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Levels of Measurement Quiz

## Levels of Measurement Answers

1. Indicate which level of measurement is being used in the given scenario. The teacher of a class of third graders records the height of each student.

- Nominal
- Ordinal
- Interval
**Ratio**

2. Indicate which level of measurement is being used in the given scenario. The teacher of a class of third graders records the eye color of each student.

**nominal**- ordinal
- interval
- ratio

3. Indicate which level of measurement is being used in the given scenario. The teacher of a class of third graders records the letter grade for mathematics for each student.

- nominal
**ordinal**- interval
- ratio

4. Indicate which level of measurement is being used in the given scenario. The teacher of a class of third graders records the percentage that each student got correct on the last science test.

- nominal
- ordinal
- interval
**ratio**

5. Indicate which level of measurement is being used in the given scenario. A meteorologist compiles a list of temperatures in degrees Celsius for the month of May.

- nominal
- ordinal
**interval**- ratio

6. Indicate which level of measurement is being used in the given scenario. A meteorologist compiles a list of temperatures in degrees Fahrenheit for the month of May.

- nominal
- ordinal
**interval**- ratio

7. Indicate which level of measurement is being used in the given scenario. A film critic lists the top 50 greatest movies of all time.

- nominal
**ordinal**- interval
- ratio

8. Indicate which level of measurement is being used in the given scenario. A car magazine lists the most expensive cars for 2017.

- nominal
- ordinal
- interval
**ratio**

9. Indicate which level of measurement is being used in the given scenario. The roster of a basketball team lists the jersey numbers for each of the players.

**nominal**- ordinal
- interval
- ratio

10. Indicate which level of measurement is being used in the given scenario. A local animal shelter keeps track of the breeds of dogs that come in.

**nominal**- ordinal
- interval
- ratio

11. Indicate which level of measurement is being used in the given scenario. A local animal shelter keeps track of the weights of dogs that come in.

- nominal
- ordinal
- interval
**ratio**

12. Is the following qualitative or quantitative data? Favorite foods of statistics class.

**Qualitative**- Quantitative

13. Is the following qualitative or quantitative data? Breeds of dogs owned by CHS Seniors.

**Qualitative**- Quantitative

14. Is the following qualitative or quantitative data? Age of statistics parent or guardians.

- Qualitative
**Quantitative**

15. Determine the level of measurement. Weight of walleye caught on Lake Erie

- Nominal
- Ordinal
- Interval
**Ratio**

16. Determine the level of measurement. List of popular video games

**Nominal**- Ordinal
- Interval
- Ratio

17. Determine the level of measurement. Height of students in inches

- Nominal
- Ordinal
- Interval
**Ratio**

18. Determine the level of measurement. Hourly wages of students in fastfood.

- Nominal
- Ordinal
- Interval
**Ratio**

19. Determine the level of measurement. Popular baby names in 2017

**Nominal**- Ordinal
- Interval
- Ratio

20. Determine the level of measurement. Birth year of employees at your work

- Nominal
- Ordinal
**Interval**- Ratio

21. Temperature of the body expressed in Kelvin

- Nominal
- Ordinal
- Interval
**Ratio**

22. Number of students in the classroom

- Nominal
- Ordinal
- Interval
**Ratio**

23. Ages of students in a statistics class

- Nominal
- Ordinal
- Interval
**Ratio**

24. A ___________ is a characteristic that we observed and measured from every element of the universe.

- Data
**Variable**- Observation
- Value

25. A qualitative variable

- A. Always refers to a sample
**B. Is not numeric**- C. Has only two possible outcomes
- D. All of the above are correct

26. The ratio scale of measurement

- A. Usually involves ranking
- B. Cannot assume negative values
**C. Has a meaningful zero point**- D. Is usually based on counting

27. The ordinal scale of measurement

- A. Has a meaningful zero point
**B. Is based on ranks**- C. Cannot assume negative values
- D. All of the above

28. A part of the population.

- biased sample
- population
- random sample
**sample**

29. The entire group of objects or individuals considered for a survey.

- biased sample
**population**- random sample
- sample

30. ___________ consists of numbers representing counts or measurements.

- Mathematical data
- Categorical data
**Quantitative data**- Population data

## Levels of Measurement Examples and Terms to Learn

Ordinal

Interval

Ratio

The precision and properties of the data are related to the level of measurement

Tells you the if there is a similarity or difference (we have one male and one female)

Categories (gender, SES), identifiers, names, labels

More qualitative variables since numbers serve to identify

Numbers are assigned arbitrarily to these categories

There really isn’t a numerical meaning

Male – 1

Female – 2

Transgendered – 3

You can’t say a 1 is less than a 3 or a 3 is one more than a 2

All numbers are equal

**Classifying and counting

Ex. Sex, eye color, zip code, I’d number

****Use with MODE

Tells you if the numbers are equal or not but doesn’t tell you the magnitude

Values can be ordered or ranked from high to low, best to worst, or least to greatest, tallest to shortest, strongly disagree to strongly agree, etc.

