Proving Significant Performance Even Though You Lost

Question

My data shows the consumption of two foods, cockroaches and a gel bait, by ants. We need to statistically prove that the gel bait is palatable and that the ants will eat a 'significant' amount. The EPA wants us to perform some statistical analysis beyond just summarizing means, but would not provide direction. Unfortunately, I cannot simply perform a t-test because we knew going in the ants would eat a greater weight of cockroaches, so that will just show cockroaches outperformed gel baits. Is there a method for showing significant consumption besides comparing against an imaginary zero consumption?

Thanks!

gzmorgan0 · Answer

@ntersteeg,

How was this data collected?  What was the plan?  For example, were multiple groups of ants tested, some with cockroaches only, some with gel bait only, some with a mix?   As @G_M suggested, it would be logical to collect consumption by time or some type of experimental plan ( day one cockroaches, day 2 gel bait, etc. or something.)

Was this just one "box" of ants or multiple "boxes" (replicates) collected?

In other words, is the data collection plan adequate to answer the question at hand?

G_M · Answer

If you want to demonstrate that the gel bait was consumed, does it make sense to look at the ratio grams consumed:total grams. Or, measure grams consumed over some time interval? Is there an extant clinical definition of "significant" amount? Perhaps randomly assign batches of ants to the gel bait, for a period of time and determine if the amount consumed (random variable) over the N trials is significantly different from zero? Is this what you mean by "significant" amount? If you are not expecting the ants to consume more grams of gel bait relative to cockroach, I am not sure what role the cockroach consumption is playing other than setting a baseline or benchmark of the grams consumed of the preferable food over a period of time.

Mark_Bailey · Answer

This problem is difficult. You want to show that the bait is palatable, if not preferable to the natural cockroach. In one sense, the cockroach response is a control (the ants are eating) and the bait response is the test (are the also eating the bait). So a test of bait consumption is simple but reasonable.

You could model the consumption = intercept + food type. Select Analyze > Fit Model. Put the consumption data column in the Y role. Add the food type data column to the effect list, and run. This analysis is related to the two-sample t-test and Analysis of Variance but takes a slightly different approach. Click the red triangle at the top and select Factor Profiling > Profiler. This plot is based on the model. It predicts the consumption based on food type.

Are there any other factors in this study?