Author Archives: Joanna Diong

Research concepts: Confidence interval of a mean

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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Research concepts: The Normal Distribution

At Scientifically Sound, we have shown how to verify whether data are Normally distributed, and discussed whether it matters that data are Normally distributed. Let’s take a step back and consider what a Normal distribution is. A Normal distribution is a bell-shaped curve observed when the number of data points that occur in a population (y-axis) is plotted against the

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Research concepts: Quantifying scatter

In a previous post we used binary data to demonstrate sampling error and calculate 95% confidence intervals (CI). Now, suppose that data can take many values; for example, normal body temperature has many values and varies continuously over a physiological range. How can we measure this variability in body temperature? For continuous data, variability can be quantified as the standard

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Research concepts: Interpreting the 95% confidence interval

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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Research concepts: Confidence interval of a proportion

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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Why Type I errors are worse than Type II errors

Most introductory statistics courses include a section explaining Type I (false positive) and Type II (false negative) errors in hypothesis testing. If you have been through such courses, you would have learned that the tolerance for Type I error is set by the significance level (alpha =0.05; the usual default) while Type II error is controlled by statistical power which

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