**classifying counting and ranking

Ex. Hardness of minerals (good, better, best), grades

****Use with MEDIAN

Grading scales (e.g., A, B, C) have order but lack other properties

Voice quality (e.g., 0 = normal while 3 = extreme)

Cannot say a 4 on a Likert Scale twice as good as a 2

Not a precise way of measuring something

Do not have the property of equal intervals

In their raw form, ordinal data are not suitable for statistical analysis

There are equal intervals (equidistant points) between data points (e.g., standard scores)

Able to describe magnitude

Able to add and subtract but not able to multiply and divide the data

Since there is no zero, there is no absence of the property being measured (IQ, language)

**Classifying counting ranking addition subtraction

Ex. Calendar dates, temperature, dress size

****Symettrical data: MEAN

****Skewed data: MEDIAN

Numbers have the property of inequality

Able to judge the magnitude

There are equal intervals between data points

There is an absolute zero (an absence of that property)

Able to add, subtract, multiply and divide the data

Length, width, height, speaking rate, words read per minute, number of dysfluencies

Classifying counting ranking addition subtraction multiplication division has a true zero

Ex. Number of patients seen, age, length

****Symmetrical data: Mean

****Skewed data: Median

Measures of location (Mean, median, mode)

Measures of Individual Location (Ranks, percentile ranks, standard scores)

Measures of Variability

Range

Variance

Standard Deviation

Coefficient of Variance

Can just express data in terms of mean, median, and mode without variability information.

Information is lost when this happens

See a degree of dispersion in a data set (i.e., variability or spread)

Number of different categories for nominal data (e.g., number of SES is divided by only 2 categories vs. 7)

If the SD is large, the values are spread further away from the mean

Ex. Ranks, percentile ranks, standard scores

Best if used for ordinal data

Measure of score variation

Difference between the lowest and highest score

12 9 15 24 20 8 11 21 22 14

Highest Lowest

Range is 24 – 8= 16

Allows you to represent data as it is dispersed around the mean

If the SD is large, the values are spread further away from the mean

Allows you to express a standard deviation as a percentage

Good when you compare 2 sets of data

Sum the scores and divide by the number of participants or entities in the data set

Best way to estimate a population parameter when compared to the other measures of central tendency

Influenced by extreme scores

Point above and below which half the scores fall (i.e., middle value in a list of numbers)

2 5 8 8 12 14 15 17 19 (12 is the median)

2 5 8 8 12 14 15 17 19 20 (12 and 14 are averaged to get median)

Not influenced by extreme scores

Used when the data set contains a few extreme scores

Describes typical salary levels since an average would be affected by outliers (i.e., billioniares)

If no number is repeated, there is no mode

1 1 1 1 8 9 12 14 15 17 19 20

The most frequently occurring responses on the survey was 5 (strongly agree)

Most frequent score on a test

Describes the spread of the scores around the mean

The larger the standard deviation (SD), the more spread out the scores

The smaller the SD, the closer the scores to the mean

All variables have distributions (or patterns of occurrence)

Tells us how often different values should occur on the distribution if samples of the same size are collected over and over from the same population

The shape of the distribution can be interpreted since it affects which statistical analysis you use

Researchers don’t typically report these

Most try to transform the data statistically to approximate a normal distribution in order to do some further statistical analyses

Three types: Unimodal, bimodal, and skewed

Simplifies the data’s structure

Makes the distribution more symmetrical (the goal)

Addresses variability in data

Make relationships more linear

*If there is an outlier and the rest test 68% interval. Random assignment failed so they did not have initial group equivalency. Go back and run numbers. Can attribute this to the outliers.

-Use logarithms, inverse operations, or square root transformations to transform the data

Visual inspection of the distribution data will help identify

Examination of the skew and kurtosis

Inferential tests of normality (e.g., Kolmorogov-Smirnov) with help identify

Best to combine visual inspection and objective tests to evaluate normality

**Blind the administrator to try and avoid this

Bell shaped curve

They are not normally distributed

Not symmetrical

Can be positive or negative

-We don’t want this because it means that there are outliers.

*Image is positively skewed

Used for determining the probability of certain outcomes

Is unimodal (one mode in the center)

Is symmetrical

Is continuous

Is asymptotic (i.e., gets closer to the horizonal axis as it moves away from the center but never touches the axis)

68% will be within 1 standard deviation (e.g., average range)

95% will fall within 2 standard deviations

99% will fall within 3 standard deviations

a) Continuous Variables

b) Discrete Variables

c) Dichotomous Variables

a) Continuous Variables

b) Discrete Variables

c) Dichotomous Variables

a) Continuous Variables

b) Discrete Variables

c) Dichotomous Variables

2. Ordinal

3. Interval

4. Ratio

a) Nominal

b) Ordinal

c) Interval

d) Ratio

a) Nominal

b) Ordinal

c) Interval

d) Ratio

a) Nominal

b) Ordinal

c) Interval

d) Ratio

a) Nominal

b) Ordinal

c) Interval

d) Ratio

a) Nominal

b) Ordinal

c) Interval

d) Ratio

a) Nominal

b) Ordinal

c) Interval

d) Ratio

a) Nominal

b) Ordinal

c) Interval

d) Ratio

a) Nominal

b) Ordinal

c) Interval

d) Ratio

a) Nominal

b) Ordinal

c) Interval

d) Ratio

a) Nominal

b) Ordinal

c) Interval

d) Ratio