Which of the following are common assumptions in parametric tests?

A. Randomness

B. Nonlinearity

C. Normality

D. Homogeneity of variances

Choose the correct answer from the options given below:

T he basic principle behind the parametric tests is that there are a fixed set of parameters that are used to determine a probabilistic model Parametric tests assume a normal distribution of values, or a “bell-shaped curve.” Parametric Tests for Hypothesis testing include: T-test, ,Z-test , F-test and  ANOVA

Important Points

• For almost all of the parametric tests, a normal distribution is assumed for the variable of interest in the data under consideration. 
• Testing for randomness is a necessary assumption for the statistical analysis.
• The randomness is mostly related to the assumption that the data has been obtained from a random sample.

Key Points

The following are common assumptions in parametric tests

Normality:

• In this  data have a normal distribution (or at least is symmetric).
• It is also known as a Gaussian distribution or a “bell-shaped” curve, refers to the degree to which data show a central tendency and symmetrical distribution relative to the mean.
• It is important for data in each group being compared to exhibit characteristics of normality. Because parametric tests compare means between data groups, the means must be a faithful representation of the data. 

Homogeneity of variances:

• ​It means Data from multiple groups have the same variance.
• This refers to the dispersion pattern of data and how similar this pattern is between groups being compared.

Linearity: It means Data have a linear relationship

Independence: It means  Data are independent

Therefore we can conclude that the correct answer is A and C only

Confusion PointsPlease note, according to the official answer key A and C is given as the correct option. However homogeneity of variances is also one of the common assumptions in parametric tests. Thus, C and D can also be correct answer.