Parametric procedures of quantitative analysis make an underlying assumption that...?
A. Dichotomous variables have been "smoothed"
B. The variables are measured at least at an ordinal level.
C. All responses are measured in a mutually exclusive manner
D. The underlying distribution of data is approximately normal.
D. Underlying distribution of data is approximately normal (most common assumption of a parametric test).
The correct answer is D. The underlying distribution of data is approximately normal.
To understand why parametric procedures of quantitative analysis make this assumption, let's break it down:
Parametric procedures are statistical techniques that are based on certain assumptions about the population and the data being analyzed. These procedures involve estimating and testing parameters of probability distributions, such as means and variances.
An underlying assumption of parametric procedures is that the data follows a specific probability distribution, most commonly the normal distribution. This assumption is important because many statistical tests and estimation methods rely on properties of the normal distribution.
When the data is approximately normally distributed, it means that the shape of the data follows a bell-shaped curve, with most of the observations clustered around the mean, and a symmetric pattern of observations on both sides of the mean.
This assumption allows researchers to use parametric procedures confidently to make inferences, perform hypothesis testing, and estimate population parameters.
However, it is important to note that parametric procedures can still be used even if the data is not exactly normally distributed as long as the deviation from normality is not extreme. In such cases, robust methods or transformations of the data can be used to account for departures from normality.
In summary, the underlying assumption of parametric procedures of quantitative analysis is that the underlying distribution of the data is approximately normal. This assumption facilitates the accurate and reliable application of statistical techniques.