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