Descriptive Statistics

Question 1

What is the role of descriptive statistics?

Answer 1

• Describe the sample of research participants
• want to convey the average/central tendency and the spread of data
• can summarise data numerically and graphically

Question 2

What is the second purpose of statistics?

Answer 2

To use data from a sample to tell us about a population

Question 3

What is the role of inferential statistics?

Answer 3

• estimating the values is a population from a sample
• to determine whether a relationship between variables is real or due to chance
• to see if differences between groups in an experiment/trial are caused by the treatments applied or due to chance

Question 4

What are the different types of data/variables?

Answer 4

• categorical/binary (e.g. gender, ethnicity)

- continuous (e.g. age, height, weight)

Question 5

What are the different levels of measurement?

Answer 5

• nominal (binary and categorical)
• ordinal (order or rank categorised)
• interval ( continuos)
• ratio (continuos)

Question 6

What is nominal data?

Answer 6

• the data is allocated into named categories only, with no implication of size, value or order
• numbers are used to code the categories of a categorical variable

Question 7

What is ordinal data?

Answer 7

• categorical data that is ordered (intervals may vary) (e.g. Disease stage, degree of pain)
• can’t have means for these results
• categories are represented by a number or words

Question 8

What is interval level?

Answer 8

• continuous data measured along a scale with equal interval/meaning
• data are represented by a number
• the scale doesn’t have a true zero point (e.g. blood pressure, time of day)

Question 9

What is ratio level?

Answer 9

• interval data but with the additional property that ratios are meaningful
• zero has a meaning (e.g. age, height)
• highest level of measurement

Question 10

What is included in central tendency?

Answer 10

• mode
• median
• mean

Question 11

What is used to show the dispersion of data?

Answer 11

• range
• inter-quartile range
• standard deviation

Question 12

Why is dispersion important?

Answer 12

Describes how spread out the data is

Question 13

What is inter-quartile range?

Answer 13

• the range between the lower quartile (1/4 of the way) and the upper quartile (3/4 of the way)
• the range of measurements for the middle 50% of the population whose values lie between the 25% and 75%

Question 14

What is standard deviation?

Answer 14

The average distance, or deviation, of each value from the mean

Question 15

How do you describe nominal data numerically?

Answer 15

• data can only be summarised as frequencies or percentages
• central tendency is represented by the mode (bi-modal or multi-modal)
• the spread of data is not applicable

Question 16

What is a frequency table?

Answer 16

• summarises all of the data visually

- in the text focus on important findings

Question 17

When are cross tabulations used?

Answer 17

Frequency tables can also be used to illustrate the relationships between categorical variables

Question 18

How do you describe ordinal data numerically?

Answer 18

• central tendency can be given as the mode and/or median
• short scales are often treated as simply nominal data and displayed using frequency tables
• spread of data can be described via the range and/or inter-quartile range

Question 19

How is nominal and ordinal data graphically described?

Answer 19

Bar chart

Question 20

How do you numerically describe interval/ratio levels?

Answer 20

• central tendency can be described using mode, median and mean
• spread of the data can be described via the range, inter-quartile range and/or standard deviation

Question 21

How do you graphically describe interval/ratio level data?

Answer 21

Frequency distribution (histograms)

Question 22

Why are histograms used to describe interval/ratio level data?

Answer 22

Used to illustrate the shape of the distribution of values in the data

Question 23

What is a parametric histogram?

Answer 23

Normal disrribution

Question 24

What is non-parametric histogram?

Answer 24

Skewed distribution, can be positively or negatively skewed

Question 25

What is normal/parametric distribution?

Answer 25

• distinctive bell shaped curve with values symmetrical about the mean
• normal distribution: 68% within 1 SD of the mean, 95% within 2 SD, 99.7% within 3 SD
• occurs naturally; many human attributes plot on a normal distribution

Question 26

What is a skewed/non-parametric distribution?

Answer 26

• the most frequent scores are clustered at one end of the scale
• numbers fall mainly below the mean = distribution is positively skewed
• numbers fall mainly above the mean = distribution is negatively skewed
• mean, median and mode aren’t the same

Question 27

What is the confidence intervals for the mean?

Answer 27

• an estimated range of values around the sample mean which are likely to include the Unknown population mean
• if many independent samples were taken from the sample population, the a certain percentage of the intervals will include the population mean
• normally 95%

Question 28

What is the first purpose of statistics?

Answer 28

• to summarise data that has been collected about/from a group of participants