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Hypothesis testing; four types of scales to measure data

Explain the concepts involved in hypothesis testing, including what hypothesis testing is, and an explanation of the four types of scales used to measure data.

Discuss where and how common tests of differences, such as t-tests, ANOVAs and Chi-squares, are used to test hypotheses.

Include an example of where and how common tests of relationships, such as correlation and regression, can be used.

Solution Preview

1. Hypothesis testing is essentially a system that we use to compare the size of the signal (differences between groups) to the noise (variation within groups - individual differences). Hypothesis testing can let us decide if the differences between groups are a lot bigger than we would expect by chance; that is, if the differences between groups are a lot bigger than the variation within groups.

Our decisions in hypothesis testing are based on a distribution (graph) that assumes the groups are not significantly different from one another. In that distribution, we know how likely it is to get a particular score. For example, imagine that the distribution has a mean of 10 and a standard deviation of 2. We know certain probabilities that correspond to the distribution and that knowledge allows us to say that while scores between 8 and 12 would be quite common (these fall within +/- 1 standard deviation of the mean), a score of 20 (+5 standard deviations) would be very unlikely, given the variation within groups - the noise in our description above. So if we observe a score (or group difference) of 20, we can conclude that since it was so unlikely if our groups were NOT significantly different from one another, it is likely that they ARE different from one another. This is a crucial concept in hypothesis testing, so I'll restate it a different way below.

The distribution assuming no significant ...

Solution Summary

Hypothesis testing for the four types of scales to measure data are examined.

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