Gathering information from various sources plays a crucial role. For a researcher, pieces of information are very important. We collect the data using various tools, one of which is a questionnaire. When we collect the data, we use open-ended and closed-ended questionnaires. When we pose a question with options or choices, such as choosing between two or five options, it clarifies our analysis based on the choices we provide in the questionnaire.
We are all familiar with the terms nominal, ordinal, interval, and ratio; these are all termed scales. We use different statistical tools for the different scales. Have you heard the term parametric or non-parametric? If your answer is yes, then you must know about the analysis tools. If your response is negative, you must have to learn. When we discuss and test the population, we are defining the parametric model. If we don’t know about the population, and this is necessary to test the hypotheses, the test will be non-parametric.
Parameters
It is a fixed measure that describes the target.
It is a fixed and unknown numerical value.
Variables
This characteristic is specific to a small portion of the population. I liked the sample size.
It is a known and variable number.
The parameters of the population distribution, from which the data originate,
Parametric statistics
That leads to assumptions about the population distribution parameters from which the data are drawn.
They assume that the data has an underlying statistical distribution.
A parametric test’s result must meet several validity conditions.
Non-parametric statistics
They make no assumptions about the parameters of a distribution.
Do not rely on any distributions.
They can be used even if the parametric validation condition is not met.
Difference between Parametric and Non Parametric
| Sr | Parametric | Non parametric |
| 1 | We make specific assumptions about the population parameter. | We make no assumptions about the population parameter. |
| 2 | Ratio and interval scale | Nominal and ordinal scales |
| 3 | For the calculation, more information is needed. | The calculation requires less information. |
| 4 | Assume a normal bell-shaped distribution curve. | Don’t assume a regular bell-shaped distribution curve. |
| 5 | More statistical power | Less statistical power |
| 6 | Less robust | More robust |
| 7 | The result can be generalized. | Results cannot be generalized. |
Table-1 Difference between Parametric and Non Parametric
The Case, Parametric and Non-Parametric Test
| Case | Parametric Test | Non Prametric Test |
| Central Tendency | Mean | Median/ Mode |
| Correlation | Pearson | Spearman |
| Independent Sample, 2 Groups | Independent Sample Test | Mann- Whitney Test |
| Independent Samples, More Than 2 Groups | One Way Analysis Of Variance | Kruskal Wallis Test |
| Dependent Samples, 2 Conditions | Paired Sample T Test | Wilcoxon Signed Rank Test |
| Dependent Samples, More Than 2 Conditions | One Way Repeated Analysis Of Variance | Friedman Anova |
Table-2 The Case, Parametric and Non-Parametric Test
The Action and Operation
|
What Can We Do |
||||
| Operation/Action | Nominal | Ordinal | Interval | Ratio |
| Categories/Classified | Yes | Yes | Yes | Yes |
| Arrange In Order (Sorting) | Yes | Yes | Yes | |
| Quantify Difference Between Values | Yes | Yes | ||
| Addition & Subtraction | Yes | Yes | ||
| True/Absolute Zero | Yes | |||
| Multiplication& Division | Yes | |||
Table 3- The Action and Operation
The above table shows that case (the case is the individual unit of the experiment). These are the individuals from whom we collect the data. We refer to the individuals who took part in our research as participants.
We understand that a category refers to a class or division of people who perform certain tasks. Arranging in order refers to assigning the correct positions in relation to each other. The degree of excellence of something is determined by comparing it to other similar objects. The ration scale features a zero, indicating the origin of the character.
The Measurement Scale
|
Measurement Scales |
|||
| Nominal | Ordinal | Interval | Ratio |
| Categories | Categories | Categories | Categories |
| Rank | Rank | Rank | |
| Meaningful Distance | Meaningful Distance | ||
| True Zero | |||
Table-4 Measurement of the Data and Categories
The measurement scale is how the variables are defined and categorized. There are four common scales of measurement that were developed by the psychologist Stanley Stevens. These scales are nominal, ordinal, interval, and ratio. It is the properties of each scale of measurement that determine how the data should be analyzed in the appropriate manner.
Inferential statistics and Testing
|
Which Statistics Can Be Used |
||||
| Non -Parametric Data | Parametric Data | |||
| Discrete Variable | Continuous Variable | |||
| Inferential Statistics | Nominal | Ordinal | Interval | Ratio |
| Chi Square | Yes | Yes | ||
| Mann-Whitney, Wilcoxon, Kruskal Wallis and Friedman | Yes | |||
| Anova and T-Test | Yes | Yes | ||
| Rank Order Correlation | Yes | |||
| Product Moment Correlation | Yes | Yes | ||
| Factor Analysis | Yes | Yes | ||
Table- 5 Inferential statistics and Testing
The two primary applications of inferential statistics are the establishment of estimates regarding populations and the testing of hypotheses in order to draw conclusions regarding populations.
|
Which Statistics Can Be Used |
||||
| Descriptive Statistics | Nominal | Ordinal | Interval | Ratio |
| Frequency Distribution | Yes | Yes | Yes | Yes |
| Percentage | Yes | Yes | Yes | Yes |
| Mode | Yes | Yes | Yes | Yes |
| Percentile | Yes | Yes | Yes | |
| Median | Yes | Yes | Yes | |
| Range | Yes | Yes | ||
| Mean | Yes | Yes | ||
| Standard Deviation | Yes | Yes | ||
| Geometric Mean | Yes | |||
| Harmonic Mean | ` | Yes | ||
Table-6: Descriptive statistics and test
The scale serves as a measurement tool for collecting data for further analysis. When we measure the data, it depends on your research questions, objectives, and hypotheses. You must determine the constructs or variables you want to measure, such as attitudes, opinions, behaviors, or perceptions.
Dr. Abid Hussain Nawaz
Post Doc and Ph.D in Management sciences
Rumana Gull
Scholar Master of Philosophy Biological Sciences
Shakeela Riaz Malik
Scholar Master of philosophy in Linguistics
appreciated
appreciated