PBH 616: Quantitative Research Method Lecture 05: Variables and Measurements Sajia Afrin Masters of Public Health (MPH) Program University of South Asia

Any factor that can change in a scientific investigation or experiment A variable is defined as anything that has a quantity or quality that varies.  Any factor that can change in a scientific investigation or experiment Example: Gender, age, eye color, motivation etc…… (can be anything)

Independent Variables (Another word “Manipulated or Experimental” Variables The variables which represents inputs / causes/ risk factors for any circumstances or for any diseases. It influences other variables.

Dependent Variables Another word “Outcome” variables Dependent variables presumed to be affected by one or more independent variables. It is the presumed effect. It responds to independent variables.

Let’s identify some independent and dependent variables “ How stress affects mental state of human being? Smoking causes cancer. Promotion effects employees motivation.

Qualitative Variables or Categorical Variables These variables are not numeric It describes data that fit into categories. Example: Eye colors (variables include: blue, green, brown, hazel). Color of a ball ( e.g: green, red, blue) A qualitative variables may be coded to appear numeric but these numbers are meaningless, as in 1=Male, 2= Female

Measurements of Qualitative Variables Qualitative/Categorical Nominal Ordinal

Nominal Nominal variables, another word categorical variable. two or more categories without following any natural order. Nominal variables: Cannot be quantified. In other words, you can’t perform arithmetic operations on them, like addition or subtraction, or logical operations like “equal to” or “greater than” on them. Cannot be assigned any order. Example: Gender (Male, Female, Transgender). Eye color (Blue, Green, Brown, Hazel).

Examples of Nominal Scales

“ Categories can be ordered or ranked” Ordinal Ordinal variables are categorical variable which have two or more categories like nominal variables. But the difference is “ Categories can be ordered or ranked” The categories are ranked but the differences between ranks may not be equal. Example: first, second, and third in a race are ordinal data. The difference in time between first and second place might not be the same the difference between second and third place.

Example of Ordinal Scales

Quantitative Variables Quantitative variables; have numerical value i.e. it is represented in numbers. Example: Height, age, crop yield, GPA, salary, temperature. -Average number of lottery tickets sold (e.g. 25, 2,789, 2 million). - How many cousins you have (e.g. 0, 12, 22). Arithmetic operations can be performed on these variables i.e. even after performing operations like addition, subtraction, multiplication or division, we get some number as the result. .

Measurements of Quantitative Variables Interval Ratio

Interval Similar to ordinal variables, except intervals between the values of the interval variable are equally spaced, but don’t have true defined true 0.   As a result , “difference between two values is meaningful”.  For example, suppose you have a variable such as annual income that is measured in dollars, and we have three people who make $10,000, $15,000 and $20,000. The second person makes $5,000 more than the first person and $5,000 less than the third person, and the size of these intervals is the same.  If there were two other people who make $90,000 and $95,000, the size of that interval between these two people is also the same ($5,000).

Interval Not only rank orders the items that are measured, but also to quantify and compare the sizes of differences between them. For Example: Students performance on a spelling test score of 16 will be higher than 14 and lower than 18 and the difference between them is 2 points (equal intervals).

Example of Interval Scales Celsius Temperature. Fahrenheit Temperature. IQ (intelligence scale). SAT scores.

Ratio Differences are meaningful (like interval; differences are equally spaced). plus ratios are meaningful and there is a true zero point. Example: Weight in pounds 10 lbs is twice as much as 5 lbs. (ratios are meaningful: 10/5=2) and zero pounds means no weight or an absence of weight (true zero point-meaningful)

Examples of Ratio Scales The following questions fall under the Ratio Scale category: What is your daughter’s current height? Less than 5 feet. 5 feet 1 inch – 5 feet 5 inches 5 feet 6 inches- 6 feet More than 6 feet What is your weight in kilograms? Less than 50 kilograms 51- 70 kilograms 71- 90 kilograms 91-110 kilograms More than 110 kilograms

Summary of data types and scale measures Offers: Nominal Ordinal Interval Ratio The sequence of variables is established – Yes Mode Median Mean Difference between variables can be evaluated Addition and Subtraction of variables Multiplication and Division of variables Absolute zero

Comparing the Scales Nominal Versus Ordinal Gender: Male, Female, Other. Religious preference: Buddhist, Mormon, Muslim, Jewish, Christian, Other. Level of Agreement: yes, maybe, no. Socioeconomic status: poor, middle class, rich.

Comparing the Scales Interval Versus ordinal : Temperature: A 1 degree difference is the same at all points on the scale. Place in race (1st, 2nd, 3rd ): The difference in finishing between 1st and 2nd is not necessarily ( and probably not) the same as the difference between 2nd and 3rd.

Comparing the Scales Interval versus ratio: Temperature: 0 degrees does not mean an absence of the property (no true zero point) and 80 degrees is not twice as hot as 40 degrees. Effectiveness of Medicine: 60 mg of fluoexetine is three times as great as 20 mg.