# statistical test to run - T test or Whitney rank test (Nov/16/2008 )

I am writing a mock grant to use a live vaccine (attenuated mutant) and see if it protects against challenge with wildtype I have put together the following procedure.

Protocol:

Thirty two BALB/c mice, six to 8 weeks old will be anesthetized. The mice will be intranasally vaccinated with 106 colony forming units (CFU) of FT subsp. novicida vgrG (ΔvgrG) mutant (FTN ΔvgrG) in phosphate buffered saline (PBS). Six of the twenty four will by mock vaccinated with PBS only.

Four weeks after vaccination all animals will be challenged with increasing CFU of U112. The LD50 of U112 is approximately 10 CFU (3), therefore the chosen doses will be 10^ 3, 10^4, and 10^5 CFU of U112. In summary, there will be the 6 mice per the following treatments: (1) PBS vaccinated mice challenged with 103 U112 CFU (2) 106 FTN ΔvgrG CFU vaccinated mice challenged with 10^3 U112 CFU (3) 106 FTN ΔvgrG CFU vaccinated mice challenged with 104 U112 CFU (4) 106 FTN ΔvgrG CFU vaccinated mice challenged with 105 U112.

The efficacy of the intranasal vaccination will be determined by plotting the percent survival of each group against the days after vaccination/challenge. The percent survival will be acquired by comparing the amount of mice alive from the vaccinated and challenged groups after the day that all the mice from mock vaccinated and challenged group die. All mice from the mock vaccination and challenge group are expected to all die due to the fact that the challenge CFU is folds higher than the known LD50.

I thought I would compare

group 1: unvaccinated challenged with group 2:vaccinated 10^3challenged

group 1: unvaccinated challenged with group 3: group vaccinated 10^4 challenged

group 1: unvaccinated challenged with group 4:vaccinated 10^5challenged

So essentially I thought that if the average amount of mice survived after unvaccinated death would be used. And since I am comparing two things it would be a students t test. However, if i ran this experiment a couple of times and found out that the amount of mice surving each time was not normally distributed among the experiments, then I would use a Whitney Rank sum test?

Is this correct assumption??

Protocol:

Thirty two BALB/c mice, six to 8 weeks old will be anesthetized. The mice will be intranasally vaccinated with 106 colony forming units (CFU) of FT subsp. novicida vgrG (ΔvgrG) mutant (FTN ΔvgrG) in phosphate buffered saline (PBS). Six of the twenty four will by mock vaccinated with PBS only.

Four weeks after vaccination all animals will be challenged with increasing CFU of U112. The LD50 of U112 is approximately 10 CFU (3), therefore the chosen doses will be 10^ 3, 10^4, and 10^5 CFU of U112. In summary, there will be the 6 mice per the following treatments: (1) PBS vaccinated mice challenged with 103 U112 CFU (2) 106 FTN ΔvgrG CFU vaccinated mice challenged with 10^3 U112 CFU (3) 106 FTN ΔvgrG CFU vaccinated mice challenged with 104 U112 CFU (4) 106 FTN ΔvgrG CFU vaccinated mice challenged with 105 U112.

The efficacy of the intranasal vaccination will be determined by plotting the percent survival of each group against the days after vaccination/challenge. The percent survival will be acquired by comparing the amount of mice alive from the vaccinated and challenged groups after the day that all the mice from mock vaccinated and challenged group die. All mice from the mock vaccination and challenge group are expected to all die due to the fact that the challenge CFU is folds higher than the known LD50.

I thought I would compare

group 1: unvaccinated challenged with group 2:vaccinated 10^3challenged

group 1: unvaccinated challenged with group 3: group vaccinated 10^4 challenged

group 1: unvaccinated challenged with group 4:vaccinated 10^5challenged

So essentially I thought that if the average amount of mice survived after unvaccinated death would be used. And since I am comparing two things it would be a students t test. However, if i ran this experiment a couple of times and found out that the amount of mice surving each time was not normally distributed among the experiments, then I would use a Whitney Rank sum test?

Is this correct assumption??

If there are only small deviations from normal distribution (an the other preconditions) you can use ANOVA (it is quite robust) and post hoc tests (e.g. Tukey's); or if you exactly know which groups you want to compare a priori tests (i.e. contrasts) with very high power. Otherwise transform your data to have data better fitting to ANOVA preconditions.

Protocol:

Thirty two BALB/c mice, six to 8 weeks old will be anesthetized. The mice will be intranasally vaccinated with 106 colony forming units (CFU) of FT subsp. novicida vgrG (ΔvgrG) mutant (FTN ΔvgrG) in phosphate buffered saline (PBS). Six of the twenty four will by mock vaccinated with PBS only.

