Wednesday, December 29, 2010

Detection of significant difference in means

Hi,

I am a student of MSc Biostatistics, 4th Semester - Final from M S University Vadodara, In this last sem we have to do a project as a part of our academics. I had several options, but I chose the following:

I went to MPharm College of M S University and meet Dr Mohan Maruga Raja. He has just finished his PHd, not awarded yet but would be shortly. I like him very much. He has that mind challenging the traditional knowledge. When I first met him, it was on a tea Shop near Fatehgunj, called Mousi Tea Shop. During 3 hours there, he showed me the excellent knowledge of Statistics which even commom Statistics student would fail to notice. He says. "I am a critic to Statistics", also says, "You statisticians see in a data what you want to see, and then show something different i.e. what they want to see. You people fool them and they are happy with being fooled." It was very nice meeting him. Anyways, let's take a look at his problem.

He is testing 4 natural extracts to find whether they are stimulants or depressants or having no effects on mice. He gave one standard drug to the mice and noted the sleeping time, the sample size was 5. And then the 4 extracts at two different levels were given. The sample size was taken to be 5 for each group. And not to misunderstand, each treatment group was tested on separate 5 mice. The point is that, the sample size was too small to detect any clinically meaningful difference. Morever, the groups were highly variable within them and their mean were near by. So it was very hard to detect the differences. I suggested to increase the sample size, and take repeated observations.

You will have an idea from the following:

So, this is our problem. To detect the significant difference between two groups.





We may have three situations as shown in the following graphs:



Low Variability:

In case of low variability the groups are apperantly different i.e. they are not overlapping much. So, if we apply statistical tools, we will get highly significant results.

Moderate Variability:

For medium variability, with sufficient sample size and appropriate statistical method we can still prove that the groups are significantly different.

High Variability:

We fall in this case, we dont have much sample size first of all. High variability is appearant in both groups. The curves overlaps too much. Do we have statistical tools to detect this difference? I was thinking of Non-Parametric tests. Box-plot can also give us an idea about the distribution. Also we may use ANOM which is a graphical method to analyze such data. But the problem is still that, how do we detect this difference?


Note one thing in graph that the difference between two distributions is the same in all the three cases. Also the variability i.e. spread is same for the two groups.

Our case is very important because we are testing the natural extracts for their efficacy. So, if there is no effect seen, the extract will be discarded from the study. The natural extracts generally have many active ingrediants, so evenif, one of them is powerful, it's effect is masked by other co-existing molecules and then it is lost in the lab.

Let's see what can be done...

Other links: http://www.socialresearchmethods.net/kb/statsimp.php







Bhavin Solanki
29th December 2010
Contact : 98252 78799
e-mail : strikeagle.lx@gmail.com

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