Question

How do I run a the test of normality? Assumptions of normality

Step 1

**Introduction:**

Several tests of normality exist, using which you can verify whether a particular data follows the normal distribution.

Usually, before conducting a formal test, we prefer to take the help of graphical methods, to see if the data may be assumed to follow the normal distribution, at least approximately. A few such graphical methods are:

- Histogram of the data , superimposed with a normal probability curve,
- Normal probability plot with confidence interval,
- Normal quantile-quantile (QQ) plot.
- Boxplot, etc.

Step 2

**Explanation:**

If the graphical display appears to show at least an approximate normal distribution, then a formal test can be used to verify the normality. A few such tests are as follows:

- Pearson’s Chi-squared test for goodness of fit,
- Shapiro-Wilk test,
- Kolmogorov-Smirnov test, etc.

The Pearson’s Chi-squared test is discussed here.

Step 3

**Pearson’s Chi-squared test for goodness of fit:**

Suppose the data set can be divided into *n* categories or classes, with observed frequency in the *i*th class as *Oi* and expected frequency in the *i*th class as *Ei* (*i* = 1, 2, …, *n*). Further, assume that the data is obtained from a simple random sampling, the total sample size is large, each cell count (for each category) is at least 5 and the observations are independent.

Then, the degrees of freedom, *df* = (number of categories) – (number of parameters in the model) – 1. For *n* categories in the data set and 2 parameters (mean and variance) of the normal distribution, *df* = *n* – 3.

The test statistic for the test is given as, *χ*2 = Σ [(*Oi* – *Ei...*

Tagged in

Q: Compute r, the correlation coefficient, using the following data. x 2 1 7 8 3 6 y 3 4 10 11 4 ...

A: In this question we have a given data for variable x and y, and we have to find the correlation coef...

Q: Determine whether or not sigma1 square is equal to sigma 2 square using a 5% significance level if w...

A: According to the given question, to test the hypothesis of H0: sigma 1 square is equal to sigma 2 s...

Q: A marketing manager for a cell phone company claims that more than 55% of children aged 8-12 have ce...

A: Null and alternative hypotheses:Here, to check whether more than 55% of children aged 8-12 have cell...

Q: You are a graduate student in an M.D./Ph.D program, attempting a study of the efficacy of different ...

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you. ...

Q: Use the normal distribution of SAT critical reading scores for which the mean is 513513 and the stan...

A: NOTE:Since, the numbers on the values of mean and standard deviation are repeating twice (513513 and...

Q: Rolling Two Dice If two dice are rolled one time, find the probability of getting these results A. ...

A: Hello there! There are more than 3 sub-parts in the question shared. According to our policies canno...

Q: Part b, c, d

A: Part b:Denote μ as the true mean breaking strength (after 24 hours) of the new bonding adhesive.The ...

Q: How would I construct a stem and leaf plot using these numbers 57 54 52 55 51 56 61 68 56 55 54 61 5...

A: Introduction:The numbers here are all two-digit numbers. So, you can consider the digit in the ten’s...

Q: The contingency table shows the distribution of a random sample of fatal pedestrian motor vehicle co...

A: a) The expected counts for each cell in the provided contingency table can be calculated by using th...

Sorry about that. What wasn’t helpful?