    Chapter 5: Analysing the Data Part II : Inferential Statistics # Sampling Distributions

In order to evaluate the accuracy of any sample statistic in terms of how well it is estimating its corresponding population parameter, we need some standard against which we can tell whether the sample statistic we calculate is a likely or an unlikely estimate of a particular parameter. This comparative standard is provided by a sampling distribution.

A standard is needed before we can say a particular number is a big number or a small number. If I tell you the answer to a question is 7 cm, you would say, "So what?". It depends on what is being measured. If it was a shoe size you would say that it was pretty small If it was the size of an ant, you would say that it was massive! We need a reference or norm for what we are measuring so that we can compare the score we found to the norm and decide if it is a large score or a small score relative to that norm. In statistics, that norm is provided by what we would expect by chance. We estimate how likely something is to have occurred just by random fluctuations. Everything we measure varies a little bit from day to day, from person to person, from instrument to instrument. This variation is called error variation or random error (or "white noise"). All the things that cause our measurement to vary but we donÕt know what those things are.

The previous example of a deck of cards allowed us to calculate an expected probability easily because there was a finite number of possibilities (i.e., only 52 cards). With statistics this is not possible because the population we are sampling from is infinite. We cannot calculate expected probabilities exactly, so we need to resort to the concept of standard error to provide our standard against which we decide if an obtained event is an unlikely event or not.

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