The Statistics Simplified series has 2 goals: to help readers understand and evaluate statistics in the veterinary literature and to help veterinary researchers select and interpret their statistics. Many statistical procedures have been described, and sorting through them may seem challenging. However, the statistical choices are much easier than they may appear at first glance.
To show the underlying structure that simplifies statistical choices, this final article presents flowcharts that summarize the reasoning process used to select appropriate statistical procedures. Examples illustrating how to use the flowcharts are also provided.
The flowcharts are intended only as guides to lead readers
In veterinary research, dependent variables are often related to multiple independent variables. For example, a study1 of cats with cardiopulmonary arrest revealed that the success of cardiopulmonary cerebral resuscitation was related to the number of people involved in the resuscitation and whether shock was the suspected cause of the arrest. In a study2 of reindeer, the degree of fluctuating antler asymmetry was found to be related to several immunologic variables. To describe relationships like these, researchers construct equations (also called models) that include multiple independent variables.
Different types of dependent variables require different
Categorical dependent variables and censored data are frequently encountered in veterinary research. Statistical methods for analyzing these types of data will be discussed here. Some of the statistics, such as relative risks, odds ratios, and hazard ratios, may seem rather technical. The effort required to understand them is well spent, however, because they provide important information in many veterinary studies.
Relationships Between Categorical Dependent Variables and Other Variables
The relationship between a categorical dependent variable and another variable is often of interest in veterinary research. For example, a study1 was conducted to determine prognostic indicators for 46 horses
Describing relationships between variables is an essential part of veterinary research. For example, a study1 of dilated cardiomyopathy in dogs revealed an association between ventricular premature complexes and a reduced probability of survival. In a different study2 of hematologic characteristics of sick and injured cockatoos, the absolute and relative monocyte counts were strongly associated.
Many statistical procedures can be used to investigate relationships between variables. Because different methods require different assumptions about the data, using the wrong method will often produce invalid results and conclusions. Such errors are common in the veterinary literature.
Veterinary researchers commonly compare means or distributions to answer research questions. For example, researchers in a study1 of anesthesia in badgers found a mean anesthesia duration of 16.8 minutes for a romifidine-ketamine-butorphanol combination, compared with 25.9 minutes for a medetomidine-ketamine-butorphanol combination. In a study2 of cats with chronic renal disease, males had a lower age distribution than did females.
When means are compared in veterinary medicine, the data are often misanalyzed. The methods used to compare means from repeated measurements are quite different from the methods used to compare means from independent samples.
Comparison of percentages is one of the most common types of comparisons in the veterinary literature. For example, a study1 of horses with abdominal pain found gastric ulceration in 68.4% of horses with duodenitis–proximal jejunitis, compared with 14.3% of horses with large colon volvulus. Another study2 found that the percentage of positive results for detecting Brucella canis in canine semen was 34.6% for a PCR assay, compared with 9.6% for the rapid slide agglutination test with 2-mercaptoethanol.
Appropriate statistical methods for comparing percentages are determined by the type of data. For
To interpret and evaluate statistics in the veterinary literature, readers need to understand statistical inference. This is the process of using the data collected by the researcher (ie, the sample) to reach conclusions about all possible observations of interest (ie, the population). For example, most veterinarians are not interested in the pregnancy rate for a sample of 19 cows given a new fertility drug. Instead, they are interested in the population pregnancy rate, which is the rate we would get if the new drug were used in the population that consists
Descriptive statistics are numerical or graphical summaries of data. A mean is a descriptive statistic; so is a line chart. Even though many descriptive statistics are simple, they are sometimes misapplied or misinterpreted in veterinary research. It is important to understand what a descriptive statistic tells us and what it does not tell us. What follows is a description of the correct application and interpretation of descriptive statistics commonly found in the veterinary literature:
• Means, medians, and modes.
• Measures of variability.
• Sensitivity, specificity, positive predictive value, and negative predictive value.
Statistics can make or break the validity of a study. If the wrong statistical methods are used, the results can be misleading at best and nonsense at worst. Unfortunately, readers cannot assume that reports in veterinary journals are based on accurate statistics. Peer review is no guarantee of statistical or scientific accuracy. One critic of the peer review process noted that “there are so many recent reports of failures of the peer-review system that the difficulty is to select the most instructive.”1 Most of the reports published in veterinary journals are not reviewed by statisticians,
Veterinary advances are often based on experiments in which new medications, devices, surgical procedures, or other treatments are tested. Because the results of these experiments can dramatically change the way veterinary medicine is practiced, it is essential that experiments be well designed. Bad experimental designs create problems that cannot be corrected by any statistical procedure. Veterinarians who understand the basic principles of experimental design can avoid errors when they design their own studies, and they can detect design errors in research by others.
Experimental design is the structure of an experiment: the experimental procedures, the selection