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Statistics 270– Lecture 26

Statistics 270– Lecture 26. Working Example (Moisture Uptake). There is a need to understand degradation of 3013 containers during long term storage Moisture uptake is considered a key factor in degradation due to corrosion Calcination removes moisture

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Statistics 270– Lecture 26

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  1. Statistics 270– Lecture 26

  2. Working Example (Moisture Uptake) • There is a need to understand degradation of 3013 containers during long term storage • Moisture uptake is considered a key factor in degradation due to corrosion • Calcination removes moisture • Calcination temperature requirements were written with very pure materials in mind, but the situation has evolved to include less pure materials, e.g. high in salts (Cl salts of particular concern) • Calcination temperature may need to be reduced to accommodate salts. • An experiment is to be conducted to see how the calcination temperature impacts the mean moisture uptake

  3. Working Example (Moisture Uptake) • Experiment Procedure: • Two calcination temperatures…wish to compare the mean uptake for each temperature • Have 10 measurements per temperature treatment • The temperature treatments are randomly assigned to canisters • Response: Rate of change in moisture uptake in a 48 hour period (maximum time to complete packaging)

  4. Completely Randomized Design • Objective: Comparing the mean of two treatments (1 and 2) • Analysis Objective: • Compare the treatment average responses, 1 vs. 2 • E.g., is there evidence that one treatment is better than other, on average? • Have a separate random sample from each treatment or population • Both populations are assumed to have normal distributions with the same standard deviation, s

  5. Two-Sample Procedure • Experimentation Method: • N experimental units available for the experiment • Randomly assign treatment 1 to n1 experimental units and treatment 2 to n2 experimental units • Note: N = n1 + n2 • Conduct experiment in random order • Measurements: A: x1,1, x1,2, …,x1,n1; B: x1,1, x1,2, …, x1,n2

  6. Useful Plot • Can compare distributions using side-by-side box-plots • What can you see from the plot?

  7. Two Sample t-Test • Goal of Analysis: Test whether or not the treatment means are the same • Statistical Hypothesis: H0: m1 = m2 • Test Statistic:Two-sample t with (n1+n2-2) degrees of freedom • sp=

  8. Two Sample t-Test • Computing p-value depends on the alternate hypothesis: • P-values are exact if the population distribution is normal and approximately correct for large samples in other cases

  9. Analysis of Working Example (Moisture Uptake) • Data:

  10. Analysis of Working Example (Moisture Uptake)

  11. Example • Hypotheses: • Test Statistic • P-value • Conclusion

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