Untitled Document

ASSESSING NORMALITY

METHOD 1

METHOD 2

METHOD 3

METHOD 4

HISTOGRAMS

STEM-AND-LEAF DISPLAYS

EMPIRICAL RULE

IQR/s RULE

NORMAL PROBABILITY PLOTS

INDICATIONS OF NORMALITY:

Symmetric, bell-shaped appearance

INDICATIONS OF NORMALITY:

Approximately 68% of the observations will be within 1 standard deviation of the mean
Approximately 95% of the observations will be within 2 standard deviations of the mean
Approximately 100% of the observations will be within 3 standard deviations of the mean

INDICATIONS OF NORMALITY:

IQR/s will be approximately equal to 1.3

Note:

IQR="Interquartile range"

s="Sample standard deviation"

INDICATIONS OF NORMALITY:

Points will fall approximately on a straight line.

ACTIVITY 1.

Step 1: Click on the "Generate" button on the Statlets window at the end of this page.
Step 2: Click on the "Random numbers" button.
Step 3: Click on the "Normal" button and type 50 in the "Sample size" box.
Step 4: Click on the "OK" button.
Step 5: Type 10 in the left window that appears, this is the m=mean, and type 4 in the right window, this is s=standard deviation. Click "OK".

To assess the normality by using the above methods carry out the following step:

Method 1.

Step 6: Select the "Histogram" then "Stem-leaf" from menu options. Interpret the plots. Does it appear bell-shaped and symmetric?

Method 3.

Step 7: Click on the "Stats" menu option. Then click on "Options" button and check the boxes for interquartile range and standard deviation.
Step 8: Calculate (Interquartile Range)/(Standard Deviation). Is it close to 1.3?

Method 4.

Step 9: Click on the "P-plot" menu option. Do the points fall approximately on a straight line?

ACTIVITY 2.

Step 1: Click on the "Input" menu option.
Step 2: Click on the "Generate" button on the Statlets window at the end of this page.
Step 3: Click on the "Random numbers" button.
Step 4: Click on the "Exponential" button and type 50 in the "Sample size" box.
Step 5: Click on the "OK" button.
Step 6: Type 30 in the window that appears, this is the q=mean. Click "OK".

To assess the normality by using the above methods carry out the following step:

Method 1.

Step 6: Select the "Histogram" then "Stem-leaf" from menu options. Interpret the plots. Does it appear bell-shaped and symmetric?

Method 3.

Step 7: Click on the "Stats" menu option. Then click on "Options" button and check the boxes for interquartile range and standard deviation.
Step 8: Calculate (Interquartile Range)/(Standard Deviation). Is it close to 1.3?

Method 4.

Step 9: Click on the "P-plot" menu option. Do the points fall approximately on a straight line?