Fish Food Analysis: Part 3
Significance Testing & Modeling
If you are joining us from Part 2, comment below and let me know! Thanks for taking the time to read through this, and I hope you gain something interesting out of it.
Let’s get straight into the meat and potatoes. This is the final chapter in a long series. We are going to confirm or reject all the insights about Growth, Survival, Sex Sorting, and Fecundity that we dealt with in Part 2. Finally, we will make a recommendation to our facility supervisor and the team based on our findings!
1.0 Significant Tests for Growth
1.1 Differences in Mass and Length between Feed Groups
Since our dataset doesn’t follow a normal distribution, I chose to work with more robust statistical tests. The Mann-Whitney U test is comparable to an independent t-test. Rather than the null hypothesis assuming the means are equal, the Mann-Whiney U test assumes the distributions of both populations are equal. This test is also known as the Wilcoxon rank sum test.
Using the above code, I iterated over each Age Category to calculate the p-value between Feed Groups for the age categories. Based on this test, we did not see any differences in Mass (mg) between the Feed Groups at any of the ages, as I first suspected.
One of my favorite uses for the ggpubr package, is its ability to combine statistical analysis with visualizations. ggpubr can calculate using the Wilcoxon test and presents everything in a simple and appealing manner.
As you can see from the p-values, we must accept the null hypothesis for each age category in both Mass and Length. There is no significant difference in Mass or Length between Feed Groups at any age.
1.2 Linear Regression of the Length-Mass Relationships
Based on the EDA in Part 2, we know the Length-Mass Relationship of the two groups falls almost right on top of one another. We also know that they don’t follow a normal distribution. Now, to understand if a linear model is appropriate, we will take a look at the residuals of the data.
We can see the residuals are not scattered randomly around the blue line, but take a clear parabolic shape. This indicates a polymetric model or a transformation to fit a linear model is required.
After log-log transforming, we can see a much better residual and Q-Q plot for our length-mass relationship (LMR).
Plotting the new log-log transformed graph, we can see a very high R-squared value for both Feed Groups, as well as the same linear equation!
It’s important to remember that these equations are not directly transferable due to our transformations. Instead, the coefficient is the percent increase of the dependent variable for every 1% increase in the independent variable. In our example, mass increases 3.2% for every 1% increase in length.
Because we don’t pass the assumptions needed for standard ANCOVA , we will go to our good ol’ friend Wilcoxon again. This time, we will use the WRS2 package, which only revealed p-values < 0.05 at the extreme ends of our regression lines, where data is sparse! Looks like there isn’t any significant difference in these regression models.
2.0 Significant Tests for Survival
2.1 Difference in Census by Feed Group
Wilcoxon will be a major theme of our analysis here, as it is a great, robust test for nonparametric data. For the census data, the sample size is quite small, so I chose nonparametric tests to help guard against that sensitivity.
It appears our intuition was a bit off, which is exactly why we perform these tests. While the standard errors don’t overlap, we don’t see any significant difference in the populations until the final event. This is still enough reason to cause concern. We want to limit the amount of aggression and deaths in our colony.
2.2 Difference in Death by Feed Group
It is important to look at data a number of ways, because insights can change based on what is being shown. If we looked at the number of deaths that occur between each census event, our story would be incomplete. We see that each individual event is not significant, however we know that the culmination of these events led to a significant impact in our sample populations.
3.0 Significant Test for Sex Sorts
The first step in our fecundity phase was assessing if there was any sex skew between the feed groups. Due to the difference in ending populations, we normalized the sex counts as a percent of total tank census. From the analysis below, I didn’t see any significant difference in sex between the Feed Types. I did, however, see a large skew towards females. This is fairly common among fish, as one male may fertilize an entire cohort of females in the wild.
4.0 Significant Test for Fecundity
Based on the sex determinations, I rerandomized the females and males within each Feed Group into equally represented tanks. Based on the limiting factor: males, this led to two tanks of Gemma and two tanks of Mysis.
After approximately three months of breeding, there was a clear and significant difference between the two Feed Groups as seen below. This is one of the most critical insights to this study. As it shows us that feeding Mysis improves the average viable embryo production in our facility.
5.0 Recommendations
I presented my insights and the data to my team, supervisor, and principle investigator. My recommendations were:
[1] Due to the significant difference in census and fecundity, the Mysis feed should be maintained in our facility. While Mysis is suboptimal for technicians, it is in the best interest of our animals and the lab.
[2] We should continue to explore alternative feeds such as black soldier fly larvae. Mysis still pose an issue both in biosecurity and labor intensity.
It is important to remember that while the dry diet did not outcompete Mysis for this feed replacement, our facility feeds three times a day. The other two feeds are dry diet. This provides quality nutrition, while still reaping the aggression-reduction benefits of the Mysis!
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