Math Assignment

As previously mentioned, the most common assumption of parametric tests is that the population from which the sample is taken has an underlying normal distribution. Knowing the underlying distribution of the variable allows for predictions to be made. That is, with repeated sampling of equal sizes of a particular population, the estimate will be approximately the same. The shape of the normal distribution is such that the closer a score is to the mean, the more frequently it occurs(Feinstein, 93).

Sample

Generally, it is not possible to collect data on an entire population; therefore, sample data are used in order to make inferences to the population. It is important to have a representative sample of a population in order to make generalizations to that population. Ways to ensure a representative sample include random sampling and sampling as large of a sample as is feasible. Having a random sample is an assumption of inferential statistics as it decreases the odds of having a biased sample. Additionally, the larger the sample size, the more likely it is that the shape of the sampling distribution will approach a normal distribution. This principle is known as the central limit theorem.

Measurement Issues

Another assumption of parametric tests is based on the level of measurement. The level of measurement is a representation of how much information the data are measuring. Parametric tests require that the data include more information and thus require interval- or ratio-scaled data. An interval scale is characterized as having an equal distance between measurements throughout the scale that correspond to equal differences in the quality being measured that can be compared in a meaningful way. Interval scales do not have a true zero. A ratio scale has the same equal and meaningful distances between measurements as the interval scale and does have a true ...