Quanti - Descriptive Statistis

Question 1

What is statistics?

Answer 1

“the practice or science of collecting and analysing numerical data in
large quantities, especially to make inferences on a population based on
a representative sample.”

To helps us turn data into information that can be interpreted, understood and used to improve evidence-based healthcare

Question 2

What are the 2 broad classifications of statistics?

Answer 2

Descriptive and inferential statistics

Question 3

What are descriptive statistics?

Answer 3

to provide description of population through numbers, graphs and tables

(COLLECT, SUMMARIZE, DESCRIBE).

Question 4

What are inferential statistics?

Answer 4

to provide meaningful inferences/conclusions on
the population based on data collected from a sample

(INTERPRET, GENERALIZE, PREDICT).

Question 5

How are continuous variables usually presented?

Answer 5

1. Measure of central tendency
2. Measure of dispersion/variability

Question 6

How are categorical variables usually presented?

Answer 6

Measure of frequency

Question 7

What kinds of statistical methods are used for inferential statistics?

Answer 7

1. Hypothesis testing
2. Regression analysis

Question 8

What do the following terms mean?

1. Population
2. Parameter
3. Variable
4. Sample
5. Statistic

Answer 8

Population: Collection of entire set of individual objects or events of interest

Parameter: Numerical characteristic of population

Variable: Characteristic that is being measured.

Sample: Subset of a population

Statistic: Measure that describes the sample

Question 9

Descriptive statistics for categorical variables - Measure of frequency

Answer 9

How are they presented?

1. Frequency (%):
   e.g. Males 70 (70%); females 30 (30%)
2. Cross-tabulation
   (present frequency in a table form)
3. Use of pictogram
4. Use of pie, bar, column, line, scatter, all sorts of charts

Question 10

Descriptive statistics for continuous variables - Measure of central tendency

Answer 10

Usually, mean, median and mode are used.

Can be illustrated via histogram (barchart stuck together) or boxplot

Question 11

What is mean?

Answer 11

• arithmetic average of a set of values
• more suitable for symmetric
  distribution
• OFTEN REPORTED WITH STANDARD DEVIATION
  e.g. mean (SD)

Formula:
Add all values divided by total number of values (frequency)

Question 12

What is median?

Answer 12

• middle value of a data set when arranged in ascending or descending order
• more suitable for SKEWED distribution
• OFTEN REPORTED WITH INTERQUARTILE RANGE
  e.g. median (IQR))

Formula:
If n (frequency)= 9,
Median: ((9+1))/2 th term: 5th term

If n (frequency)= 10,
Median: (5th term + 6th term)/2

Question 13

What is mode?

Answer 13

value that occurs most frequently in a data set

Example:
Data set {2, 3, 4, 4, 5, 6, 6, 6, 7}.
Mode = 6

Question 14

What is a normal distribution?

Answer 14

Mean, median and mode coincides at one point on the x-axis. (see slide 12)

Question 15

What is a left skewed distribution?

Answer 15

Mean is on the left side of x-axis. (see slide 15)

Question 16

What is a right skewed distribution?

Answer 16

Mean is on the right side of the x-axis. (see slide 15)

Question 17

What is the normality of distribution?

Answer 17

• All kinds of naturally occurring variables are usually normally distributed (Bell curve)
  e.g. height, weight

Central limit theorem: If sample size > 30, should follow a normal distribution

• Main property: mean, median and mode are the same (symmetrical curve)

Question 18

What is skewness in a normal distribution?

Answer 18

lack of symmetry

• tells us direction of variability
• different from variance, which tells magnitude of variability

Question 19

What is variance?

Answer 19

• average of squared differences of each datapoint
  from mean (squared unit of mean)
• if sigma, σ2=0: all data values are the same
• Small variance= data are close to mean and each other
• Large variance= data are far from mean and each other

Question 20

What is standard deviation?

Answer 20

square root of variance (same unit as mean)

Question 21

What is the 68-95-99.7 rule?

Answer 21

a statistical principle that applies to bell-shaped, normal distributions

tells you where most of your values lie in a normal distribution:

~68% of values are within 1 SD from the mean

~95% of values are within 2 SD from the mean

~99.7% of values are within 3 SD from the mean