STA644 Official Handouts

Course: Non Parametric Statistics · Course code: STA-644 ·  Lecture: 01 · Topics: 1-7

In statistics there are two branches, one is known as Descriptive statistics and other is known as inferential statistics. In descriptive we usually collect the data and summarize it and in inferential statistics we infer the facts and figures of the collected data and the parameters of data distributions.

1-1: Parametric statistics:

When the parameters are going to test and conclude about the facts of parameters of the data then it will be done through parametric statistics. So

“Parametric statistics are the procedures which involve parameter of the populations and we need to test the certain assumptions about them.”

Whereas the non-parametric tests are not involved certain assumption about parameters. In parametric statistics the parameter of interest that must satisfy certain assumption. For example, in applying t-test for testing population mean there is that assumption the data must be drawn from normal distribution. If that assumption of normality is not met, then we are requiring certain procedures that deal with the nonnormal data distributions. Then we are going to use the non-parametric procedures.

1-2: Non Parametric Statistics:

In non-parametric statistics necessary assumptions for the valid use of a parametric procedure are not met. The results are needed in a hurry, a computer is not readily available and calculations must be done by hand. In this case we use non-parametric procedures.

In order to test hypothesis does not involve a population parameter, the data have been measured on a scale weaker than that requires for the parametric procedures that would otherwise be employed.

1-3: Measurement:

It is an important part of modern science as well as of engineering, commerce and daily life. Despite its importance there is little consensus among philosophers as how to define measurement, what sort of information are measurable or which condition make measurement possible.

Measurement is the assignment of numbers to an object. Whenever we measure it takes into account the types of unit. To quantify there are some things which can be measure and also some cannot be measured.

For Example:

Things can be measured: Height, Weight, Length,

Things cannot be measured: Happiness, Emotions, Feelings,

For measuring the units are Inches, centimeters, Pounds, Kilograms etc. In statistics there are two types of variables a) Quantitative b) Qualitative

As variable are of different types so measurement scales quantify the variables. In order to analyze the data using parametric techniques, data is required to be measured at least on interval scale.

1-4: Measurement Scales Examples:

. There are four types of measurement scales.

Nominal Scale:

A nominal scale is a scale that uses labels to classify categories and objects into classes. Some examples of variables that use nominal scales would be religious affiliation. It is called the weakest scale than all.

Also an example of Gender has categories Male and Female and numeric codes are assigned to these categories as Male=1 and Female=2.

Ordinal Scale:

Ordinal scale is defined as a variable measurement scale used to simply depict the order of variables and not the difference between each of the variables. These scales are generally used to depict nonmathematical ideas such as frequency, satisfaction, happiness, a degree of pain, etc. It is quite straightforward to remember the implementation of this scale as „Ordinal‟ sounds similar to „Order‟, which is exactly the purpose of this scale.

For example, a semantic differential scale question such as:

How satisfied are you with your Job?

Highly Dissatisfied – 1 Dissatisfied – 2 Neutral – 3 Satisfied – 4 Highly Satisfied – 5 Here, the order of variables is of prime importance and so is the labeling. Very unsatisfied will always be worse than unsatisfied and satisfied will be worse than very satisfied. This is where ordinal scale is a step above nominal scale. The order is relevant to the results and so is their naming. Here is an order but the difference between these categories cannot be measured.

Interval Scale:

It is used for the quantitative data. The difference between the categories are significant. It contains arbitrary zero value and No ratio can be calculated. Descriptive statistics are used to summarize the data.

For example, Temperature in Fahrenheit and time scale are the best examples of interval scale of measurement. Here zero temperature does not mean the complete absence of temperature.

Ratio Scale:

Ratio scale is also deals with the quantitative variable. This scale consists of order, Length and volume and contains actually zero value (Absence of any category). It is highest level of scale. It can have measured differences and ratios between successive categories. It has many characteristics. We can calculate descriptive and inferential both statistics on this scale.

For example, Height of students, weight and age are suitable for ratio type of scale.

1-5: Ranks

Ranking is the data transformation into numeric and order data. The reason behind the ranks is most of the non-parametric procedures need the data in ranks and orders. We can have ranked data into ascending and descending order It is placement of categories or things according to some quality or based on some characteristic into an order such as size of things. In tied ranks we average the same categories.

For example, ranking of schools, colleges and universities. We can rank them according to the total students enrolled in the institute. Which institute have maximum no of students enrolled can be ranked as one and so on. We can rank the students according to their class position. we can rank candidates in a contest or race also universities are ranked according to no of researches produced or most funded projects. Non parametric methods involve population ranked data. Ranks make the calculation easier. Ranks are assigned in form of integers and fractions.

1-6: Measures of Location

Measures of central tendency or location are numbers that tend to cluster around the “middle” of a set of values. It gives single representative value for data. These measures provide point estimate. Three such middle numbers are the mean, the median, and the mode.

1-6.1: Median

The middle value that separates the higher half from the lower half of the data set. The median is measures of central tendency that can be used for ordinal data, in which values are ranked relative to each other but are not measured absolutely. It is not affected by outliers or extreme values. It is calculated for