Hypothesis Testing Roadmap
Discrete Data
1 Proportion Test
Ho: Ppop = Pt
Ha: Ppop ≠ Pt
t = target
Stat>B.S>1 Prop.
(same as CI for P)
1
Start
Tips to Remember
1) Proper sample size selection is required
for tests to be effective.
Levels
of Interest
for X
1
2) Ha can be <,>, or ≠
3) If p>α, then fail to reject Ho
If p<α, then reject Ho
Type
of
Y
Number of
Factors for
X
Attribute
Variable
Variable Data Not Normal
DOE
Stuck
Proceed with
caution
>1
2
2 Proportion Test
Ho: Ppop1 = Ppop2
Ha: Ppop1 ≠ Ppop2
Stat>B.S>2 Prop.
2
>2
Contingency Table
Ho: F1 independent of F2
Ha: F1 dependent on F2
Stat>Tables>Chi Sq Test
No. of
X's
ANOM
Ho: Ppop1=Ppop2 =........
Ha: At least one Ppop is different
Stat>ANOVA>ANOM
No
Kruskal-Wallis or
Mood's Median Test
Ho: M1 = M2 = M3 ...
Ha: at least 2 ≠
Stat> Nonparametrics>
KW or MM
Yes
Non-Normal
Mann-Whitney Test
Ho: M1 = M2
Ha: M1 ≠ M2
Stat>Nonparametrics>
Mann-Whitney
Levene's Test
Ho:σ1 = σ2 = σ3.....
Ha: at least 2 ≠
Stat>ANOVA>
Test for Equal Variances
Ho: Data is normal
Ha: Data is not normal
Stat>B.S.>Normality Test
or
STAT>B.S.>D.D.S>G.S.
1
Are σ's
equal
Is Y
Normal
for each
level of
X?
DOE, Logistic Regression
Ho: Ppop < or > f(x)
Ha: Ppop = f(x)
Stat>ANOVA>DOE
Stat>Regression>Logistic Regression
>2
Normal
>2
Yes
Are σ's
equal
No
Stuck
Proceed with
caution to
2 sample-t or
Mann-Whitney
Levene's Test
Ho: σ1 = σ2
Ha: at least 2 ≠
Stat>ANOVA>
Test for Equal
Variances
Median
One Sample Wilcox or
1 Sample sign
Ho: M1 = Mt
Ha: M1 ≠ Mt
t = target
Stat>Nonparametrics
& either a
1 Sample Sign
or a
1 Sample Wilcox
2
Levels
of Interest
for X
Variable Data Normal
1
Test
Median
or σ?
Bartlet's Test
Ho: σ1 = σ2 = σ3.....
Ha: at least 2 not equal
Stat>ANOVA>
Test for Equal
Variances
Sigma
No
Chi Sq Test
Ho: σ1 = σt
Ha: σ1 ≠ σt
t = target
Stat>B.S.>D.D.S>G.S
(if S1 falls between CI,
then fail to reject Ho)
>2
Stuck
Proceed with
caution to One
Way ANOVA
Are σ's
equal
Levels
of Interest
for X
1
µ or σ?
2
sigma (σ)
F-Test
Ho: σ1 = σ2
Ha:σ1 ≠ σ2
Stat>ANOVA>Test for
Equal Variances (Requires
Stacked Data) or Stat >
Basic Stat > 2 Variance
(stacked or unstacked)
Yes
One Way ANOVA
Ho: µ1 = µ2 = µ3.....
Ha: at least 2 not equal
Stat>ANOVA>One Way
(then select stacked or
unstacked data)
No
Are σ's
equal
2-Sample t-test
Ho: µ1 = µ2
Ha: µ1 ≠ µ2
Stat>B.S.>2-sample t
(Uncheck the Assume
Equal Variances Box)
Yes
2-Sample t-test
Ho: µ1 = µ2
Ha: µ1 ≠ µ2
Stat>B.S.>2-sample t
(Click the Assume Equal
Variances Box)
mu (µ)
1 Sample t test
(used for Paired-t also)
Ho: µ1 = µt
Ha: µ1 ≠ µt
t = target
Stat>B.S>1 Sample t
(or use CI from
graphical Summary)
Chi Sq Test
Ho: σ1 = σt
Ha:σ1 ≠ σt
t = target
Stat>B.S>D.D.S>G.S
(if σt falls between CI,
then fail to reject Ho)