Hypothesis Roadmap

Hypothesis Testing Roadmap ¾ If P > 0.05, then fail to reject HO ¾ If P < 0.05, then reject HO ¾ Ensure the correct sample size is taken.

Contingency Table HO: Data is normal HA: Data is not normal

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Variable or Attribute Data?

Stat>Basic Stat>Normality Test or Stat>Basic Stat>Descriptive Statistics (graphical summary)

Levene's Test H O : σ 1 = σ 2 = σ 3 ... H A : σ i ≠ σ j for i ≠ j

Attribute

2 Factor

1 or 2 Factor?

HO: FA Independent FB HA: FA Dependent FB Stat>Tables>Chi2 Test

Variable

1 Factor

(or at least one is different)

Stat>ANOVA> Homogeneity of Variance If HO is rejected, then you can go no further

2 or more levels

Fail to reject HO

1, 2 or more levels?

Data not Normal

1 Factor

Is data normal?

1 level

1, 2 or more Factors?

1 or >1 Levels?

1-Proportion Test HO: P 1 = P t HA: P 1 ≠ P t

1 Sample 1 level to test

t = target

Stat>Basic Stat> 1-Proportion

2 or more Factors 2-Proportion Test Data Normal

2 or more levels

2 levels or > 2 levels?

Test median or sigma?

2 levels only

Test for sigmas

Mann-Whitney Test

Chi2 Test

HO: M 1 = M 2 HA: M 1 ≠ M 2

HO: σ1 = σt HA: σ 1 ≠ σ t

Stat>Non-parametric> Mann-Whitney

t = target

Mood's Median Test (used with outliers) H O: M 1 = M 2 = M 3 ... HA: M i ≠ M j for i ≠ j

Test Medians

Stat>Basic Stat>Display Desc> Graphical Summary (if target sigma falls between CI, then fail to reject HO)

(or at least one is different)

Stat>Non-parametric> Mood's test

Kruskal-Wallis Test (assumes outliers) HO: M 1 = M 2 = M 3 ... H A: M i ≠ M j for i ≠ j (or at least one is different)

Stat>Non-parametric> Kruskal-Wallis

More than 2 levels

HO: P 1 = P 2 HA: P 1 ≠ P 2 Stat>Basic Stat> 2-Proportion

Bartlett's Test HO: σ1 = σ2 = σ3 ... HA: σ i ≠ σj for i ≠ j

Test for means

(or at least one is different)

Stat>ANOVA>Homogeneity of Variance If sigmas are NOT equal, proceed with caution or use Welch's Test, which is not available in Minitab

1 level

Test for mean or sigma?

2 levels

Test for mean or sigma?

Test for sigmas

Test for means

(or at least one is different)

Stat>ANOVA>1-Way (then select stacked or unstacked data)

Test for means 1-Sample t Test HO: μ1 = μt HA: μ 1 ≠ μ t

Test for sigmas

t = target

Chi2 Test HO: σ1 = σt HA: σ 1 ≠ σt t = target

Stat>Basic Stat>Display Desc> Graphical Summary (if target sigma falls between CI, then fail to reject HO)

1-Way ANOVA (assumes equality of variances) HO: μ1 = μ2 = μ3 ... HA: μ i ≠ μj for i ≠ j

Is Data Dependent?

No, Data is drawn independently from two populations

Yes, Data is Paired

Stat>Basic Stat> 1-Sample t

t = target

Stat>Non-parametric> and either 1-Sample Sign or 1-Sample Wilcoxon

DoE

1, 2 or >2 levels?

1-Sample Wilcoxon or 1-Sample Sign HO: M 1 = M t HA: M 1 ≠ Mt

2 Samples 2 levels to test for each 2 levels

2-Sample t Test F Test HO: σ1 = σ2 HA: σ 1 ≠ σ2 Stat>ANOVA> Homogeneity of Variance

HO: μ1 = μ2 HA: μ1 ≠ μ 2 Stat>Basic Stat> 2-Sample t (if sigmas are equal, use pooled std dev to compare. If sigmas are unequal compare means using unpooled std dev)

Paired t Test HO: μ1 = μ 2 HA: μ 1 ≠ μ2 Stat>Basic Stat> Paired t