At the very least you’d want to test the null hypothesis that the mean diameter of a treated disc is the same as an untreated disc, against the one-sided alternative that the diameter of a treated disc is greater than an untreated disc. The p-value has to be looked up on a table for the number of degrees of fredom for the particuar test. There is no problem with unequal sized groups. There is a version of the test that uses pooled estimates for the standard deviation used to make the t-statistic. I don’t know what your control (non-treated) disc diameter is, unless that is what the four discs of chlorox wipes is supposed to be. Google t-test.

You’re not saying this, but I assume that the diameter you’re talking about is the diameter of the disc plus any halo surrounding the disc. If the antibiotic works, there should be a halo of clear agar surrounding the disc, where the antibiotic prevented the bacterial lawn from encroaching.

The null hypothesis states that there is no significant difference between your controls and treatments. Usually this means difference is within 2 SD(95% confidence level).

The null hypothesis here, is the assertion that the mean diameter of the experimental discs is the same as the mean diameter of the control discs. The only things you “put in” are the means and standard deviations of the two groups when you calculate the t-statistic for the comparison. If you know how to do this for equal-sized groups, then you already know how to do it for unequal-sized groups. The only difference is the treatment of the standard deviations. You can easily find the formula for both kinds of tests (equal or unequal sized groups) by googling “t-test” or maybe “Student’s t-test”. Once you’ve calculated your t, you have to compare it to a tabulation of t-values calculated for your degrees of freedom and see whether your observed t is large enough to reject the null hypothesis or not. If it is, then you can reject the null hypothesis of no difference and claim that the antiobiotic had a significant effect.

Mith is saying the same thing. This way is just more formal.

Oh yeah, and you should take blcr’s suggestion of using the student curve if your sample size is small.

The function, =TTEST(array1,array2,tails,type), returns the p-value for a student’s t-test between the data in array1 vs array2. Tails will be either 1 (one-tailed or one-sided) or 2 (two-tailed or two-sided) test. Type will be 1 (paired), 2 (equal-variance), or 3 (unequal variance). If you have a calculator with statistical function capability, you can probably do the t-test there, as well. I think a TI-83 or better will even calculate the p-value of the test.

The null hypothesis is that the mean disc diameter of Group A = the mean disc diameter of Group B. The observed t-statistic is large enough to reject the null hypothesis at the p=0.01 (or 99%) confidence level. What the p-level is telling you is that there is only a 1% chance of the null hypothesis being correct, given the observed t-statistic. The interpretation is that the antibiotic inhibited the growth of the bacteria as indicated by the significantly larger halo of non-growth surrounding the treated discs compared to control, non-treated discs. That the 95% confidence intervals about the means don’t overlap for the two groups is also evidence that the means are significantly different at the p=0.05 level, but you can reject the null at the stronger, p=0.01 level, so who cares.

p = 0.01 means 1% probability the results are due chance… it doesn’t mean 1% chance null hypothesis being correct…

Both statements say the same thing.

It’s one of those stat professor semantics thing, the null hypothesis is either correct or not, there is no probability associated with it.

no… it doesn’t mean the same thing… if p>0.05 the null hypothesis isn’t ‘correct’… you can’t say if it is correct or not using the t-test… you would need a p value of 1 to state this (which is impossible)… you can say if it is incorrect or there is not enough evidence that it is incorrect…

it means that there is more than a 5% chance that the results are due to chance and therefore the results are not stastically significant at the 95% confidence interval… this is because there is not enough evidence that the null hypothesis is incorrect…

It is a subtle point and I don’t want to belabor it. Both ways do, in fact, say the same thing: rejecting the null at p=0.01 is the same thing as saying there is only a 1% chance that the null is correct (maybe I should have said, “True”). The power of a statistical test is the probability of committing a Type I error—falsely rejecting the null when it is true in favor of an alternative. That Pr[Mean1 = Mean2] = 0.01 means that it is unlikely the null hypothesis is true relative to an alternative. In making the decision to reject the null at the 0.01 level, you are saying you will accept the 1 in 100 chance of making a Type I error in favor of an alternative that is more likely to be true based on the observations. I’m not saying that the phrase “can happen by chance” is wrong—it is, in fact, the customary language of statistics. But our questioner seemed to be having trouble even with the idea of a null hypothesis; I figured formal language would be a wash here, so I tried to use something more akin to plain English. If that offends statistical purists, then I’m offensive, but not wrong.