Hypothesis Testing – Critical Values and Regions

There is a certain method of conducting hypothesis tests which makes it very suitable for automation. If we could know the set of values of a statistic – typically a single occurrence or mean – which results in the null hypothesis being rejected, these could be written down on the side of a machine and […]

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The Coefficient of Determination

Pearson’s correlation coefficient is given by Pearson’s correlation coefficient r tells us how good a fit to a straight line a set of data points is. If the data is a perfect fit to a straight line, and ifthere is absolutely no fit that can be made to a straight line. Almost as useful is […]

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Populations, Samples and Censuses

A population is the set of individuals in a group. Often information needs to be collected about the population, Taking a census and taking a sample are methods of collecting data about the population. A govenrnent for example needs to plan the supply of public services in advance. A hospital might cost £100m to build, […]

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The Cumulative Distribution Function

A probability distribution is usually defined in terms of it’s probability distribution function (if continuous), the probability that it takes a value in a certain range, or probability mass function (if discrete), the probability that it takes a certain value Sometimes it is more convenient to define it in terms of it cumulative distribution function. […]

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Mode of a Continuous Distribution

The mode of a continuous distribution is the most probable value of the random variable associated with the distribution. If we sketch the probability distribution function againstit will typically have a maximum. Finding the mode then becomes a matter of finding the turning point, or solving the equation Example: Find the mean of the probability […]

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Formulating Null and Alternative Hypotheses

Every hypothesis test seeks to prove or disprove a statistical statement about a population to a particular level of certainty. In order to do this the statement needs to be clearly phrased. Typically the statement is about the mean of a distribution or the probability of an event occurring. The null hypothesis is the value […]

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Prediction and Extrapolation

Extrapolation is a bad idea. It involves using a set of data to make predictions for data outside the range used to construct a statistical model. Suppose for example that a drug is being tested. The drug is designed to lower cholesterol. The drug is tested on healthy people first to minimise the risks of […]

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