Module 4 - Levels / Scales of Measurement in Research

• Nominal

• Ordinal

• Interval

• Ratio

What are the 4 types of numerical data?

• Surveys

• Scales

What are some examples of ordinal data?

Standardized tests

What is an example of interval data?

• Objects

• People

• Events

Measurement is the process of assigning numbers to what?

Prescribed rule

Do we assign numbers in an arbitrary fashion or in a prescribed rule?

Equally

In research, are numbers created equally or unequally?

Precise they are

In research, numbers aren’t just different in terms of what they measure, but also what?

Nominal Level

What level of data is the lowest level of precision?

Nominal Level

This level of measurement tells you if there is a similarity or difference based on category. Numbers aren’t assigned arbitrarily to these categories

If there are similarities or differences

Nominal level of measurement is good for telling you what?

Ordinal Level

This level of measurement where numbers have the property of inequality. For example, on a scale, 1 could be terrible and 5 could be amazing

Likert Scale

What specific scale is associated with the ordinal level of measurement?

If they are equal or not

Rather than telling you magnitude, what do the numbers in the ordinal level of measurement tell you?

Magnitude

What do the numbers at the ordinal level NOT tell you?

• Best to worst

• Least to greatest

• Tallest to shortest

• Strongly agree to strongly disagree

How are values ordered or ranked in the ordinal level?

Order

What do we need when doing ordinal level data?

Arithmetic Properties

What type of properties does ordinal levels lack?

Grading scales

What type of scales have order but lack other properties?

Interval Level

This level of measurement have numbers that have the property of inequality and there are equal intervals between the data points

Magnitude

What does the interval level describe?

• Add

• Subtract

What 2 math properties can interval level do?

Nominal Level Data

We put a number to a category to determine if there is a balance and good for looking at initial group equivalency

Ordinal Level Data

We want to get more at that ambiguous types of issues (e.g., satisfaction, preference, agreement, etc.) and problems with THIS type of data level has to do with problems with analyzing those as we are nog going to have sophisticated ways to organize this type of data

Interval Levels of Data

This level of data allows us to do more sophisticated analyses with and researchers want something in their study that can be based off of an interval

Ratio Level

This level of measurement has a robust measurement scale as numbers have the property of inequality

Equal

Are intervals between data points in a ratio level equal or unequal?

Inequality

What type of property do numbers have in the ratio level?

Magnitude of change

What are you able to judge using the ratio level?

Absolute zero

This is present in the ratio level and that is the absence of a property

• Proportions

• Ratios

• Percentages

• Fractions

What are some ways that researchers and clinicians use ratio level data to determine?

Descriptive statistics

This type of statistics allows us to use ratio level data to calculate the things like mean and standard deviation

• Mean

• Standard deviation

What does descriptive statistics calculate?

Ratio Level Data

This type of ratio level data is observed or tallied and emerges when we count up the number of occurrences something occurs or if something is right or wrong

• Table (tabular) form

• Measures of location / performance

• Measures of individual location - central tendency

• Measures of variability

What are 4 ways to describe data in terms of descriptive statistics?

Descriptive Statistics

Statistics that describe how the sample performed in your study

Percentile ranks

This tells us where the specific individual fell

Table / tabular form

• They are going to find that central tendency

• They are somehow going to combine those data and tell you where the majority of participants fell

Measures of location / performance

• Mean, median, mode

• Information of data on pre to post test

• Ranks

• Percentile Ranks

• Standard scores

What are examples of measures of individual location?

Standard Deviation

The measure of variability that we are most familiar with as the higher this number is, the more variability there is

Average

What washes out all the variability as we are only looking for that one central score and can’t capture and appreciate the variability?

Sort data and look to see in the smaller groups to see the difference

What does having more categories allow us to do?

Measures of Variability

Experimenters often find unequal values where you see a dispersion in a data set

Range

Largest value minus the smallest value for the difference

Variance

This allows us to represent data as it is dispersed around the mean

• Interval

• Ratio

What 2 types of data is used with variance?

Close

If the SD is small, does that mean that the values are spread close or further away from the mean?

Relative variation

Difference between 2 groups

Mean

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

Outliers

What is the mean influenced by?

When you have outliers

When is the median used?

Nominal Level Data

What type of level data is used with mode?

Nominal

What measurement scale is used with mode?

Ordinal

What measurement scale is used with the median?

Mean

When there is symmetrical data for interval and ratio measurement scales, what measure is used?

Median

When there is skewed data for interval and ratio measurement scales, what measure is used?

More spread out

The largest the SD, are the scores more spread out or closer together?

Distributions

A pattern of scores that 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

Bell curve

Considered a distribution and is a thing where the majority of individuals in a group will perform in the average range

Normal distribution theory

Tells us how values SHOULD occur if the study was done again on a sample that was collected on the same population

Variability

You use distribution to help understand what?

Statistical analysis that we use

The shape of the distribution can be interpreted since it affects what?

• Unimodal

• Bimodal

• Skewed

What are 3 types of frequency distribution?

Data Transformation

This is the process that makes data “good” to analyze

• Simplifies the data’s structure

• Makes the distribution more symmetrical

• Addresses variability in the data

• Make relationships linear

What are some ways that data transformation makes data “good” to analyze?

• Watch for mistakes in data entry and extreme values

• Visual inspection of the distribution will help identify

• Inferential tests of normality will help

• Best to combine visual inspection and objective tests to evaluates normality

What are some questions to ask ourselves to determine if the data is non-normally distributed?

Kolmorogov-Smirnov

What is a type of test to determine normality?

Test for Normality

This test determines problems with data entry or mistakes and identifies outliers by analyzing to figure out why they are there

• Logarithms

• Inverse operations

• Square root transformations

What are some ways to transform data if the data is not normally distributed?

Unimodal

Type of frequency distribution where several average scores and there are fewer high and low scores on either side of the mean

Bell-shaped curve

What is an example of a unimodal frequency distribution?

Bimodal Distribution

Type of frequency distribution where scores accumulate at 2 different parts of the scale with 2 different modes

Skewed Distributions

Type of frequency distribution where scores are mainly high or low and they aren’t symmetrical

• Sample wasn’t representative of the population

• Problems with data analysis

What types of problems could have occurred if we have a skewed distribution?

Kurtosis

Measures the peakedness of a symmetrical distribution of interest to researchers. In other words, it measures how fat or thin the tails are

Mesokurtic

The normal curve with a moderate degree of peakedness

Leptokurtic

When a large proportion of the scores are located in the center of the distribution where there may be 98% of the population around the mean rather than 68%

Platykurtic

When a large proportion of the scores occur in the tails and the distribution is flatter - there is some clustering but it isn’t enough

68%

what % will be within 1 SD of the average?

95%

What % will fall within 2 SDs of the mean?

99%

What % will fall within 3 SDs of the mean?

Continuous

Ends never touch the bottom

Asymptotic

Gets closer to the horizontal axis as it moves away from the center but never touches the axis

• Unimodal

• Symmetrical

• Continuous

• Asymptotic

What are some characteristics of normal distribution?