Lecture 2: Descriptive Statistics and Data Visualization

Question 1

What are the 3 data measures in SPSS?

Answer 1

Scale (Ratio and Interval)
Ordinal
Nominal

Question 2

What is scale measure?

Answer 2

used for interval and ratio variables (both considered continuous data)

Question 3

What is ratio scale?

Answer 3

measurement scale uses the same interval between one measurement and the next, with a true 0 point.
- you can perform an arithmetic on: height, weight, blood pressure, nutrient intakes

Question 4

What is interval scale?

Answer 4

same as ratio scale but has an arbitrary zero point

- you cannot perform an arithmetic on: temperature, time, etc.

Question 5

What is ordinal data?

Answer 5

variable has two or more categories with an intrinsic ranking/order (temporal position, superiority(, but the difference between each value is not necessarily known.
- gender, ethnicity, etc.

Question 6

What is nominal data?

Answer 6

variable has two or more categories without a natural order (categorical data)
- eye color, hair color, etc.

Question 7

What are the 3 aspects of descriptive statistics?

Answer 7

• shape of the data distribution
• measures of central tendency
• dispersion (variability)

Question 8

What is distribution?

Answer 8

function showing all the possible data values and how often they occur

Question 9

What is normal distribution (Gaussian)?

Answer 9

useful because of central limit theorem: averages of variable independently drawn become normally distributed when the number of observations are sufficiently large.

Question 10

What is a histogram?

Answer 10

A histogram is an accurate representation of the distribution of numerical data. It is an estimate of the probability distribution of a continuous variable

Question 11

What is a standard normal curve?

Answer 11

has a mean of 0 and standard deviation of 1

Question 12

Why is the distribution of data important?

Answer 12

distribution of data can be a factor in deciding whether to use a parametric or non-parametric statistical test.

Question 13

Parametric vs Non-parametric tests

Answer 13

Parametric test: have assumptions regarding shape of data distribution and its parameters (e.g. mean, SD)

Non-parametric test: have few/no assumptions regarding shape of data distribution or parameters

Question 14

Non-normal distributions

Answer 14

Positively skewed (skewed to the right)
Negatively skewed (skewed to the left)
Bimodal distribution
Uniform distribution

Question 15

What are the measures of central tendency?

Answer 15

mode
median
mean

Question 16

What is mode?

Answer 16

the most frequent value in a dataset

- not a very good indicator of central tendency (but the only method for a dataset containing normal categorical data)

Question 17

What is median?

Answer 17

central datum when all of the data are arranges in numerical order
- literal measure of central tendency

Question 18

What is mean?

Answer 18

average of central tendency

- most influenced by outliers –> best used when data is normally distributed.

Question 19

True/False

The mean and median are computable with categorical variables

Answer 19

False

Question 20

Where are the mean, median, and mode located on a normally distributed data?

Answer 20

all three of them are in the middle of the distribution and they will overlap on the highest point of the distribution

Question 21

Where are the mean, median, and mode located on a positively skewed distribution?

Answer 21

mode will fall on the highest peak of this distribution (the most frequent observation)
the mean will fall on the right of the curve
the median will be in between the mode and the mean

Question 22

Where are the mean, median, and mode located on a negatively skewed distribution?

Answer 22

mode will fall on the highest peak of this distribution (the most frequent observation)
the mean will fall on the left of the curve
the median will be in between the mode and the mean

Question 23

How to calculate the mean?

Answer 23

sum of all data divided by the sample size

Question 24

What is the difference between population mean and sample mean?

Answer 24

population all McGill Students

sample 1000 McGill Students that will represent the population.

Question 25

How to calculate median?

Answer 25

• order the values of your variable from lowest to highest
• if it is odd number of observations then the median is the number in the middle
• if it is even number of observations then the median is the 2 middle values divided by 2

Question 26

What is variability?

Answer 26

also referred to as dispersion, spread, or scatter

Question 27

What is range?

Answer 27

the simplest measure of dispersion (largest data values - smallest data value)

Question 28

What is variance?

Answer 28

average of the squared differences from the mean

Question 29

What is standard deviation?

Answer 29

degree to which individual values differ from the mean

- the square root of the variance

Question 30

What are the measures of variability?

Answer 30

range
variance
standard deviation
standard error of the mean (SEM)

Question 31

What is the standard error of the mean (SEM)?

Answer 31

estimate of how fat the sample mean is from the population mean

• measures how accurately the sample represents the population
• a sample mean will always deviate from the population mean. This deviation is the standard error of the mean
• Large SEM indicated inaccuracy in estimate

Question 32

Describe the descriptive statistics for categorical variable

Answer 32

not appropriate to calculate mean or median but can calculate mode
- instead calculate proportions (percentages)

Question 33

Bar chart

Answer 33

displays summary statistics for continuous variables according to some category(ies).
- helpful to compare means/medians across groups.

Question 34

Pie chart

Answer 34

illustrates proportions for categorical data that total to 100

Question 35

Histogram

Answer 35

displays the distribution of continuous data

• frequency displayed on y-axis
• helpful to evaluate shape of data distribution
• can add dimensions by stacking variables on x-axis

Question 36

Boxplot

Answer 36

standardized format for displaying min, max and quartiles, and interquartile range (IQR)
- SPSS displays outliers

Question 37

Scatterplot

Answer 37

displays values for two variables in a dataset (generally independent variable (x-axis) and dependent variable (y- axis)).
o Helpful when assessing correlations and linear relationships
o Can display two dependent variables using two different coloured circles.