Normality
Continuous variables must possess normality in order to use parametric statistics
The statistical assumption of normality is central to conducting inferential statistics using continuous variables and outcomes. A normal distribution resembles the "bell curve" where the mean, median, and mode of a distribution are all the same. In a normal distribution, 68% of all observations will fall within one standard deviation above and below the mean, 95% will occur within two standard deviations above and below the mean, and 99.5% of all observations will exist within three standard deviations above and below the mean. The assumption of normality is tested for when employing parametric statistics with continuous variables and outcomes.
Normality and applied statistics
Whenever using a continuous variable, researchers must check the normality of the continuous variable's distribution using skewness and kurtosis statistics. If a continuous variable has a skewness or kurtosis statistic above an absolute value of 2.0, then the variable is assumed to have a non-normal distribution. Check for outliers, or observations that are more than 3.29 standard deviations away from the mean, and make a decision to 1) delete the observation in a listwise fashion, 2) conduct a logarithmic transformation to "normalize" the distribution, or 3) employ non-parametric statistics to yield inferences.
If a continuous variable's distribution yields skewness and kurtosis statistics below an absolute value of 2.0, then the assumption of normality has been met. More powerful parametric statistics can be used on continuous variables that meet the assumption of normality.
In certain instances, an ordinal variable can be upgraded to an interval scale of measurement if the assumption of normality is met for the ordinal distribution. This is especially true if the ordinal variable is a Likert-type score yielded from an empirically-validated instrument. More statistical power is achieved for these types of ordinal variables if the assumption of normality can be met and parametric statistics are used.
If a continuous variable's distribution yields skewness and kurtosis statistics below an absolute value of 2.0, then the assumption of normality has been met. More powerful parametric statistics can be used on continuous variables that meet the assumption of normality.
In certain instances, an ordinal variable can be upgraded to an interval scale of measurement if the assumption of normality is met for the ordinal distribution. This is especially true if the ordinal variable is a Likert-type score yielded from an empirically-validated instrument. More statistical power is achieved for these types of ordinal variables if the assumption of normality can be met and parametric statistics are used.
Hire A Statistician - Statistical Consulting for Students
DO YOU NEED TO HIRE A STATISTICIAN?
Eric Heidel, Ph.D. will provide the following statistical consulting services for undergraduate and graduate students at $75/hour. Secure checkout is available with Stripe, Venmo, Zelle, or PayPal.
- Statistical Analysis
- Research Design
- Sample Size Calculations
- Diagnostic Testing and Epidemiological Calculations
- Survey Design and Psychometrics