Testing of Hypothesis Hypothesis: A statistical hypothesis is an assumption that we make about a population parameter, which may or may not be true concerning one or more variables. According to Pr...
Full description
Hypothesis FormulationFull description
hiFull description
sFull description
Answer of Hypothesis Testing One Sample Test
hypotesis testDeskripsi lengkap
mkjk;;;;;Full description
hypotesis testDeskripsi lengkap
Full description
Potensi pengembangan teknologi nano di Indonesia. Mulai dari bahan mentah hingga teknologi yang dapat di kembangkan di Indonesia. Dokumen juga mencakup data-data kekinian yang dibutuhkan untuk meng...
Full description
~
Probabilistic Multi-Hypothesis Tracking
Full description
Iso 27001 Implementation RoadmapFull description
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 we reject the null hypothesis. The significance level (α or alpha) is typically set at 95% or p-value = 0.05.
Six Sigma Hypothesis Testing Using Minitab For all of the hypothesis tests: p-value ≥ 0.05 – fail to reject H0 p-value < 0.05 – reject H0
NOTE: Nonparametric tests generally require larger sample sizes to discern the same difference (e.g., 10 minutes between 2 cycle time medians vs. 10 minutes between 2 averages). As a general rule of thumb, use 100% to 115% of the sample size computed in Minitab for the comparable parametric test (see also: Asymptotic Relative Efficiency (ARE) or Pitman efficiency).
If your data is not normally distributed, you should analyze 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 window active), type %EDA (column reference) Attempt to fit the curve Stat>Reliability/Survival>(pick one) etc.
no nonparametric methods yes
Do you have more than one sample?
Start
continuous (variable)
Is the data normally distributed?
no
What type of data do you have?
NOTE: Remember to evaluate your sample size requirements β is usually set at 10% for test of means: Stat>Power and Sample Size>(appropriate test)
yes parametric methods
How many samples?
one
attribute (discrete) NOTE: Remember to evaluate your sample size requirements β is usually set at 10% for test of proportions: Stat>Power and Sample Size>(appropriate test)
more than 2
one
variance
two (2) Levene’s Test
mean/median/proportion
only two
How many samples are you testing?
MannWhitney
Ho: ŋ1 = ŋ 2 Ha: ŋ1 ≠ ŋ 2 (where ŋ is the population median) Data: unstacked only Stat>Nonparametrics> Mann-Whitney see Note 2
Ho: σ1 = σ2 = σ3 ... Ha: at least one is different Data: stacked only Stat>ANOVA>Test for Equal Variance use Levene’s statistics
Kruskall Wallis
1-Sample Sign
Ho: all of the population Ho: all treatment Ho: median = medians are equal effects are zero hypothesized median Ha: the medians are not all Ha: not all treatment Ha: median ≠ equal effects are zero hypothesized median Data: stacked only Data: stacked only Data: stacked or Stat>Nonparametrics> Stat>Nonparametrics> unstacked Kruskal-Wallis Friedman Stat>Nonparametrics> see Note 2 see Note 2 1-Sample Sign more powerful than Moods for many distributions Moods One-Sample except Median Test Wilcoxon outliers
Note 1 The hypothesis tests for the Paired t-test (Ho: μ1 μ2 = 0) and Two Sample t-test (Ho: μ1 = μ2) shown in Minitab are different than those traditionally shown. Note that the default Test Mean in Minitab for the Two Sample t-test and Paired t-test is 0 and can be user-defined under using the Options button. Note 2 Generally, the nonparametric median tests assume that the distributions are the same (e.g., sample 1 and sample 2 are both right-skewed).
Ho: all of the population medians are equal Ha: the medians are not all equal Data: stacked only Stat>Nonparametrics> Mood’s Median Test see Note 2 better than Kruskall Wallis for handling outliers
Ho: median = hypothesized median Ha: median ≠ hypothesized median Data: stacked or unstacked Stat>Nonparametrics> 1-Sample Wilcoxon assumes data are a random sample from a continuous, symmetric population
no
One Sample t-Test
Ho: μ = μ0 Ha: μ ≠ μ0 (where μ is the population mean and μ0 is the hypothesized mean) Data: unstacked Stat>Basic Statistics> 1-Sample t
more than 2
two ( 2)
F-Test
two or more
How many samples?
Bartlett’s Test
Are the variances equal?
yes
Two Sample t-Test
Ho: σ1 = σ2 = σ3…. Ha: at least one is different Data: unstacked Stat>ANOVA>Test for Equal Variance use Bartlett’s statistics (F-test if only 2 samples)
yes
no
Two Sample Proportion Test
Evaluate samples two-at-a-time using t-test
H0: p1 - p2 = p0 Ha: p1 - p2 ≠ p0 (where p1 and p2 are the sample proportions and p0 is the hypothesized difference) Data: unstacked or stacked Stat>Tables>Chi Square Test
Ho: μ1 – μ2 = δ0 Ha: μ1 – μ2 ≠ δ0 (where μ1 and μ2 represent population means and δ0 the hypothesized difference) Data: stacked or unstacked Stat>Basic Statistics> 2-Sample t Assume Equal Variances (check)
Paired t-Test
Ho: μd = μ0 Ha: μd ≠ μ0 (where μd represents the population mean of the differences and μ0 the hypothesized mean) Data: unstacked only Stat>Basic Statistics>Paired t See Note 1
Two Sample t-Test
Ho: μ1 – μ2 = δ0 Ha: μ1 – μ2 ≠ δ0 (where μ1 and μ2 represent population means and δ0 the hypothesized difference) Data: stacked or unstacked Stat>Basic Statistics> 2-Sample t Assume Equal Variances (do not check) see Note 1 use (vs. Paired t-Test) when samples are drawn independently from two populations
One Way ANOVA
Ho: μ1 = μ2 = μ3… Ha: at least one is different Data: stacked Stat>ANOVA>One-way for unstacked data use: Stat>ANOVA>One-way (Unstacked)
One Sample Proportion Test Ho: p = p0 Ha: p ≠ p0 (where p is the population proportion and p0 is the hypothesized value) Data: stacked or unstacked Stat>Basic Statistics> 1 Proportion
Contingency Table
Ho: p1 = p2 = p3… Ha: at least one is different Data: unstacked Stat>Tables>Chi Square Test
