Hypothesis Testing with Excel and the QI Macros

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Hypothesis testing helps identify ways to reduce costs and improve quality. Hypothesis testing asks the question: Are two or more sets of data are the same or different, statistically:

What's cool about Hypothesis Testing in the QI Macros?
Unlike other statistical software, the QI Macros is the only SPC software that compares the p-values to the significance level and tells you when to "Accept or Reject the Null Hypothesis." The QI Macros results also tell you: "Means are Same or Different or Variances are Same or Different. "

Watch the Hypothesis Testing in Excel Video

In Six Sigma, hypothesis testing helps identify differences between machines, formulas, raw materials, etc. and are the differences statistically significant or not. Without such testing, teams can run around changing machine settings, formulas and so on causing more variation. These knee-jerk responses can amplify variation and cause more problems than doing nothing at all.

In manufacturing, you might want to compare two or more types of raw materials and determine if they produce the same quality. In other words, do the products have the same or different means and variances? If they are the same, which one is less expensive to produce? If they are different, which one best meets the customer's requirements?

There are Three Types of Hypothesis Tests

  • Classical Method - comparing a test statistic to a critical value
  • p value Method - the probability of a test statistic being contrary to the null hypothesis
  • Confidence Interval Method - is the test statistic between or outside of the confidence interval

Setting Up a Hypothesis Test

First, you will need to define a null (H0) and an alternate (Ha) hypothesis.

By default, the null hypothesis assumes that differences among observations are due to chance. In other words, it assumes that the means, averages or variation are statistically the same. The goal is to prove that they are not statistically the same at some level of confidence (usually 95%, 99%).

Tests can be either two sided or one sided depending on how the null hypothesis is stated.

Null Hypothesis- two sided test Alternate Hypothesis - two sided test

Average1 = Average2
Mean1 = Mean2
Mean1 - Mean2 = 0 (no difference)

Average1 not = Average2
Mean1 not = Mean2
Mean1 - Mean2 not = 0
Variance1 = Variance2 Variance1 not = Variance2

Null Hypothesis - one sided test Alternate Hypothesis - one sided test

Average1 <= Average2
Average1 >= Average2
Mean1 <= Mean2
Mean1 >= Mean2
Mean1 - Mean2 <= 0
Mean1 - Mean2 >= 0

Average1 > Average2
Average1 < Average2
Mean1 > Mean2
Mean1 < Mean2
Mean1 - Mean2 > 0
Mean1 - Mean2 < 0

Variance1 <= Variance2
Variance1 > = Variance2
Variance1 > Variance2
Variance1 < Variance2

Then, using data from the test:

  1. Calculate the test statistic (t test, f test, z test, ANOVA, etc.).
    The test statistic is often converted to a p value (probability), but not always.
  2. Compare the test statistic to:
    • a significance level (a) or confidence level (1-a)
    • a critical value (e.g., Fcrit)
    to determine if you can accept or reject the null hypothesis.
Hypothesis Test
Compare
Result
Classical Method test statistic > critical value
(i.e. F > F crit)
Reject the null hypothesis
Classical Method test statistic < critical value
(i.e. F < F crit)
Accept the null hypothesis
p value Method p value < a Reject the null hypothesis
p value Method p value > a Accept the null hypothesis

Determining the Correct Test Statistic

Consider your data.
Is it variable (i.e., measured - 3.4 lbs) or attribute (i.e., counted - 3 defects)?
Are there one, two or more samples?

Variable Data 1 Sample 2 Samples 2 or More Samples
Variances   F-Test for normal data
Levenes Test for non-normal data
One Factor t-test one sample t-test of Means

Tukey Quick Test
ANOVA
One Way ANOVA
Two Factor     Two Way ANOVA
Two Way ANOVA with Replication

Attribute Data 1 Sample 2 Samples 2 or More Samples
One Factor One Sample Proportion Test Two Sample Proportion Test Chi Square Test
Two Factor     Chi Square Test

Are you comparing the means or variance?

Number of levels or treatments 1 2 3+
Mean (Average) t-test
one sample
t test ANOVA
One Way ANOVA

Two Way ANOVA
Two Way ANOVA with Replication
Variance (Standard Deviation2)   F test ANOVA
One Way ANOVA
Two Way ANOVA
Two Way ANOVA with Replication
    Z Test  

Type I and II Errors

Hypothesis testing seeks to determine if the means or variances are the same or different at some level of confidence. Since we can never be totally confident, it is possible to encounter two types of errors:

  • Type I error - Reject a null hypothesis that is true (Producer's Risk)
  • Type II error - Not reject a null hypothesis that is false (Consumer's Risk)

Choose a confidence (or significance) level that will minimize the risk associated with these errors.

Watch the Hypothesis Testing in Excel Video

All of these hypothesis tests are included in the QI Macros Statistical Process Control software.

Download the FREE 30-day Evaluation copy of the QI Macros Excel SPC Software for Six Sigma

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