Chapt 2-5

What are Type I and Type II errors?

A Type I error occurs when we believe that there is a genuine effect in our population, when in fact there isn't. A Type II error occurs when we believe that there is no effect in the population when, in reality, there is.

What is a test statistic and what does it tell us?

A test statistic is a statistic for which we know how frequently different values occur. The observed value of such a statistic is typically used to test hypotheses, or to establish whether a model is a reasonable representation of what's happening in the population.

What do the sum of squares, variance and standard deviation represent? How do they differ?

All of these measures tell us something about how well the mean fits the observed sample data. Large values (relative to the scale of measurement) suggest the mean is a poor fit of the observed scores, and small values suggest a good fit. They are also, therefore, measures of dispersion with large values indicating a spread-out distribution of scores and small values showing a more tightly packed distribution. These measures all represent the same thing, but differ in how they express it. The sum of squared errors is a 'total' and is, therefore, affected by the number of data points. The variance is the 'average' variability but units squared. The standard deviation is the average variation but converted back to the original units of measurement. As such, the size of the standard deviation can be compared to the mean (because they are in the same units of measurement).

What is an effect size and how is it measured?

An effect size is an objective and standardized measure of the magnitude of an observed effect. Measures include Cohen's d, the odds ratio and Pearson's correlations coefficient, r.

What's the difference between the standard deviation and the standard error?

The standard deviation tells us how much observations in our sample differ from the mean value within our sample. The standard error tells us not about how the sample mean represents the sample itself, but how well the sample mean represents the population mean. The standard error is the standard deviation of the sampling distribution of a statistic.