tutorial questions 4,Significance Tests – Part 3: One-way ANOVA

1.     The data in the table below give the concentrations of albumin measured in the blood stream of one adult. On each of four consecutive days a blood sample was taken, and three replicate determinations of the serum albumin concentration were made.

Show that the mean concentration for the different days differs significantly. Estimate the variance of the day-to-day variation (i.e. sampling variance)

2.     In order to estimate the measurement and sampling variances when the halofugnone concentration in chicken liver is determined, four sample increments were taken from different parts of the liver and three replicate measurements were made on each. The following results were obtained (mg kg-1):

Verify that the sampling variance is significantly greater than the measurement variance and estimate both variances.

3.     Four analysts take part in a study to evaluate the repeatability and intermediate precision of a method for the determination of arsenic in a sample of PVC. The analysts each analysed five portions of the same, essentially homogeneous, PVC sample under repeatability conditions, each analyst working on a different day. The results recorded are:

a.     Complete a one-way ANOVA table for the data in the table.

b.     Is there a significant difference between the analysts’ results at the 95% level of confidence? If so, is it also significant at the 99% level?

P < 0.05, there difference is significant, P is also < 0.001 so the difference is also significant at this level.