Chapter 18
Study Unit 2.4
NONPAREMETRIC METHODS
, Nonparametric Method:
Most of the statistical methods referred to as parametric require the use of interval- or
ratio- scale data.
Nonparametric methods are often the only way to analyze categorical (nominal or
ordinal) data and draw statistical conclusions.
Nonparametric methods require no assumptions about the population probability
distributions.
Nonparametric methods are often called distribution-free methods.
Whenever the data are quantitative, we will transform the data into categorical data in
order to conduct the nonparametric test.
Study Unit 2.4.1
The Sign Test:
The sign test is a versatile method for hypothesis testing that uses the binominal
distribution p= .05 as the sampling distribution.
We present two applications of the sign test:
o A hypothesis test about a population median. Remember the median is the
datapoint in the middle of the array of observations whith half of he values (0.5)
less than it and half the values (0.5) grater than it.
o A matched sample test about the difference between two populations. (Not
important)
Hypothesis Test About the Population Median:
o We can apply the sign test about a population Median:
o Using a plus sign whenever the data in a sample are above the hypothesized
value of the median.
o Using a minus sign whenever the data in the sample are below the
hypothesized value of the median.
o Discarding (Delete) any data exactly equal to the hypothesized median.
o This assigning of the plus and minus signs makes the situation into a binominal
distribution application.
o The sample size is the number of trials.
o There are two outcomes possible per trial, a plus or minus sign.
o The trials are independent.
o We let p denote the probability of a plus sign.
o If the population median is in fact a particular value, p should equal .5.
2
Study Unit 2.4
NONPAREMETRIC METHODS
, Nonparametric Method:
Most of the statistical methods referred to as parametric require the use of interval- or
ratio- scale data.
Nonparametric methods are often the only way to analyze categorical (nominal or
ordinal) data and draw statistical conclusions.
Nonparametric methods require no assumptions about the population probability
distributions.
Nonparametric methods are often called distribution-free methods.
Whenever the data are quantitative, we will transform the data into categorical data in
order to conduct the nonparametric test.
Study Unit 2.4.1
The Sign Test:
The sign test is a versatile method for hypothesis testing that uses the binominal
distribution p= .05 as the sampling distribution.
We present two applications of the sign test:
o A hypothesis test about a population median. Remember the median is the
datapoint in the middle of the array of observations whith half of he values (0.5)
less than it and half the values (0.5) grater than it.
o A matched sample test about the difference between two populations. (Not
important)
Hypothesis Test About the Population Median:
o We can apply the sign test about a population Median:
o Using a plus sign whenever the data in a sample are above the hypothesized
value of the median.
o Using a minus sign whenever the data in the sample are below the
hypothesized value of the median.
o Discarding (Delete) any data exactly equal to the hypothesized median.
o This assigning of the plus and minus signs makes the situation into a binominal
distribution application.
o The sample size is the number of trials.
o There are two outcomes possible per trial, a plus or minus sign.
o The trials are independent.
o We let p denote the probability of a plus sign.
o If the population median is in fact a particular value, p should equal .5.
2
