7/27/2019 Hypothesis Testing Roadmap 1

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Hypothesis tests are typically used in the Analyze phase to identify the critical x’s (inputs) for a process. Generally, these critical x’s are assumed to exist when

null hypothesis. The significance level ( α or alpha) is typically set at 95% or p-value = 0.05.Six SigmaHypothesis Testing Using Minitab

Two Samplet-Test

Friedman

What typeof data doyou have?

How many

samplesare youtesting?

Levene’s Test

Mann-Whitney

1-SampleSign

Paired t-Test

One Samplet-Test

Bartlett’s Test

KruskallWallis

F-Test

Are the

variancesequal?

Do youhave morethan onesample?

MoodsMedian Test

Ho: σ1 = σ2 = σ3 ...Ha: at least one is differentData: stacked onlyStat>ANOVA>Test for 

Equal Varianceuse Levene’s statistics

onlytwo

two ormore

Two Samplet-Test

One SampleProportion

Test

One WayANOVA

One-SampleWilcoxon

yes no

Ho: ŋ1 = ŋ 2

Ha: ŋ1 ≠ ŋ 2

(where ŋ is thepopulation median)

Data: unstacked onlyStat>Nonparametrics>

Mann-Whitneysee Note 2

no

If your data is not normally distributed, you shouldanalyze the distribution (first look at its shape);consider using: Box Cox transformation

Stat>Control Charts>Box Cox Transformation… EDA macro & brush outliers

Editor>Enable Commands (Session windowactive),type %EDA (column reference)

 Attempt to fit the curveStat>Reliability/Survival>(pick one)

etc.

Ho: all treatmenteffects are zero

Ha: not all treatmenteffects are zero

Data: stacked onlyStat>Nonparametrics>

Friedmansee Note 2

Ho: all of the populationmedians are equal

Ha: the medians are not allequal

Data: stacked onlyStat>Nonparametrics>

Kruskal-Wallissee Note 2more powerful thanMoods for manydistributions -except

outliers

Ho: all of t he populationmedians are equal

Ha: the medians are notall equal

Data: stacked onlyStat>Nonparametrics>Mood’s Median Test

see Note 2better than KruskallWallis for handlingoutliers

Two SampleProportion

Test

C

How manysamples?

nonparametricmethods

parametricmethods

yes

one

two (2)

yes

no

Is the datanormally

distributed?

continuous(variable)

Start

attribute(discrete)

How manysamples?

morethan 2

Ho: σ1 = σ2

Ha: σ1 ≠ σ2

Data: unstacked or stacked

Stat>Basic Statistics>2 Variances

Ho: σ1 = σ2 = σ3….Ha: at least one is differentData: unstackedStat>ANOVA>Test for 

Equal Varianceuse Bartlett’s statistics

(F-test if only 2 samples)

two ( 2)

one

Ho: p = p0

Ha: p ≠ p0

(where p is the populationproportion and p0 is thehypothesized value)

Data: stacked or unstackedStat>Basic Statistics>

1 Proportion

Ho: pHa: aDataStat

Te

H0: p1 - p2 = p0

Ha: p1 - p2 ≠ p0

(where p1 and p2 are the samproportions and p0 is thehypothesized difference)

Data: unstacked or stackedStat>Tables>Chi Square Te

Ho: median =hypothesized median

Ha: median ≠hypothesized median

Data: stacked or unstacked

Stat>Nonparametrics>1-Sample Sign

Ho: median = hypothesized medianHa: median ≠ hypothesized medianData: stacked or unstackedStat>Nonparametrics>

1-Sample Wilcoxonassumes data are a random samplefrom a continuous, symmetricpopulation

Ho: μ = μ0

Ha: μ ≠ μ0

(where μ is the populationmean and μ0 is thehypothesized mean)

Data: unstackedStat>Basic Statistics>

1-Sample t

Ho: μ1 – μ2 = δ0

Ha: μ1 – μ2 ≠ δ0

(where μ1 and μ2 represent populationmeans and δ0 the hypothesized difference)

Data: stacked or unstackedStat>Basic Statistics>

2-Sample t Assume Equal Variances (do not check)see Note 1use (vs. Paired t-Test) when samples aredrawn independently from two populations

Ho: μd = μ0

Ha: μd ≠ μ0

(where μd represents thepopulation mean of thedifferences and μ0 thehypothesized mean)

Data: unstacked onlyStat>Basic Statistics>Paired tSee Note 1

Ho: μ1 – μ2 = δ0

Ha: μ1 – μ2 ≠ δ0

(where μ1 and μ2 represent population meansand δ0 the hypothesized difference)

Data: stacked or unstackedStat>Basic Statistics>

2-Sample t

Assume Equal Variances (check)

Ho: μ1 = μ2 = μ3…Ha: at least one is differentData: stackedStat>ANOVA>One-way

for unstacked data use:Stat>ANOVA>One-way(Unstacked)

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Rev:

Are the

variancesequal?

yes

Evaluate samplestwo-at-a-time using

t-test

no

NOTE: Remember to evaluateyour sample size requirements

β is usually set at 10% for test of means:Stat>Power and SampleSize>(appropriate test)

NOTE: Reyour samp

β is usu for test Stat>PoSize>(a

NOTE: Nonparametric tests generally requirelarger sample sizes to discern the samedifference (e.g., 10 minutes between 2 cycletime medians vs. 10 minutes between 2averages). As a general rule of thumb, use100% to 115% of the s ample size computed in

Minitab for the comparable parametric test(see also:  Asymptotic Relative Efficiency(ARE) or Pitman efficiency).

Note 1The hypothesis tests for the Paired t-test (H o: μ 1 -μ2 = 0) and Two Sample t-test (H o: μ1 = μ2) shownin Minitab are different than those traditionallyshown. Note that the default Test Mean in Minitabfor the Two Sample t-test and Paired t-test is 0 andcan be user-defined under using the Optionsbutton.Note 2Generally, the nonparametric median tests assumethat the distributions are the same (e.g., sample 1and sample 2 are both right-skewed).

For all of the h ypothesis tests: p-value ≥ 0.05 – fail to reject H0

p-value < 0.05 – reject H0