Which of the following is useful for testing univariate normality of distribution?
(a) Q-Q plot
(b) Shapiro-Wilk test
(c) Jarque-Bera test
(d) Scatter plot

Correct option is D

The correct answer is A, B and C only.
1. Univariate normality refers to the distribution of a single variable following a normal distribution. This assumption is fundamental in many statistical analyses that require normality, such as t-tests, ANOVA, and regression.
2. A. Q-Q plot: The Quantile-Quantile (Q-Q) plot is a graphical tool to compare the quantiles of a sample distribution with those of a normal distribution. If the data follows a normal distribution, the points will lie along a straight line.
3. B. Shapiro-Wilk test: The Shapiro-Wilk test is a statistical test that checks the null hypothesis that the data is normally distributed. A non-significant result (p > 0.05) suggests that the data does not significantly differ from a normal distribution.
4. C. Jarque-Bera test: The Jarque-Bera test evaluates skewness and kurtosis to test if a dataset's shape matches a normal distribution. It specifically looks at deviations from normality in terms of skewness (asymmetry) and kurtosis (peakedness).
5. D. Scatter plot: A scatter plot is used to visualize relationships between two variables, not for testing normality. While it can show trends or clusters in bivariate data, it does not assess univariate normality.

Information Booster

1. Univariate Normality:
1.1. Univariate normality refers to the assumption that the distribution of a single variable follows a normal distribution, which is bell-shaped and symmetric around the mean.
1.2. Many parametric statistical methods, such as t-tests, ANOVA, and linear regression, rely on the assumption of normality for valid results. If the data significantly deviates from normality, it can affect the reliability of these statistical tests.
1.3. To test univariate normality, there are several graphical and statistical methods available, including Q-Q plots, the Shapiro-Wilk test, and the Jarque-Bera test. These methods help to check whether the data fits the characteristics of a normal distribution.

2. Testing Univariate Normality:
2.1. Q-Q Plot: The Q-Q plot compares the quantiles of the observed data with those of a normal distribution. A perfect fit to normality will show data points falling along a straight diagonal line. Deviations from this line suggest that the data is not normally distributed.
2.2. Shapiro-Wilk Test: The Shapiro-Wilk test is a formal statistical test that evaluates the null hypothesis that the data follows a normal distribution. If the p-value is greater than 0.05, there is no significant departure from normality. However, a p-value less than 0.05 indicates a significant departure from normality, suggesting that the data may not be normally distributed.
2.3. Jarque-Bera Test: This test assesses normality by evaluating skewness (the asymmetry of the data distribution) and kurtosis (the peakedness of the distribution). The null hypothesis of the Jarque-Bera test is that the data is normally distributed with zero skewness and a kurtosis value of 3 (the same as a normal distribution). A significant result (p < 0.05) suggests that the data does not follow a normal distribution.

Additional Information

Option D (Scatter plot):
4.1. A scatter plot is primarily used to visualize the relationship between two variables. It plots one variable on the x-axis and another on the y-axis to assess whether there is a linear or non-linear relationship between them.
4.2. Although scatter plots can be used to visually assess whether data points follow a particular trend or distribution, they do not provide a formal method for testing univariate normality. For normality testing, tools like histograms, Q-Q plots, and specific tests like Shapiro-Wilk and Jarque-Bera are more appropriate.
4.3. Scatter plots can be helpful in identifying outliers or understanding the correlation between variables but are not useful for testing the normality of a single variable's distribution.