# Some Basic Statistical Concepts and Notations

**Quantitative Variables** take values that very in terms of magnitude. They are easy to measure and compare with one another. These may be scores obtained in a test, weight, height, age, distance, number etc.

** Qualitative Variables** are those that differ in kind. They are only categorized. The differences are usually in kind such as marital status, gender, nationality, social economic status, educational qualifications etc.

** Quantitative variables** may be discrete or continuous.

**A discrete variable** is one which can take only a finite set of values, implying that fractional values are usually not allowed.

These variables are generated by a counting process usually in whole numbers i.e. the number of goals scored in a football match, the number of teachers in a school, number of girls and boys in a class etc.

A **continuous variable** is that which can take on any value over a range of feasible values. Measured data can be whole numbers or fractions 1-2 weight, height, distance values etc. Variables could also be dependent or independent depending on their functions in a given context.

A **variable** that is dependent in one context may be independent in another.

The **Independent Variable** is one that is manipulated or treated. The effect of this manipulation is manifested on the dependent variable. The value of the dependent variable thus depends on that of the independent variable. Also, the value of the dependent variable is usually predicted from that of the independent variable.

When comparing the effects of two teaching methods on students’ learning achievement, the teaching methods are the independent variables while learning achievement is the dependent variable.

Note that in graphing, the dependent variable is placed on the vertical, Y axis while the

independent variable is placed on the horizontal, X-axis.

There are two types of independent variables – Treatment or Active variables and Organismic or Attribute variables.

**Treatment or Active Variable** is defined as one that can be directly manipulated by the researchers and to which he or she assigns subjects. This group includes method of teaching,method of grouping and reinforcement procedures.

**Organismic or Attribute Variables** are those variables that cannot be actively manipulated by the researchers. These variables are sometimes called assigned variables and they are characteristics of individuals that cannot be manipulated at will.

Such independent variables as age, sex, aptitude, social class, race, and intelligence level had already been determined but the researchers can decide to include or remove them as variables to be studied.

**Confounding Variables**: confounding variables are those aspects of a study or sample that might influence the dependent variable or the outcome measure and whose effect may be confused with the effects of the independent variable. There are two types of these – Intervening and Extraneous variables.

**Intervening variables** are those variables that cannot be measured directly or controlled but may have an important effect upon the outcome. They are usually modifying variables that interfere between the cause and the effect.

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Evaluation

1. Quantitative variables are easy to measure and compare because they vary in terms of ___________.

a) Kind

b) Magnitude

c) Category

2. Examples of qualitative variables include marital status, gender, and ___________.

a) Weight

b) Age

c) Educational qualifications

3. A discrete variable can only take a finite set of values and is generated by a ___________ process.

a) Counting

b) Measuring

c) Continuous

4. A continuous variable can take on any value over a range of ___________ values.

a) Qualitative

b) Discrete

c) Feasible

5. The value of the dependent variable is often predicted from that of the ___________ variable.

a) Kind

b) Continuous

c) Independent

6. In graphing, the dependent variable is usually placed on the ___________ axis.

a) Y

b) X

c) Z

7. Treatment or Active variables can be directly manipulated by ___________.

a) Participants

b) Researchers

c) Observers

8. Organismic or Attribute Variables are characteristics of individuals that cannot be manipulated ___________.

a) Directly

b) Actively

c) Easily

9. Confounding variables might influence the dependent variable and their effects could be confused with those of the ___________ variable.

a) Independent

b) Continuous

c) Dependent

10. Intervening variables interfere between the cause and the ___________.

a) Experiment

b) Manipulation

c) Effect

11. Qualitative variables differ in ___________.

a) Kind

b) Magnitude

c) Measurement

12. Quantitative variables can be ___________ or continuous.

a) Discrete

b) Dependent

c) Categorized

13. An example of a continuous variable is ___________.

a) Gender

b) Age

c) Number of goals scored

14. The effect of manipulating the independent variable is seen in the ___________ variable.

a) Continuous

b) Qualitative

c) Dependent

15. Treatment or Active variables include method of teaching and ___________ procedures.

a) Social

b) Grading

c) Reinforcement