# The Naked Scientists Forum

### Author Topic: Calculating Statistical Significance???  (Read 5389 times)

#### _Stefan_

• Hero Member
• Posts: 814
##### Calculating Statistical Significance???
« on: 26/08/2007 06:38:50 »
Hi All,

I can't find any info on the internet that would help me to determine the statistical significance of the differences between the results I obtained from a plant growth experiment I completed.

The experimental variable was the color of light the plants received for the entire duration of the experiment. All other factors were generally identical.

I measured the growth of the plants by mass at the end of the experiment.
The results are as follow:

Plants grown under Red light:
13.99 grams

Green light:
12.24 grams

Blue light:
13.47 grams

Clear or White light (control condition):
12.57 grams

Under minimal to no light:
10.03 grams

Assuming all factors excluding the experimental variables were the same, how do I determine the statistical significance of the mass data? I particularly want to know whether the result obtained from the plant growth under green light condition is statistically significant compared to the rest of the conditions. Is there a mathematical formula that will work in grams?

Stefan.

#### Bored chemist

• Neilep Level Member
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##### Calculating Statistical Significance???
« Reply #1 on: 26/08/2007 10:48:30 »
You won't thank me for saying this, but I don't think you have enough data to answer the question.
You don't have any data that tells you how much variation ther is on weight gain under identical conditions. Say you repeated the "plants in green light" experiment a number of times, you would hardly expect to get 12.24g of growth each time.
If you got (and these sre made up numbers)
12.24,
12.28,
12.19,
12.20,
12.25
you could get some idea of the spread of weights that is just due to the natural variation between plants. What you would do would be to calculate a mean and standard deviation for those numbers. (I will let you look up how to do that but the mean is 12.232g and the sd is 0.037g).
If you have a large enough set of data then you can say that 95% of the results will be within 2 times the sd of the average so 95% will be between 12.158g and 12.306g.
Based on that you could say that the 13.47g you got under blue light was odd because it's more than twice the sd away from the average "green" result.
Unfortnately I srtongly suspectr that if you did the experiment on the green lit plants repeatedly you would get a much bigger spread of results and then you couldn't tell if the difference between the green result and the controll result was due to the different lighting, or just part of the natural variation of growth rates.

Did you, by any chance, measure lots of plants and the numbers you gave above are just the total?
If so then you might have enough data to show if there's a real difference or not.

I may get lynched for saying this, but the moral of the story is to talk to a statistician (or learn some statistics) before you do the experiment.

#### _Stefan_

• Hero Member
• Posts: 814
##### Calculating Statistical Significance???
« Reply #2 on: 26/08/2007 11:48:28 »
Hi BC :)

The experiment involved cress seedlings grown from seed for 3 weeks, with approx. the same amount of seeds in each condition (several hundred; I don't have the number with me now). The mass data is the mass of all the seedlings grown in the same condition, clumped together and weighed as one bunch on an electronic balance after washing the soil off of them. So I don't have a mean for them. Counting each and every seedling in each condition and weighing each separately would have been a bit too much to do for such an experiment.

Should I disregard the 'statistical significance' of these results in my experimental report? The teacher is satisfied with simply discussing possible reasons for the differences. I just wanted to know if it could be calculated with my results.

#### WylieE

• Sr. Member
• Posts: 236
##### Calculating Statistical Significance???
« Reply #3 on: 27/08/2007 23:53:11 »
Hi Stefan,

Unfortunately for your homework, I have to agree with BC here.  Unless you measured each of your seedlings individually (I agree, not worth the effort) or had several pots for each light treatment- you have no replicates and so you can't obtain any statistical confidence measurement.  So I don't see how you could possibly put anything down for an answer to "statistical significance" other than "not enough replicates to determine."

If you measured each pot several times you could get an estimate of your technical error.  For example, if you measured the green light grown pot three times you could determine the technical error of your balance and how accurate it is.  But without several replicates (at least three- and more would be better) for each pot in each condition you can't determine statistical significance.

BC's right, this is a good lesson in "understand the statistics before doing the experiment!"  Sometimes it takes people a LONG time (and a lot of money) to learn this lesson, so it is a good thing you are asking these questions now.

Colleen

#### eric l

• Hero Member
• Posts: 514
##### Calculating Statistical Significance???
« Reply #4 on: 28/08/2007 09:40:24 »
What I suggest here is not the "official" procedure, but a very simple one.
From the start, you make one experiment of the series "in duplo" or "in triplo", meaning that you keep all controlled parameters equal for two or three sets.  The level of difference you find between those is surely to be considered insignificant.

#### The Naked Scientists Forum

##### Calculating Statistical Significance???
« Reply #4 on: 28/08/2007 09:40:24 »