Inferential statistics are often used to compare the differences between the treatment groups. Inferential statistics use measurements from the sample of subjects in the experiment to compare the treatment groups and make generalizations about the larger population of subjects.
There are many types of inferential statistics and each is appropriate for a specific research design and sample characteristics. Researchers should consult the numerous texts on experimental design and statistics to find the right statistical test for their experiment. However, most inferential statistics are based on the principle that a test-statistic value is calculated on the basis of a particular formula. That value along with the degrees of freedom, a measure related to the sample size, and the rejection criteria are used to determine whether differences exist between the treatment groups. The larger the sample size, the more likely a statistic is to indicate that differences exist between the treatment groups. Thus, the larger the sample of subjects, the more powerful the statistic is said to be.
Virtually all inferential statistics have an important underlying assumption. Each replication in a condition is assumed to be independent. That is each value in a condition is thought to be unrelated to any other value in the sample. This assumption of independence can create a number of challenges for animal behavior researchers.
Inferential statistics helps to suggest explanations for a situation or phenomenon. It allows you to draw conclusions based on extrapolations, and is in that way fundamentally different from descriptive statistics that merely summarize the data that has actually been measured.
One of the advantages of working with samples is that the investigator does not have to observe each member of the population to get the answer to the question being asked. A sample, when taken at random, represents the population. The sample can be studied and conclusions drawn about the population from which it was taken.
Let us focus on the group that makes up the sample. We are not as interested in an individual's response as we are in the group's response. The individual values, of course, are accounted for in the group, but the way to compare outcomes is by looking at an overall response. The data from the groups are used to estimate a parameter. As you recall, these are values that represent an average of a collection of values, such as average age or standard (which is really “average”) deviation from the mean age.
To see how this is done, let us first look at a hypothetical situation. Consider what would happen if we were to study a population variable with a normal distribution. If we were to take multiple samples from this population, each sample theoretically would have a slightly different mean and standard deviation. When all sample means ( s) are plotted (if this could be done), they would tend to cluster around the true population mean, μ. Many would even be right on the mark.
The problem, of course, is that we don't know with certainty how close we are by looking at just one sample. The mean of any given sample ( ) could be on either side of μ and at a different distance from μ.
Statistical methods can analyze one variable at a time (i.e., univariate analysis) or more than one variable together at the same time (i.e., multivariate analysis). Bivariate analysis is analyzing two variables together. An example of a univariate analysis would be simply looking at the death rate (mortality) in different countries. An example of a bivariate analysis would be analyzing the relationship between alcoholism and mortality.
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