t*SE
b0
CONFIDENCE LEVEL FOR THE SLOPE: : t*SE
b1
PREDICTION INTERVAL:
HYPOTHESIS TESTING – MEANS:
STANDARD ERROR:
MARGIN OF ERROR: m = or m =
CONFIDENCE INTERVAL: C.I. =
SAMPLE SIZE FOR A GIVEN m:
ONE SAMPLE Z-TEST: T-TEST:
TWO SAMPLE Z-TEST:
TWO SAMPLE T-TEST:
PROPORTION: , where X= number of successes
STANDARD ERROR:
MARGIN OF ERROR: m =
Z-TEST, ONE-SAMPLE PROPORTION:
STD ERR, 2-SAMP PROP:
MARGIN OF ERR, 2-SAMP PROP: m =
PLUS FOUR PROPORTIONS:
EST DIFF BTWN PROPS:
STD DEV:
POOLED PROPORTION:
POOLED STD ERR:
TWO SAMPLE Z-SCORE:

Reference: Moore DS, McCabe GP & Craig BA. Introduction to the Basic Practice of Statistics . Ne w York: W.H. Freeman & Co, 5
th
edition.