Probability Distribution: Variability and Frequency
Increasing the sample size in a study serves to decrease the variability in a study because larger sample sizes are more likely to reflect the true characteristics of the overall population that is being sampled. In this context, the term variability is used to refer to the extent to which individual data points are different from each other. For instance, a set of data with a low variability level will have data points that are clustered close to the mean and, conversely, high variability means the data points are spread out.
Frequency is used to inform probability because probability is based on the likelihood of an outcome occurring, which is directly related to the frequency that outcome is typically observed. In other words, the more frequently an event happens, the higher the probability it will happen again at some point in the future and this relationship is important for making empirical probability judgments. Likewise, P-values in statistics also rely heavily on frequencies and probability. For example, based on the frequency distribution of the data, a p-value represents the probability of achieving results at least as extreme as the current data, in those cases where the null hypothesis is assumed to be true. In sum, without the frequency distributions that inform probability, drawing statistical inferences from data would be much more difficult.
References
Morrow, J. A. (n.d.). Normal Distribution Probability.
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