Four weeks after vaccination all animals will be challenged with increasing CFU of U112. The LD50 of U112 is approximately 10 CFU (3), therefore the chosen doses will be 10^ 3, 10^4, and 10^5 CFU of U112. In summary, there will be the 6 mice per the following treatments: (1) PBS vaccinated mice challenged with 103 U112 CFU (2) 106 FTN ΔvgrG CFU vaccinated mice challenged with 10^3 U112 CFU (3) 106 FTN ΔvgrG CFU vaccinated mice challenged with 104 U112 CFU (4) 106 FTN ΔvgrG CFU vaccinated mice challenged with 105 U112.

The efficacy of the intranasal vaccination will be determined by plotting the percent survival of each group against the days after vaccination/challenge. The percent survival will be acquired by comparing the amount of mice alive from the vaccinated and challenged groups after the day that all the mice from mock vaccinated and challenged group die. All mice from the mock vaccination and challenge group are expected to all die due to the fact that the challenge CFU is folds higher than the known LD50.

I thought I would compare

group 1: unvaccinated challenged with group 2:vaccinated 10^3challenged

group 1: unvaccinated challenged with group 3: group vaccinated 10^4 challenged

group 1: unvaccinated challenged with group 4:vaccinated 10^5challenged

So essentially I thought that if the average amount of mice survived after unvaccinated death would be used. And since I am comparing two things it would be a students t test. However, if i ran this experiment a couple of times and found out that the amount of mice surving each time was not normally distributed among the experiments, then I would use a Whitney Rank sum test?

Is this correct assumption??

If there are only small deviations from normal distribution (an the other preconditions) you can use ANOVA (it is quite robust) and post hoc tests (e.g. Tukey's); or if you exactly know which groups you want to compare a priori tests (i.e. contrasts) with very high power. Otherwise transform your data to have data better fitting to ANOVA preconditions.

But what I dont understand is that I am not looking to compare within the treatments just between the unvaccinated and vaccinated. I just happen to have different amounts of CFU vaccinations that I will also be looking at, each one independently.

I agreed with Hobglobin. You also can use general linear model (GLM) for test for normal distribution.

Reading it again I'd rather use a regression analysis, and with the p-value and r

^{2}you see if there is a relation between drug dose and mortality. Or better Kaplan-Meier analysis (survival analysis) that can then be tested with Wilcoxon or Mantel-Cox tests if there a differences between groups. But I never did this type of analysis, don't know if it's too laborious.

BTW if you use ANOVA you can use Dunnett's test, it tests one reference group against the other groups.

Reading it again I'd rather use a regression analysis, and with the p-value and r

^{2}you see if there is a relation between drug dose and mortality. Or better Kaplan-Meier analysis (survival analysis) that can then be tested with Wilcoxon or Mantel-Cox tests if there a differences between groups. But I never did this type of analysis, don't know if it's too laborious.

BTW if you use ANOVA you can use Dunnett's test, it tests one reference group against the other groups.

I appologize I essentially would like to compare the amount of animals that survived for each vac/challenge group against the mockvac/challenge group.

So it would be like percent survival.

A paper did something that I want to do. but they report their statistics using the Mann Withney Rank sum test. However my impression was that this test is like a students t test however, your values are not normally distributed. But since I have not run the tests I would not know if my data is going to be equally distributed.

I uploaded a figure. Essentially he did a percent survival. So group vaccinated then challenged with 10^3 CFU had 80% survival.....sort of statement. Hope maybe this will clarify.

Off note,

Additionally, I was told that a students t test was almost identical to a one way anova except an anova has more power. So when do you use a one way and when do you use a students t test.

ANOVA is for multiple samples, t-test is for 2 samples. Essentially an ANOVA is similar to performing multiple t-tests all at once, however if you actually try to perform multiple t-tests to compare more than two samples you run into the problem of increased chance of type one errors.

thanks I read up on that just recently, and I now see that one might run an ANOVA and then check between each group with a tukey test...so essentially like doing a t test between the ones you want is that right?

Thanks to previous person I believe a one way anova followed by a dunnette test is the best is my case.

thanks I read up on that just recently, and I now see that one might run an ANOVA and then check between each group with a tukey test...so essentially like doing a t test between the ones you want is that right?

Thanks to previous person I believe a one way anova followed by a dunnette test is the best is my case.

Yes except that anova avoids the problem of increased chance of type one errors as bob1 wrote. Use it with Dunnett's post hoc test.

BTW the picture really looks like Kaplan-Meier analysis.

From the figure you showed, the test is survival analysis either by constructing kaplan-Meier survival curves or using cox proportional regression model. Both approaches can be easily done by SAS or SPSS. Survival analysis is an appropriate method for your data after reading your message again (agree with hobglobin).