Why are proportions useful measures

For example, in the Kelvin temperature scale, there are no negative degrees of temperature — zero means an absolute lack of thermal energy. The level at which you measure a variable determines how you can analyze your data. The different levels limit which descriptive statistics you can use to get an overall summary of your data, and which type of inferential statistics you can perform on your data to support or refute your hypothesis. In many cases, your variables can be measured at different levels, so you have to choose the level of measurement you will use before data collection begins.

At an ordinal level, however, you only know the income bracket for each participant, not their exact income. Since you cannot say exactly how much each income differs from the others in your data set, you can only order the income levels and group the participants.

What can proofreading do for your paper? Scribbr editors not only correct grammar and spelling mistakes, but also strengthen your writing by making sure your paper is free of vague language, redundant words and awkward phrasing. See editing example. When measuring the central tendency or variability of your data set, your level of measurement decides which methods you can use based on the mathematical operations that are appropriate for each level.

The methods you can apply are cumulative; at higher levels, you can apply all mathematical operations and measures used at lower levels. Frequently asked questions about levels of measurement What are the four levels of measurement? Levels of measurement tell you how precisely variables are recorded. There are 4 levels of measurement, which can be ranked from low to high:.

Depending on the level of measurement , you can perform different descriptive statistics to get an overall summary of your data and inferential statistics to see if your results support or refute your hypothesis. Some variables have fixed levels.

For example, gender and ethnicity are always nominal level data because they cannot be ranked. However, for other variables, you can choose the level of measurement. You can set up a proportion to determine the length of the enlarged photo. Determining Whether a Proportion is True or False. A proportion is usually written as two equivalent fractions. For example:. Notice that the equation has a ratio on each side of the equal sign. Each ratio compares the same units, inches and feet, and the ratios are equivalent because the units are consistent, and is equivalent to.

Proportions might also compare two ratios with the same units. For example, Juanita has two different-sized containers of lemonade mix. She wants to compare them. She could set up a proportion to compare the number of ounces in each container to the number of servings of lemonade that can be made from each container.

Since the units for each ratio are the same, you can express the proportion without the units:. When using this type of proportion, it is important that the numerators represent the same situation — in the example above, 40 ounces for 10 servings — and the denominators represent the same situation, 84 ounces for 21 servings. Juanita could also have set up the proportion to compare the ratios of the container sizes to the number of servings of each container. Sometimes you will need to figure out whether two ratios are, in fact, a true or false proportion.

Below is an example that shows the steps of determining whether a proportion is true or false. Is the proportion true or false? The units are consistent across the numerators. The units are consistent across the denominators. Write each ratio in simplest form. Since the simplified fractions are equivalent, the proportion is true. The proportion is true.

Identifying True Proportions. To determine if a proportion compares equal ratios or not, you can follow these steps. Check to make sure that the units in the individual ratios are consistent either vertically or horizontally. For example, or are valid setups for a proportion. Express each ratio as a simplified fraction. If the simplified fractions are the same, the proportion is true ; if the fractions are different, the proportion is false.

Sometimes you need to create a proportion before determining whether it is true or not. An example is shown below. One office has 3 printers for 18 computers. Another office has 20 printers for computers.

Is the ratio of printers to computers the same in these two offices? Identify the relationship. Note that in certain ratios, the numerator and denominator are different categories of the same variable, such as males and females, or persons 20—29 years and 30—39 years of age. In other ratios, the numerator and denominator are completely different variables, such as the number of hospitals in a city and the size of the population living in that city.

During —, enrollees were documented either to have died or were still alive. The results are summarized as follows. Calculate the ratio of non-diabetic to diabetic men. Example A: A city of 4,, persons has clinics. Calculate the ratio of clinics per person. Then the ratio becomes:. You could also divide each value by 1. Calculate the ratio of the infant mortality rate in Delaware to that in New Hampshire.

Death-to-case ratio is the number of deaths attributed to a particular disease during a specified period divided by the number of new cases of that disease identified during the same period. It is used as a measure of the severity of illness: the death-to-case ratio for rabies is close to 1 that is, almost everyone who develops rabies dies from it , whereas the death-to-case ratio for the common cold is close to 0.

For example, in the United States in , a total of 15, new cases of tuberculosis were reported. Dividing both numerator and denominator by the numerator yields 1 death per Both expressions are correct. Note that, presumably, many of those who died had initially contracted tuberculosis years earlier.

Thus many of the in the numerator are not among the 15, in the denominator. Therefore, the death-to-case ratio is a ratio, but not a proportion. A proportion is the comparison of a part to the whole. It is a type of ratio in which the numerator is included in the denominator. Still more units of energy per unit time power exist kilocalories per day, liters of oxygen per hour, ergs, and Watts. Scale Examples The following are the most commonly used examples: 1.

What is your height in feet and inches? Less than 5 feet. What is your weight in kgs? Less than 50 kgs 70 kgs 90 kgs kgs More than kgs 3. How much time do you spend daily watching television? Less than 2 hours hours hours hours More than 6 hours Let us take the example of speed to understand this scale better.

Advantages of Ratio Scale A ratio scale has a point zero characteristic, where the value of the variable has no value at all. Weight, height etc can be calculated on it because they have a real zero value. But most of the scientific variables can be measured on this scale.

Point zero is an essential characteristic to measure a ratio between any two variables because in the absence of zero there is no ratio. In fact, in the absence of a ratio scale, scientific variables cannot be measured. Related Posts. Create online polls, distribute them using email and multiple other options and start analyzing poll results.