Measurement and Graphical Representations of Data

Question 1

What do descriptive statistics tell us?

Answer 1

What type of variable we have and what are their values in our sample

Question 2

When we want to study a _________, we ____ what happens in the __________ by studying a ______________

Answer 2

1. characteristic
2. infer
3. population
4. representative sample

Question 3

What is categorical data?

Answer 3

Qualitative data that can be divided into groups, usually based on the limited and fixed number of possible values it can have (e.g. colours)

Question 4

What are the two main types of categorical data?

Answer 4

Nominal and Ordinal

Question 5

What is a nominal variable?

Answer 5

Categorical data with no inherent order (e.g. ethnicity). It cannot be a number or measured but may be coded for ease of analysis

Question 6

What is an ordinal variable?

Answer 6

Categorical data that can be ranked, although not necessarily easily spaced (e.g. SES status). Numbers may represent an order but have no mathematical meaning.

Question 7

What is numerical data?

Answer 7

Quantitative data with values that are always expressed in number form

Question 8

What are the three main types of numberical data?

Answer 8

Interval, discrete, and continuous data

Question 9

What is an interval variable?

Answer 9

Data which is ordinal but with equidistant and meaningful spaces, usually with 5 or more categories

Question 10

What is discrete data?

Answer 10

A countable variable that involves a specific, limited number of possible integer values (e.g. number of kids, shoe size). It may have decimals to include halves if logical.

Question 11

What is continuous data?

Answer 11

A variable that can be measured. It is not fixed and can have an infinite number of possible values in a prespecified interval (e.g. height, weight, age)

Question 12

What is the least informative type of variable?

Answer 12

Categorical nominal

Question 13

What is the most informative type of variable?

Answer 13

Numerical continuous

Question 14

If a variable has four equidistant categories, what type of variable is it?

Answer 14

Categorical ordinal - there is not enough information to approximate the underlying variable

Question 15

If a variable has five equidistant categories with mathematical meaning, what type of variable is it?

Answer 15

Numerical interval - we can treat it as continuous as we can sufficiently estimate the underlying continuum

Question 16

If a variable has ordered values and we know that the difference between two values is meaningful, what type of data is this?

Answer 16

Numerical interval

Question 17

A measure of agreement asks participants to rate their agreement 1) strongly disagree, 2) disagree, 3) agree, 4) strongly agree. What type of variable is this?

Answer 17

Categorical ordinal

Question 18

A survery on fruit intake asks participants to rate how often then eat fruit per week: 1-2 days per week, 3-4 days, 5-6 days, or everyday. What type of variable is this?

Answer 18

Numerical interval

Question 19

A survery asks participants to rate their agreement with 1) I am not sure, 2) I agree to some extent, 3) Depends on the occasion, 4) I am not informed. What type of variable is this?

Answer 19

Categorical nominal

Question 20

A survery asks participants to rate quality of communication on a scale where 1=very poor and 10=very good. What type of variable is this?

Answer 20

Numerical interval/continuous

Question 21

What is a valid percentage?

Answer 21

The frequency of a category amongst those who responded (excluding those who did not)

Question 22

What are the best descriptive indices for categorical data?

Answer 22

Frequencies and percentages

Question 23

What are the best types of graphical representation for categorical data?

Answer 23

Bar charts or pie charts

Question 24

What is the best use of pie charts in research?

Answer 24

For nominal data with 2 or more categories

Question 25

What goes on the X and Y axis of a bar chart?

Answer 25

X=category Y=count/frequency

Question 26

What are the two main measures used to describe numerical data?

Answer 26

Location (central tendency) and dispersion (variability)

Question 27

What is the variance used for?

Answer 27

To understand how far values are from the mean (the average squared distance)

Question 28

What does the standard deviation measure?

Answer 28

How spread out a group of numbers are from the mean

Question 29

If you have the variance, how do you calculate the standard deviation?

Answer 29

Take the square root

Question 30

If you have the standard deviation, how do you calculate the variance?

Answer 30

Square it

Question 31

Why do you divide by n-1 when working out the variance or SD when using a sample?

Answer 31

To obtain an unbiased estimate for the population

Question 32

What are examples of measures of location and central tendency?

Answer 32

Mean, median, and mode

Question 33

What are examples of measures of dispersion?

Answer 33

Standard deviation, minimum and maximum, range and IQR

Question 34

What are the best types of graphical representation for numerical data?

Answer 34

Histograms and box plots

Question 35

What do the bins represent in a histogram?

Answer 35

Intervals, not values

Question 36

What can you add to a histogram to help visualise the spread compared to what may be expected?

Answer 36

A normal distribution curve

Question 37

What is the normal curve?

Answer 37

A bell shaped symmetrical curve around the mean

Question 38

In a normal distribution, what percentage of values are lower than the mean?

Answer 38

50%

Question 39

In what type of distribution does the mean equal the median and the mode?

Answer 39

The normal distribution

Question 40

What is the name for data that is not normal?

Answer 40

Skewed/non-symmetrical

Question 41

If the median and mode are smaller than the mean, what is the distribution?

Answer 41

Positively skewed

Question 42

If data is positively skewed, the mean is ________ than the median and the mode.

Answer 42

Greater

Question 43

If the median and mode are greater than the mean, what is the distribution?

Answer 43

Negatively skewed

Question 44

If data is negatively skewed, the mean is _______ than the median and the mode.

Answer 44

Smaller

Question 45

What are the best descriptive indices to use for normal (symmetrical) numerical data?

Answer 45

Mean and standard deviation

Question 46

What are the best descriptive indices to use for skewed (non-symmetrical) numerical data?

Answer 46

Median, minimum and maximum, and interquartile range

Question 47

What is the best measure of dispersion for normal data?

Answer 47

Standard deviation

Question 48

What is the best measure of dispersion for skewed data?

Answer 48

Minimum and maximum, and interquartile range

Question 49

What is the best measure of central tendency for normal data?

Answer 49

Mean

Question 50

What is the best measure of central tendency for skewed data?

Answer 50

Median

Question 51

What are the best descriptive indices for discrete numerical data?

Answer 51

Median, mode, min-max, and IQR

Question 52

What is the benefit of using a box plot?

Answer 52

To visualise outliers and depict the distribution of data across groups

Question 53

In a box plot, what percentage of values are greater than Q3?

Answer 53

25%

Question 54

In a box plot, what does the middle line represent?

Answer 54

The median

Question 55

What type of distribution would produce a box plot where (Q2 - Q1) < (Q3 - Q2) ?

Answer 55

A positively skewed distribution

Question 56

What type of distribution would produce a box plot where (Q2 - Q1) = (Q3 - Q2) ?

Answer 56

A normal distribution

Question 57

What type of distribution would produce a box plot where (Q2 - Q1) > (Q3 - Q2) ?

Answer 57

A negatively skewed distribution

Question 58

If the mean, median, and mode are all close together, what can we infer from the data?

Answer 58

That it is normally distributed

Question 59

What are usually the best descriptive indices for numerical interval data?

Answer 59

Median and range (assuming it is skewed)