Sam

Cramming Sam's top tips from chapter 2

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The standard error

The standard error of the mean is the standard deviation of sample means. As such, it is a measure of how representative of the population a sample mean is likely to be. A large standard error (relative to the sample mean) means that there is a lot of variability between the means of different samples and so the sample mean we have might not be representative of the population mean. A small standard error indicates that most sample means are similar to the population mean (i.e., our sample mean is likely to accurately reflect the population mean).

Confidence intervals

  • A confidence interval for the mean is a range of scores constructed such that the population mean will fall within this range in 95% of samples.
  • The confidence interval is not an interval within which we are 95% confident that the population mean will fall.

Null hypothesis significance testing

  • NHST is a widespread method for assessing scientific theories. The basic idea is that we have two competing hypotheses: one says that an effect exists (the alternative hypothesis) and the other says that an effect doesn’t exist (the null hypothesis). We compute a test statistic that represents the alternative hypothesis and calculate the probability that we would get a value as big as the one we have if the null hypothesis were true. If this probability is less than 0.05 we reject the idea that there is no effect, say that we have a statistically significant finding and throw a little party. If the probability is greater than 0.05 we do not reject the idea that there is no effect, we say that we have a non-significant finding and we look sad.
  • We can make two types of error: we can believe that there is an effect when, in reality, there isn’t (a Type I error); and we can believe that there is not an effect when, in reality, there is (a Type II error).
  • The power of a statistical test is the probability that it will find an effect when one exists.
  • The significance of a test statistic is directly linked to the sample size: the same effect will have different p-values in different-sized samples, small differences can be deemed ‘significant’ in large samples, and large effects might be deemed ‘non-significant’ in small samples.