In previous posts, we learned that the aim of statistics is to extrapolate properties of samples to make inferences about population. However, random variation in individuals in the population produces sampling error, which means a single sample may not accurately reflect properties of the population. When data are binary, we learned how the 95% confidence interval (CI) of a sample
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Understanding the meaning of a confidence interval can take a little effort. The key idea is we want to infer findings from a study to subjects who were not part of the study. Sometimes, reading explanations in different words can help. Let’s pause in our series and see how others have explained what confidence intervals mean: Harvey Motulsky: The true
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Data which exist in categories that only have 2 possible values are known as binary data. “Yes” or “No” survey responses, dead or alive, male or female, etc. are examples of binary values. These data can be expressed as proportions (e.g. the proportion of male students in a class), are known as binomial variables, and follow a binomial distribution. The
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An important part of conducting sound science involves interpreting data correctly. Unfortunately, we don’t do that very well. For example, we are fooled by regression to the mean, we report findings when there are none, and we are overconfident about statistical power and significance. As scientists and lay persons, we want to be certain about research findings. But statistics only
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Hypothesis testing vs. Estimation Hypothesis tests require that populations are Normally distributed in order for the tests to be reliable. When samples are drawn from Normally distributed populations, the distributions of F or t statistics can be calculated for any given sample size, and the F or t statistic for a specific experiment can be obtained from the distribution. This
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When we run a statistical test, we almost always obtain a p-value. Many statistical tests will also generate a confidence interval. Unfortunately, many scientists report the p-value and ignore the confidence interval. As pointed by Rothman (2016) and the American Statistical Association, relying on p-values forces a false dichotomy between results that are significant and those that are non-significant. This
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Scientifically Sound 