DATA ANALYSIS20 NOVEMBER 2014

THEORY, PROPOSITIONS, LOGIC

Hypotheses are“tested”

Hypotheses are never“proved”

Hypotheses only are“rejected”

Theories are built and verified by testing hypotheses

TruthHo true Ho false

Decision

Fail to reject Ho

Reject Ho

Error

Error

TruthHo true Ho false

Decision

Fail to reject Ho

Reject Ho

Type 1error

Type 2error

TruthHo true Ho false

Decision

Fail to reject Ho

Reject Ho

TRADITIONALLY, probability of Type 1

error set at .05

Minimize Type 2error by

increasing sample size

TruthHo true Ho false

Decision

Fail to reject Ho

Reject Ho

Fitting a straight line through a swarm of bivariate data

Y = a + bx

Y

X

(x, y)

e

a y = a + bx + e

b = y / x

Y = + X

Is there no relationship between Y and X in the population?

• H0: yx = 0

Is the slope of the line = 0 in the population?

• H0: = 0

Null hypothesis is H0: yx = 0

Alternate hypothesis is H1: yx ≠ 0

a = .05 Y = + X

Null hypothesis is H0: = 0

Alternate hypothesis is H1: ≠ 0

a = .05 Y = + X

Rscript

Attaches mtcars and examines its characteristics

Rscript

Console

Rscript

Console

a b

Rscript

Console

Rscript

Console

Rscript

Console

Rscript

Console

Rscript

Plot

DATA ANALYSIS20 NOVEMBER 2014