1 / 13

An example of single factor ANOVA

An example of single factor ANOVA.

andrew
Download Presentation

An example of single factor ANOVA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. An example of single factor ANOVA E. coli O157:H7 is one of hundreds of strains of the bacterium Escherichia coli. Although most strains are harmless and live in the intestines of healthy humans and animals, this strain produces a powerful toxin and can cause severe illness.(http://www.cdc.gov/ncidod/dbmd/diseaseinfo/escherichiacoli_g.htm)

  2. An example of single factor ANOVA Suppose that a researcher is interested in comparing the ability of 5 different kinds of antibiotics to eliminate E. coli O157:H7. These antibiotics areAmikacin, Gentamicin, Kanamycin, Neomycin, and Streptomycin. The researcher sets up an experiment in which 50 agar-plates are prepared with the same concentration of nutrients mixed with the same concentration of antibiotics for each plate. To eliminate the effect of experience in preparing these plates the researcher picks a number at random between 0 and 4 (using a random number generator)

  3. An example of single factor ANOVA The researcher, then, inoculates each plate with 1mL from 50, 1L, flasks that are previously prepared and continuously shacked to maintain the homogeneity of the E. coli O157:H7 within. This inoculation process was also randomized as described for the plate preparation procedure.

  4. An example of single factor ANOVA The plates were left in the lab over night and were randomly chosen, one at a time, using the same strategy to count the number of surviving cultures or colonies on each of them. This count was used to study the effect of the different antibiotics on E. coli O157:H7 The following table shows these counts.

  5. Counts of antibiotic resistant colonies This data is made up and can’t be used for any purpose other than explaining the concepts of experimental design.

  6. Exploratory analysis: Hypotheses: Linear Model:

  7. Exploratory analysis: Step1: have a look at your data! Step2: Have even a closer look, check the adequacy of the model. 1) Normality of the residuals, and hence the Yij’s (qq-plots). 2) Homogeneity of the variance and outliers (BF-test, standardized-residual plots against predicted values). Step3: Transform (to stabilize the variance and adjust for the violation of normality assumption?). 1) What kind of transformation (regression analysis,if you have enough data, or just a look at the data and try)? Remember that the analysis is on the transformed data!

  8. Exploratory analysis: Step1: have a look at your data again! Step2: Have even a closer look, check the adequacy of the model again. 1) Normality of the residuals, and hence the Yij’s (qq-plots). 2) Homogeneity of the variance and outliers (BF-test, standardized-residual plots against predicted values). 3) Independence of the observations (standardized-residual plots against time of processing). 3) Other candidate variables (standardized-residual plots against other variables). Step3: Transform again? (to stabilize the variance and adjust for the violation of normality assumption). Remember that the analysis is on the transformed data!

  9. Exploratory analysis: Step4: Estimates of summary statistics. Step5: Conduct the ANOVA Step6: Make a decision! 1) Calculate the test statistic. 2) Use either the p-value or the critical value to test.

  10. Exploratory analysis: Step 7: Data snooping 1) Specific contrasts (all of them, Scheffe’)?

  11. Exploratory analysis: Step 7: Data snooping (Cont.) 2) All pair-wise differences (Tukey’s)?

  12. Exploratory analysis: Step 7: Data snooping (Cont.) 3) Assuming the first treatment level was a Control, compare against a control (Dunnett)?

  13. Confirmatory data analysis: Pre-specified orthogonal hypotheses:

More Related