Working with Ratio Scales

 

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Ratio Scales, Definition, Examples, and Data Analysis

1. A ratio scale is quantitative with true zero and equal intervals between neighboring points.
2. A ratio scale of zero means a total absence of the variable you are measuring.
3. An interval scale does not have any of the above mentions.
4. Length, area, and population are examples of ratio scales.
5. The ratio level contains all of the features of the other 3 levels.
6. At the ratio level, values can be categorized, and ordered, have equal intervals, and take on a true zero.
7. Nominal and ordinal variables are categorical variables
8. Interval and Ratio variables are quantitative variables
9. Many more statistical tests can be performed on quantitative than categorical data

So What is a True Zero?? 🟥🟥🟥🟥🟥🟥🟥

1. On a ratio scale, a zero means there's a total absence of the variable of interest.
1. For example, the number of children in a household or years of work experience are ratio variables.
2. A respondent can have no children in their household or zero years of work experience.
2. With a true zero in your scale, you can calculate ratios of values.
1. For example, you can say that 4 children are twice as many as 2 children in a household and eight years is double 4 years of experience
3. Some variables, such as temperature, can be measured on different scales
1. Celcius and Fahrenheit are interval scales
2. Kelvin is a ratio scale
3. In all three scales, there are equal intervals between neighboring points
4. The Kelvin scale has a true zero, where nothing can be colder.
5. That means that you can only calculate ratios of temperatures in the Kelvin scale
6. A true zero makes it possible to multiply, divide, or square root values.
7. Collecting data on a ratio level is always preferable to the other levels because it is the most precise.

Examples of ratio scales  ⏹️⏹️⏹️⏹️⏹️⏹️⏹️

• Interval variables and ratio variables can be discrete or continuous.
• A discrete variable is expressed only in countable numbers
• A continuous variable can potentially take on an infinite number of values.
  
  
  
• Number of vehicles owned in the last 10 years                                 discrete
• The number of people in a household                                                      discrete
• The number of students who identify as religious                                           discrete
• reaction time in a computer task                                                                 continuous
• Years of work experience                                                                                      continuous
• Speed in miles per hour                                                                                      continuous

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Ratio Data Analysis

1. After you have collected ratio data, then you can gather descriptive and inferential statistics
2. Almost all statistical tests can be performed on ratio data because all mathematical operations are permissible

• Ratio data example - you collect data on the commute duration of employees in a large city
• the data is continuous and in minutes
• To summarize your data, you can collect the following descriptive statistics :
• the frequency distribution in numbers or percentages
• the mode, median, or mean to find the central tendency
• the range, standard deviation, and variance to indicate the variability
  
• You can get an overview of the frequency of different values in a table and visualize their distribution in a graph
  
  
  
• Enter your data into a grouped frequency distribution table.
• Create groups with equal intervals on the left-hand column and enter the number of scores that fall within each interval into the right-hand column.

1. To visualize the data, plot it on a frequency distribution polygon.
2. Plot the groupings on the x-axis and the frequencies on the y-axis
3. Join the midpoint of each grouping using lines

Variability

1. The range, standard deviation and variance describe how spread your data is.
2. The range is the easiest to compute
3. The standard deviation and the variance describe how spread your data is and they are also more informative.
4. The coefficient of variation is a measure of spread that only applies to ratio variables

Range

• To find the range subtract the lowest value from the highest value in your data set.
• the range equals72.5 - 7 = 65.5

Statistical Tests

• With a normal distribution of ratio data then parametric tests are best for testing hypotheses
• Parametric tests are more powerful than non-parametric tests and you can make stronger conclusions with your data
• The data must meet several requirements for parametric tests to apply
• The following chart lists parametric tests that are some of the most common ones applied to test hypotheses about ratio data

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References

Bhandari, P. (2020, August 28). Ratio Scales | Definition, Examples, & Data Analysis. Scribbr. https://www.scribbr.com/statistics/ratio-data/

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