Statistics - how do you know which test to apply to experimental results?

Answer 1

The experimental design will determine which statistical tests are appropriate to determine whether there is a difference between (among) the control and experimental treatments. Your hypothesis is that there will be a difference. Your null-hypothesis is that there is no difference between (among) the treatments. You cannot "prove" your hypothesis, instead you calculate the probability that the null-hypothesis is incorrect. If you accept that probability as being "significant", you then reject the null-hypothesis and accept the hypothesis you are testing. I strongly recommend taking a course in experimental design and statistics, I've seen poorly designed research where millions of dollars were spent collecting data in poorly designed studies that would have been much more useful had the studies been properly designed.

Answer 2

In your textbook, each test comes with a description of the assumptions and the hypothesis. Ask yourself these questions:
- Are the assumptions fullfilled in your case?
- Is the hypothesis tested the one you're interested in?

Example: the unpaired t-test:
Assumptions:
- The observations in both groups are normal distributed. This is critical. If you have "outliers", the variances and means are meaningless so you can't use the test.
- The observations are independent. For example, if some subjects are family members of other subjects, this is not the case. This is often not so critical. In particular, if a pair of dependent measurements are equally likely to be in the same group as in different groups, the errors you make tend to cancel each other out.

Hypothesis tested: The means in the two groups are the same. Maybe this is not what you want to know. You could use a Kolmogorov-Smirnov test to find out if the distributions are the same, or an F test to find out if the variances are the same.

Answer 3

I have been doing Statistics as a hobby and giving private tuition for a long time. The 'best' approach is to find an expert, or near-expert to advise *before* any experiments are done.

There can be more than one appropriate approach.

Often you should prepare a graph to visualise the sample data which would give you a fair idea about the population values. For example a scatter graph is advisable before trying to calcualte a least squares line and a correlation coefficient.

In General:
Try to use parametric analysis i.e. using the Normal Distribution (Z statistic) or a t-test.

An example would be comparing two unknown population means based on two independent samples of less than 30 each, randomly sampled.

This would be a t-test.

Answer 4

The decision is simple but unfortunately most books make things difficult.

Each test does a particular job. So if you know that and what you want to do with your results, it is a simple matter to decide.

However statistical tests are divided into parametric ones which are suitable for normally distributed results and non parametric tests which are suitable for all distributions. In practise when the results are normally distributed, we always use parametric tests like t- test or ANOVA, because they are more powerful and easier.

In any case see what tests are used in the field you are working and use the same. The people who will read your results will then accept them more readily.

Answer 5

there are loads to choose from and most students only get taught a few also remember the tests can be tweaked a bit. you should decide on what stats test to use before you get your results ideally when designing the experiment. any stats book will give guidnence on which one to use but when i was a student i would check what stats people doing similar experiments were using this gets you better grades as the test is often more closely matched to your needs as it is often a variation your not normally taught.

Answer 6

If you are not a statistician you'll want to keep it simple (I'm a biologist not a statistician too).

* If your data is parametric you more than likely want a t-test or ANOVA
* If it's non-parametric then probably Mann-Whitney or Chi-squared.

Of course in theory you should have consulted a statistician before you started the research to ensure that you had a sufficiently powerful test to evaluate your hypothesis.

Answer 7

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Answer 8

Here is a nice chart to help you do that for most basic tests. You have to of course understand them in the first place to use them. I presume you do, but can't choose.

http://www.ats.ucla.edu/stat/stata/whatstat/default.htm

Answer 9

I would guess the set that proves your hypothesis ... ;-) ...

That may be cheating but you will be following the likes of advertisers and governments so can it be all that bad ???

........ ; -) .....