Identifying a probability distribution II—normal, t and chi-square

By Tutor GuyNo Comments


Often the first step in determining the probability of an event is determining the probability distribution to which the event belongs. Good statisticians can identify the correct distribution right away; if you learn some simple rules, you can specify the correct distribution just like the experts. In this post, I describe how to identify the three most common continuous distributions: normal, t and chi-square.

Requirements for a normal distribution

Many times you will be told when a distribution is normally distributed. When you are conducting hypotheses tests, you will often assume that the distribution is normal (or at least approximately normal) when the following conditions hold:

  • The standard deviation (σ) of the population is known
  • The sample size (n) is ≥30
  • The statistic you are measuring is the sample mean


Requirements for a t distribution

If you are performing a hypothesis test and you are measuring the sample mean, you will need to use a t distribution instead of a normal distribution if either of the following conditions holds:

  • The standard deviation (σ) of the population is not known.
  • The sample size (n) is < 30


Requirements for a chi-square (Χ2) distribution

There are numerous situations where a chi-square distribution is indicated. In a first year stats class, you will use chi-square distributions when you are performing a contingency test, a goodness-of-fit test or a test of homogeneity.

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