In contrast, nonparametric statistics are typically used on data that nominal or ordinal. Nominal variables are variables for which the values have not quantitative value. Common nominal variables in social science research, for example, include sex, whose possible values are discrete categories, "male" and "female. Ordinal variables are those in which the value suggests some order.
An example of an ordinal variable would be if a survey respondent asked, "On a scale of 1 to 5, with 1 being Extremely Dissatisfied and 5 being Extremely Satisfied, how would you rate your experience with the cable company? Parametric statistics may too be applied to populations with other known distribution types, however. Nonparametric statistics do not require that the population data meet the assumptions required for parametric statistics.
Nonparametric statistics, therefore, fall into a category of statistics sometimes referred to as distribution-free. Often nonparametric methods will be used when the population data has an unknown distribution, or when the sample size is small.
Although nonparametric statistics have the advantage of having to meet few assumptions, they are less powerful than parametric statistics. This means that they may not show a relationship between two variables when in fact one exists. Nonparametric statistics have gained appreciation due to their ease of use. As the need for parameters is relieved, the data becomes more applicable to a larger variety of tests. This type of statistics can be used without the mean, sample size, standard deviation, or the estimation of any other related parameters when none of that information is available.
Since nonparametric statistics makes fewer assumptions about the sample data, its application is wider in scope than parametric statistics. In cases where parametric testing is more appropriate, nonparametric methods will be less efficient. This is because nonparametric statistics discard some information that is available in the data, unlike parametric statistics. Common nonparametric tests include Chi-Square , Wilcoxon rank-sum test , Kruskal-Wallis test, and Spearman's rank-order correlation.
Consider a financial analyst who wishes to estimate the value-at-risk VaR of an investment. Symptom severity might be measured on a 5 point ordinal scale with response options: Symptoms got much worse, slightly worse, no change, slightly improved, or much improved.
Distribution of Symptom Severity in Total Sample. The distribution of the outcome symptom severity does not appear to be normal as more participants report improvement in symptoms as opposed to worsening of symptoms. In some studies, the outcome is a rank. Each of the 5 criteria is rated as 0 very unhealthy , 1 or 2 healthy based on specific clinical criteria.
Infants with scores of 7 or higher are considered normal, low and 0 to 3 critically low. Sometimes the APGAR scores are repeated, for example at 1 minute after birth, at 5 and at 10 minutes after birth and analyzed. Virginia Apgar and is used to describe the condition of an infant at birth.
The score, which ranges from , is the sum of five component scores based on the infant's condition at birth. APGAR scores generally do not follow a normal distribution, since most newborns have scores of 7 or higher normal range. In some studies, the outcome is continuous but subject to outliers or extreme values.
For example, days in the hospital following a particular surgical procedure is an outcome that is often subject to outliers. Suppose in an observational study investigators wish to assess whether there is a difference in the days patients spend in the hospital following liver transplant in for-profit versus nonprofit hospitals.
The number of days in the hospital are summarized by the box-whisker plot below. This can be the case when you have both a small sample size and nonnormal data. However, other considerations often play a role because parametric tests can often handle nonnormal data. Finally, if you have a very small sample size, you might be stuck using a nonparametric test.
Please, collect more data next time if it is at all possible! Your chance of detecting a significant effect when one exists can be very small when you have both a small sample size and you need to use a less efficient nonparametric test! Minitab Blog. Nonparametric analysis to test group medians. Hypothesis Tests of the Mean and Median Nonparametric tests are like a parallel universe to parametric tests.
Parametric analyses Sample size guidelines for nonnormal data 1-sample t test Greater than 20 2-sample t test Each group should be greater than 15 One-Way ANOVA If you have groups, each group should be greater than If you have groups, each group should be greater than My profile. What is the difference between a parametric and a nonparametric test?
What is the advantage of using a nonparametric test? What is the advantage of using a parametric test? English French German Japanese Spanish.
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