This repository contains Excel-based case study demonstrating how to apply parametric testing to real-world manufacturing operations data including:
- 1 Sample T.Test and Z.Test
- Chi-Square Hypothesis test
- 2 Sample Independent T.Test
- 2 Sample Paired T.Test
- F.Test for independent groups
- Means of Two groups - Comparison
- Analysis of Variance (ANOVA)
These tests help to determine whether a sample mean differs significantly from a known or hypothesized population mean. But they differ in when and why you use each.
| 1 Sample Z.Test | 1 Sample T.Test |
|---|---|
| 1. Population standard deviation is known | 1. Population standard deviation is unknown |
| 2. Sample size is large (typically n≥30) | 2. Sample size is small (n<30) |
| 3. Population is normally distributed | 3. Population is assumed to be approximately normal |
| 4. To test if the sample mean (x̄) is significantly different from a known population mean (μ), assuming σ is known | 4. To test if sample mean differs from the population mean. But the t-distribution accounts for extra uncertainty in estimating σ from the sample |
- To test if two categorical variables are independent (e.g. gender vs. preference)
- Or to test goodness-of-fit - whether observed frequencies match expected ones
- To determine if there's a statistically significant association between categorical variables
- To compare two related samples (same group before and after treatment)
- To test if the mean difference is significantly different from 0
- To evaluate if a treatment, intervention, or change has had a statistically significant effect
- To compare two independent groups (e.g Group A vs Group B)
- The population standard deviations are unknown but assumed equal or unequal
- To test whether the means of two independent samples are significantly different
- To test if two groups have equal variances
- Often used before running a T.Test to determine if equal-variance T.Test or Welch's T.Test should be used
- To compare variability between two independent samples
- Understand the significant difference in the outcome of two process
- Understand whether a new process is better than the old process
- Understand whether two samples belong to the same population or different populations
- Benchmark the existing process with another benchmarked process
- Used to compare more tha two samples
- Stands for Analysis of Variance
- Helps in understanding that all sample means are not equal
- ANOVA based significant samples can be tested further
- Generalize the T.Test to include more than two samples
- Steel rod length validation using one-sample Z.Test
- Test whether the mean fill weight differs from the target using one-sample T.Test
- Determine if the variance in diameter of rods from a new batch significantly differs from the historical variance using Chi-Square test
- Determine whether the batch numbers from Day shift differs significantly from the night shift using Two sample T.Test
- Determine whether the variances of batch output from Machine A and Machine B are significantly different using F.Test
- Test whether the means of batch productions by Machine A, Machine B and Machine C are significantly different using one-way ANOVA
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Situation: On the shop floor, the planning manager at the Hot Rolling division recently changed the Slitting machine to improve the parting (cut along the length) process of output steel sheet. To understand the quality of the machine on parting, the team has taken the 75 data points. Subsequently, the manager decided to consider the population for analysis taking sample of 50 data points.
Inference: One sample Z.Test || From the excel analysis, p-value ~ 0, it means the probability of observing such an extreme result (or more extreme) under the null Hypothesis (H₀) is extremely low - so low that is effectively 0. You have a very strong evidence against H₀
Conclusion: - Reject H₀ at any common significance level - The selected sample provides overwhelming evidence that the true population parameter is not equal to the null hypothesis value
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Situation: At the warehouse, the Inbound inventory manager suspects that there's a packaging fill weight has drifted from the target of 250 gm of paper. Ideally, identical steel rods possess same weight, if there's any deviation in the packaging weight, then the root cause lies in the machine through which the steel rod has passed finally. In steel manufacturing plant, it is packaging machine. Now, the manager wants to audit the machine accuracy but he is not sure about the population standard deviation.
Inference: One sample T.Test || From the excel analysis, p-value ~ 0, it means the probability of observing sample result (or more extreme) assuming the null hypothesis (H₀) is true.
Conclusion: - Reject H₀ as we have extremely low p-value i.e., we have overwhelming evidence against H₀ - The result is statistically significant - There is an extremely strong difference between the groups (or treatment effect)
-
Situation: At the factory, the quality engineer wants to check the current batch coming out of the punching machine. The punching machine was changed a few days ago and the plant is targetting variance in rod thickness to be 0.01 mm². In this aspect, the engieer wants to checks the sample of nearly 50 batches of steel. When cleansed, the sample size of punching machine turns out to be only 7
Inference: Chi-Square Test for variance || From the excel analysis, p-value ~ 0, it means the probability of observing sample result (or more extreme) assuming the null hypothesis (H₀) is true.
Conclusion: - Reject H₀ as we have extremely low p-value i.e., we have overwhelming evidence against H₀ - The result is statistically significant - There is an extremely strong difference between the groups (or treatment effect)
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Situation: The factory manages two different production shifts (Day & Night) that manufactures steel rods. Now, the quality engineer wants to test if there's a significant difference in the average number of batches produced during each shift
Inference: Two-sample T-Test || From the excel analysis, p-value ~ 0, it means the probability of observing sample result (or more extreme) assuming the null hypothesis (H₀) is true.
Conclusion: - Reject H₀ as we have extremely low p-value i.e., we have overwhelming evidence against H₀ - The result is statistically significant - There is an extremely strong difference between the groups (or treatment effect)
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Situation: At the factory, the quality engineer in the steel manufacturing plant received a call that one of the two machines used to slit the product BPL_F is slitting the produced parts with more variability than the other.
Inference: F-Test || From the excel analysis, p-value = 0.692, it means the probability of observing sample result (or more extreme) assuming the null hypothesis (H₀) is not true
Conclusion: - Fail to reject H₀ as we have high p-value - The result is no statistically significant difference in variance between the two machines - The process variability is considered similar
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Situation: At the factor, the production planning analyst wants to check if three different slitting machines (A, B, C) perform slitting operation with significantly different average rates
Inference: ANOVA single factor || From the excel analysis, p-value = 0.692, it means the probability of observing sample result (or more extreme) assuming the null hypothesis (H₀) is not true
Conclusion: - Fail to reject H₀ as we have high p-value - The result is no statistically significant difference in variance between the two machines - The process variability is considered similar
CharacteristicValue3_dataset.xlsx
- IF()
- T.DIST()
- RAND()
- RANDBETWEEN()
- STDDEV.P()
- COUNTIF()
- AVERAGE()
- SQRT()
- NORM.S.DIST()
- Dynamic Arrays
- COUNT()
- T.DIST.RT()
- ABS()
- T.DIST.2T()
- VAR.S()
- CHISQ.DIST.RT()
- CHISQ.INV()
- CHISQ.INV.RT()
- MAX()
- MIN()
- F.TEST()
- ANOVA()
- Microsoft Excel 2016 or later
- Business Statistics, Production Scheduling
"Torture the data, and it will confess to anything. - Ronald Coase"