Kindly requesting help for JASP Data Input to run a ANOVA (?)
Dear All,
I am new to statistical analysis trying to interpret results from a experiment via JASP. I kindly would like to request Your help how to enter the data correctly in JASP with the aim to run a test (ANOVA?) to identify effects induced by the factorial combinations.
Briefly, the experiment is to assess the effects of two factors (substrate & fertilization level) on the germination rate of seeds. In the experiment in total 4 different substrates (Sphagnum, Sand, Compost and Manure) and 5 fertilization levels were used. All substrates were fertilized with the fertilization levels 15, 75, 150 and 450 whereby fertilization level 0 was mixed only with 1 substrate (marked blue). Each combination was tested in 3 repetitions.
The attached file gives You an overview of all the samples.
I have managed to run a one way ANOVA for the factor substrate or fertilizer showing significant (p < 0,05) effects on the germination level only caused by the factor substrate not by the fertilization level. However I would like to run a test that compares the combination of both factors. I have unsuccessfully tried to run multifactorial ANOVAS and am thinking that my way of entering the data is completely wrong as no statistics show up in the descriptive part....
Can You please help?
Thank You very much.
Comments
Hi @Mientusz,
Running a two-way ANOVA is just normally a matter of introducing two nominal variables as fixed factors in the ANOVA analysis menu. However, in the case of your design, there are several problems that make them unsuitable for an ANOVA.
First, your our design is incomplete. You're trying to run a 4 (substrate) x 5 (Level of fertilizer) ANOVA while your data does not match that design. You have no data for Compost, Manure, and Sand with 0 level of fertilizer. Here's a count of your data broken down by the two independent factors:
Second, your data does not meet the requirements for parametric statistics.
Third, even if you solve problem 1 by removing the data for the 0 level of fertilizer, and if ignore problem 2 and run the ANOVA despite your data not meeting the requirements, you'll get an error message because some of the cells (after grouping using both factors) in your design have no variance (all the data in some cells of your design are the same). The error message in JASP tells you what's going on:
Note that not all statistical packages complain about zero variance in design cells (running these data in Statistica, for example, I got the two main effects and interaction). I suspect there is a reason why JASP complains. Calculating statistics when the variance is zero amounts divisions by zero, which has no solution. It's possible that other packages replace that zero variance by a very small amount to bypass that problem.
Going back to JASP, you have two possible options (both requiring you remove from the data set the 0 fertilizer level data, because otherwise, your design is not orthogonal and not suitable for an ANOVA).
Your first option is to remove the interaction from the model. That would leave you with only the main effects for substrate and level of fertilizer. Since your data violate the assumptions of parametric statistics, you'd also want to ask for the nonparametric statistics (Kruskal-Wallis). This method does not allow you to get any statistic about the interaction, which may be problematic depending on your hypotheses and the objectives of your study.
The second option is to add very small random variations to the dependent variable in order to avoid ending up with zero variance in any cell. For example, you could add or subtract 0.01 at random to generate a new Rate of Germination variable (Rate_Germination2). The random amount added or subtracted should be tiny so that you introduce some non-zero variance but you don't mess up the data. Then, provided that you filtered out the 0 Level of fertilization data, JASP will run the ANOVA:
Note that because the analysis runs does not mean it is appropriate. In this case, you still have data that violate the assumptions of parametric statistics, so you should interpret the data with caution.
In any case, the fundamental problem is that you have an incomplete design and too little data to get something meaningful from a statistical analysis.
Hope this helps.
Fabrice.
Fabrice,
yes - this helps me a lot! Thank You so much.
I will follow Your advice and go through the several aspects. The germination test is part of a bigger experiment with - I believe - a complete dataset (according to Your text). I will give that a try now!
Thank You very much. Your help is very much appreciated.