# Statistical Significant Difference between 5 groups of data

I'm trying to compare 5 different gears used by fishermen and the amount of bycatch found in each. The values have a unit of "% of time encountered" and range between 0% (ie: never have bycatch) and 100% (ie: encounter bycatch every time they go out). I chose this as not all the fishermen fished the same amount of time.

I do not have the same number of fishermen using each gear (eg: for gear 1, n = 4 fishermen; gear 2, n=13; gear 3, n=24; gear 4, n= 5; gear 5, n=4).

Is there a way of figuring out if there is a statistical significant difference between the bycatch in each gear?

I have minitab, but do not know how to use it well yet.

Thanks!

I'm guessing that the raw data for bycatch are counts (cf. http://en.wikipedia.org/wiki/Bycatch) so a purist might say that ANOVA may not be the way to go, since that best suited for testing differences in a continuous variable (eg. length, mass, etc.) between multiple groups. ANOVA on count data can be done, but caution is required when interpreting the output (cf. http://sci.tech-archive.net/Archive/sci.stat.math/2004-12/0076.html).

After you've had a look at the data by plotting (including the regression as @PeterFlom suggests), you might use a goodness-of-fit test (with equal expected frequencies) to test your null hypothesis that there is no difference in bycatch between the gear categories.

A popular goodness-of-fit test is the chi-square test which is well-documented for minitab, eg. http://www.minitab.com/en-US/support/answers/answer.aspx?ID=1255 and http://www.minitab.com/en-US/training/tutorials/accessing-the-power.aspx?id=6138

Some of the important limitations of the chi-square test are that you can't input percentage data, only raw counts, all counts should be greater than five, and that the sample should come from a simple random distribution (cf. http://www.minitab.com/support/documentation/Answers/Chi-Square%20Test%20Assumptions.pdf).

If your data don't satisfy the assumptions of the chi-square test, you can use an exact test or a randomization test. A quick look suggests these are available in minitab, but I'd suggest getting familiar with R, since it has a very large community of active users to seek advice from and substantial amounts of user-contributed tutorials on all of these methods (here is one of the best: http://www.statmethods.net/). R is also free to use and gives easy access to more exotic tests that you might consider, such as Bayesian contingency table analysis and likelihood tests.

That said, if ANOVA is the convention for count data in your field, or you convert the counts to a ratio (would bycatch per person per hour be sensible?), here is a nicely documented example of how to do it with R: http://ww2.coastal.edu/kingw/statistics/R-tutorials/oneway.html

A first attempt, at least, would be a regression with bycatch as the dependent variable and type of gear as the independent variable.

I can't help with MINITAB, though.

• would I not have to do a test before that to see whether it is normally distributed and/or whether there is a statistical significant difference? (I am a novice) Thanks!
– Guy
Apr 8 '12 at 18:16
• The regression is to determine if there is a difference. Regression assumes that the residuals from the model are normally distributed. Methods for checking the assumptions are included in R, SAS and SPSS; they are probably in MINITAB, but I have never even seen MINITAB used, so I don't know Apr 8 '12 at 19:05