I am doing an experiment and collecting the data. Now I want to do data analysis. I used water as control, Gibberellic acid and steviol. I make 5 different concentrations in micrograms per mL of each compound, i.e. 0.195, 0.39, 0.78, 1.56, 3.13, 6.25 and give it to lettuce seeds. 30 seeds areused for each compound. After 4 days, I measure the hypocotyl length in cm. Then I find the mean. The mean data are given below.

`Conc. 0.195 0.39 0.78 1.56 3.13 6.25 Water 5.85 5.85 5.85 5.85 5.85 5.85 GA 6.71 7.88 7.65 6.89 5.94 5.92 Steviol 8.46 10.09 8.49 9.18 6.67 5.84 `

How do I find its standard deviation, standard error and P-value?

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#### Best Answer

**Calculating standard deviation**

I hope you still have the data for your 30 cabbage seeds, you will need all of the data, not just the mean.

For the GA with conc 0.195 you had a mean of 6.71cm.

Let $X$ be the length a hypocotyl, the measurements for your 30 seeds are $x_1, x_2, … , x_{30}$

The sample standard deviation $s_{GA}$ can be calculated as:

$s_{GA} = sqrt{frac{1}{30-1} sum_{i=1}^{30}(x_i-6.71)^2}$

You must do the same for the water samples, I don't know if you also had 30 water samples or more. In general, if you have $n$ samples with a mean of $bar{x}$ then the sample standard deviation is

$s = sqrt{frac{1}{n-1} sum_{i=1}^{n}(x_i-bar{x})^2}$

The standard error is simply the standard deviation divided by the square root of the sample size. For your GA chemical that is $SE=frac{s_{GA}}{sqrt{n}}$

**Getting a p-value**

One way you can test the difference between water and GA is to use a one sided t-test for every concentration, you should conduct six hypothesis tests. Doing a t-test is too much to explain in this answer, you will have to learn it yourself.

Since you are doing many hypothesis test you are more likely to find a significant difference when in reality there is no difference (a false positive). You should look into multiple compasison correction to fix this issue.

Estimating the concentration when GA is better than water can be done with a simple interpolation. Or if you want to know the concentration of GA that you are 95% sure is better than water then that will be quite complicated, you should ask a new question for that.

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