I need to perform a paired t-test on the following data (i thinki, it might be unpaired???)

 

 

the null hypothesis is "The size of the zone of inhibition caused the antibiotic is not influenced by the gram type of the bacteria".

 

Any help plz plz!

 

p.s. E.coli, and the two pseudomonas are gram negative and the rest are gram positive.

i have so far done this

 

[pre]

Statistical test

 

I will be using an paired t-test for my statistical test.

 

My null hypothesis is:-

 

The size of the zone of inhibition caused the antibiotic is not influenced by the gram type of the bacteria.

 

Let G+ represent gram positive and G- represent gram negative

 

Ampicillin

 

n = 9

 

Mean of G+ = (4+3+4+5.5+5+6+7.5+7+6.5)/9

= 48.5/9

= 5.389

 

G+ G+ - G+

(G+ - G+)2

(G+ - G+)2/n

 

4 -1.389 1.929 0.214

3 -2.389 5.707 0.634

4 -1.389 1.929 0.214

5.5 0.111 0.0123 1.37 x10-3

5 -0.389 0.151 0.0168

6 0.611 0.373 0.0415

7.5 2.111 4.457 0.495

7 1.611 2.596 0.288

6.5 1.111 1.235 0.137

Total = (s+2) 2.043

 

Mean of G- = (0+0+0+0+0+0+4+4+4)/9

= 12/9

= 1.333

 

G- G- - G -

(G- - G-)2

(G- - G-)2/n

 

0 -1.333 1.778 0.198

0 -1.333 1.778 0.198

0 -1.333 1.778 0.198

0 -1.333 1.778 0.198

0 -1.333 1.778 0.198

0 -1.333 1.778 0.198

4 2.667 7.111 0.790

4 2.667 7.111 0.790

4 2.667 7.111 0.790

Total = (s-2) 3.556

 

t-value = G+ - G- = 4.242

 

s+2 + s-2

n

 

I have n-1 degrees of freedom = 9 - 1 = 8

 

For 8 degrees of freedom the 5% limit is 1.860. I have a value larger than this so I reject my null hypothesis, the gram type of the bacteria does influence the action of ampicillin.

 

[/pre]

 

and presumbable iu just do this for each antibiotic?

arrg, my html is rusty as a very rusty thing, but you get the idea i'm sure.

I had to do this once and its rather a bugger and made a simple Highschool bio project a b@5tard, ill go look for the method to do it.

was lying round here somewhere.........

It's not a paired t-test you need. The bacteria are either G+ or G-. You have split your sample into two independent groups using this variable, so you need to use an independent t-test.

 

The paired t-test uses the pooled variance and is therefore more conservative, than the independent t-test as it assumes the two samples of data are from the same population (and thus that the inherent variance is less than it would be for two separate groups). Thus you have an increased probability of a type II error using a paired t-test on independent samples.

By the way, I just read the bit where you said "and presumably I just do this for each antibiotic?". Running multiple t-tests is a very tedious way of doing it. You'd be better of using a 2x3 2-Way ANOVA. Your two factors are Gram, with two levels: +ve or -ve, and Antibiotic, with three levels: Ampicillin, Tetracycline and Streptomycin (or four if you include your control, which would make it a 2x4 2-Way ANOVA).