The One Sample Variance Test is a statistical hypothesis test used in the Analyze Phase of Lean Six Sigma to determine whether the variance of a single sample differs significantly from a known or hypothesized population variance. This test is essential when you need to assess process consistency a…The One Sample Variance Test is a statistical hypothesis test used in the Analyze Phase of Lean Six Sigma to determine whether the variance of a single sample differs significantly from a known or hypothesized population variance. This test is essential when you need to assess process consistency and variability against established standards or specifications.
In Lean Six Sigma projects, understanding variance is crucial because excessive variation often indicates process instability and potential quality issues. The One Sample Variance Test helps Green Belts evaluate whether observed variation in their process data deviates from an expected or target variance value.
The test uses the chi-square distribution to compare the sample variance against the hypothesized population variance. The null hypothesis states that the population variance equals the specified value, while the alternative hypothesis suggests the variance is different from, greater than, or less than the specified value, depending on whether you conduct a two-tailed or one-tailed test.
To perform this test, you need to calculate the chi-square test statistic using the formula: χ² = (n-1) × s² / σ², where n represents sample size, s² is the sample variance, and σ² is the hypothesized population variance. The resulting value is then compared against critical values from the chi-square distribution table based on your chosen significance level and degrees of freedom.
Key assumptions for this test include that the data must come from a normally distributed population, observations must be independent, and the sample should be randomly selected. Violating these assumptions can lead to unreliable results.
Practical applications in Lean Six Sigma include verifying that a manufacturing process maintains acceptable variability levels, comparing current process variation against historical benchmarks, and validating that implemented improvements have reduced process variance. This test provides Green Belts with objective evidence to support data-driven decisions about process performance and capability during the Analyze Phase.
One Sample Variance Test: Complete Guide for Six Sigma Green Belt
Why is the One Sample Variance Test Important?
The One Sample Variance Test is a critical statistical tool in Six Sigma because process consistency is just as important as hitting target values. In manufacturing and service industries, excessive variation leads to defects, customer dissatisfaction, and increased costs. This test allows quality professionals to determine whether a process meets variance specifications, making it essential for the Analyze phase of DMAIC.
What is the One Sample Variance Test?
The One Sample Variance Test (also called the Chi-Square Test for Variance) is a hypothesis test used to compare the variance or standard deviation of a single sample against a known or specified population variance. It helps answer the question: Is our process variability different from what we expect or require?
The test uses the chi-square distribution and is appropriate when: - You have continuous data from a single population - The data is approximately normally distributed - You want to test claims about population variance or standard deviation
How Does the One Sample Variance Test Work?
Step 1: State the Hypotheses - Null Hypothesis (H₀): σ² = σ₀² (population variance equals the specified value) - Alternative Hypothesis (H₁): σ² ≠ σ₀², σ² > σ₀², or σ² < σ₀² (depending on the test type)
Step 2: Calculate the Test Statistic The chi-square test statistic formula is: χ² = (n - 1) × s² / σ₀²
Where: - n = sample size - s² = sample variance - σ₀² = hypothesized population variance
Step 3: Determine Critical Values or P-value Using the chi-square distribution with (n - 1) degrees of freedom, find the critical values based on your significance level (α).
Step 4: Make a Decision Compare your test statistic to the critical values or compare the p-value to α. Reject H₀ if the test statistic falls in the rejection region or if p-value < α.
Example Application
A manufacturer specifies that the variance in fill weights should be no more than 4 grams². A sample of 25 containers shows a variance of 5.2 grams². At α = 0.05, test if the variance exceeds specifications.
H₀: σ² ≤ 4 H₁: σ² > 4
χ² = (25 - 1) × 5.2 / 4 = 31.2
Critical value at α = 0.05 with 24 df = 36.415
Since 31.2 < 36.415, we fail to reject H₀. There is insufficient evidence that variance exceeds specifications.
Exam Tips: Answering Questions on One Sample Variance Test
1. Know the Formula Inside Out Memorize χ² = (n - 1) × s² / σ₀². Exam questions frequently require calculating this statistic.
2. Understand When to Use This Test Choose this test when the question asks about variance or standard deviation of a single sample compared to a standard. Do not confuse it with tests for means.
3. Pay Attention to One-Tailed vs Two-Tailed Tests - Use two-tailed when testing if variance is different from a value - Use upper-tailed when testing if variance exceeds a value - Use lower-tailed when testing if variance is less than a value
4. Watch for Standard Deviation vs Variance If given standard deviation, square it to get variance before using the formula. This is a common trap in exam questions.
5. Remember Degrees of Freedom Always use (n - 1) for degrees of freedom, not n.
6. Check Assumptions If asked about test validity, remember the normality assumption is crucial for this test. The chi-square test for variance is sensitive to departures from normality.
7. Interpret Results Correctly When p-value < α, reject the null hypothesis. When p-value ≥ α, fail to reject the null hypothesis. Never say you accept the null hypothesis.
8. Connect to Six Sigma Context Understand that this test helps verify process capability and consistency, which are key concerns in the Analyze phase when investigating root causes of variation.