A 2-sample t-test of a canine diet experiment
April 11 of every year is National Pet Day in the United States. Nowadays, pets are part of our everyday lives. According to the American Pet Products Association (APPA), 67% percent of United States households own a pet.
Data in 2018 by Statista (2018) showed that dogs came out on top as the leading type of pet with over 470 million dogs kept as pets worldwide, compared to approximately 370 million pet cats. The five countries with the highest dog and cat pet populations in 2019 are shown below.
In the same year, the American Kennel Club listed the top five dog breeds as Labrador retrievers, German shepherds, Golden retrievers, French bulldogs, and bulldogs. On the other hand, Maine coons, Siamese cats, and American shorthairs are well known breeds of cats.
Psychologists have also shown in some studies that looking a dog or cat in the eyes can boost levels of oxytocin (a social bonding hormone) in both the person and the pet. As pet owners know, their pets have the capacity for unconditional love, and it’s not just “cupboard love” triggered by a hungry belly! To help your pet live a long and healthy life, an important factor is feeding them a high-quality diet.
Let me show you a dog example.
A “dog diet” refers to commercially prepared food which provides proper nutrition to dogs. It is Dog diet is generally enriched with some ingredients such as oatmeal, potatoes, pea protein, bone meal, chicken, sugar-based sweeteners and liver chunks.
In our example, a dog feed company needs to compare two diet formulas for puppies. The experimental units are 30 male Basset hounds: 15 were randomly assigned to each of the two diets (A and B). The dependent variable is the average daily weight gain (ADG, g/day) between 12 to 28 weeks of age. This is calculated by dividing the weight gained (in grams) over this time by the duration of this time period in days. The ADG data for the trial is given below.
Unfortunately, data for one Basset hound is missing. This missing data is represented by an asterisk (*).
The hypotheses for this experiment are Ho: µA = µB vrs Ha: Ha: µA ≠ µB. We can assess the evidence against our null hypothesis (Ho) in favour of our alternative hypothesis (Ha) using a 2-sided two-sample t-test. This test makes the following assumptions:
- The data for both samples are continuous and normally distributed
- The two samples are independent and random
We’ll use the “Genstat” statistical software to perform a 2-sided two-sample t-test on the ADG data.
This dataset is stored in an MS-Excel spreadsheet, so we’ll begin by importing this into Genstat.
To calculate the t-test, from the main menu select Stats | Statistical Tests | One- and two-sample t-tests.
We select “Two-sample” as the test and “Two variates” as the data arrangement. We can then enter “A” and “B” into the data variate 1 and 2 fields. Chose “Two-sided” as the type of test.
- From the Test dropdown list select Two-sample.
- In the Data arrangement section select Two variates.
- Select A as Data variate 1 and B as Data variate 2.
- In the Type of test section select Two-sided.
Clicking “Run” generates the output below.
The t-statistic is -2.55 on 27 degrees of freedom. The probability of getting a t-statistic as extreme as -2.55 under the null hypothesis of no difference between the means is 0.017. Since this probability is small (i.e. less than 0.05) we will reject the null hypothesis in favour of the alternative hypothesis. That is, we have evidence that the mean ADG of the two dog diets is significantly different at the 5% level. Examining the means, we can conclude that the mean ADG of Basset hounds on diet B (mean = 82 g/day; sem = 4.0 g/day) is significantly greater than those on diet A (mean = 68 g/day; sem = 3.8 g/day).
This article offers an example of basic statistical analysis. Pets in your household give so much in terms of love and emotional support. This is particularly important now with the stress and anxiety the COVID-19 pandemic is causing. Our pets deserve good food, a warm and safe place to live, and your love and attention. I hope you are enjoying time with your pet at the moment. Happy pet day!