Statistical Procedures, Assumptions and Analysis

Statistical Procedures, Assumptions and Analysis

Step (A). Evaluate the equality of variance assumption using the folded

form of the F statistic (Snedecor and Cochran 1980).1 The null hypothesis is that

the variance of group 1 is equal to the group 2 variance. The alternative

hypothesis is that the variance of group 1 is not equal to the group 2 variance.

These results are shown in Tables B3, B6, and B9. If probability Pr > F is less

than 0.05, the null hypothesis was rejected.

Step (B). If the equality of variance hypothesis is not rejected, the test

statistic was calculated using a pooled estimate of the variance. If the equality of

variance hypothesis is rejected, a test statistic that assumes unequal population

variances was utilized (Snedecor and Cochran 1980). These results are shown in

Tables B2, B5, and B8. The respective hypotheses were expressed as HO: Feed

≤ Bulk and HA: Feed > Bulk; HO: Underflow ≤ Sand and HA:

Underflow > Sand; HO: Overflow ≤ Silt/Clay and HA: Overflow >

Silt/Clay. The one-tailed t-test was conducted at α=0.05. For a one-tailed t-test

halve the Prov >|T| value. Reject the null hypothesis if half the Prob > |T| is less

than 0.05.

From the underflow and sand data one would conclude that the underflow

mean concentrations are less than or equal to the sand mean concentrations

(Table B2). For the current experimental design, the mean comparison for nickel

was the only comparison with a power greater than 0.75. From the overflow and

silt/clay data one would conclude that the arsenic, cadmium, chromium, copper,

lead, mercury, nickel, selenium, silver, zinc, barium, PCB 1242, PCB 1260, oil

and grease, and TRPH overflow mean concentrations are less than or equal to the

silt/clay mean concentrations and the TOC overflow mean concentration is

greater than the silt/clay mean concentration (Table B5). For the current

experimental design, the TOC and TRPH comparisons were the only

comparisons with a power greater than 0.75. From the feed and bulk data one

would conclude that the arsenic, cadmium, chromium, copper, lead, mercury,

nickel, selenium, silver, zinc, barium, PCB 1242, TOC, oil and grease, and TRPH

feed mean concentrations are less than or equal to the bulk mean concentrations

and the PCB 1260 feed mean concentration is greater than the bulk mean

concentration (Table B8). For the current experimental design, the PCB 1242

comparison was the only comparison with a power greater than 0.75.

An alternate way to write the respective hypotheses was HO: Feed = Bulk

and HA: Feed ≠ Bulk; HO: Underflow = Sand and HA: Underflow ≠

Sand; HO: Overflow = Silt/Clay and HA: Overflow ≠ Silt/Clay. Reject

the null hypothesis if the Prob > |T| is less than 0.05.

From the underflow and sand data one would conclude that the underflow

mean concentrations are equal to the sand mean concentrations (Table B2). For

the current experimental design, the nickel and PCB 1260 comparisons were the

References cited in this appendix are included in the References section at the end of the

main text.

Appendix B Statistical Analysis of Results