Descriptive and Inferential Statistics

Question 1

What is descriptive statistics?

Answer 1

Deal with an entire dataset e.g. population, goal is to summarise raw data and represent graphically and not extend conclusions beyond the observed dataset.

Question 2

What is inferential statistics?

Answer 2

Goal is to make inferences beyond your data. To infer something about a population based on a smaller model, or sample. Make an estimation of a population parameter from a statistic or test a hypothesis.

Question 3

What is the arithmetic mean?

Answer 3

Add all values and divide between number of values. Sensitive to outliers.

Question 4

What is the geometric mean?

Answer 4

Multiply values and take nth root. Can reduce the effect of outliers.

Question 5

What is the weighted mean?

Answer 5

Times each value but its ‘weight’, add together and divide by value of all weights.

Question 6

What measure of centrality is best for normally distributed data?

Answer 6

Mean, median or mode

Question 7

What measure of centrality is best for negatively or positively skewed data?

Answer 7

Mode (3 measures of centrality will not coincide)

Question 8

What measure of central tendency would we use for categorical data?

Answer 8

Mode

Question 9

Define variation

Answer 9

Average distance an observation is from the mean

Question 10

How do you calculate variation?

Answer 10

Subtract each value from the mean, then square the result. Then work out arithmetic mean of these numbers.
‘sum of squared differences from the mean’

Question 11

What is standard deviation?

Answer 11

Square root of variance.

Larger sd= wider spread of data

Question 12

Why and how to we adjust variance equation?

Answer 12

Divide by n-1 instead of n.

This brings variance estimation closer to true population variance.

Question 13

Can we use variance and sd for all types of data?

Answer 13

Only for normally distributed data.

Question 14

What measures of variation can we use for skewed data?

Answer 14

Quartiles or box plots

Question 15

What is the empirical rule?

Answer 15

States that 68.26% data values lie within +/- 1 sd

95. 45% within +/- 2sd
96. 74% within +/-3 sd

Question 16

What is the standard error and how do we calculate it?

Answer 16

Value that tells us the precision of a sample based estimate.
sd/ square root of n

Question 17

How would you represent continuous data?

Answer 17

histograms, box-plots, normal plots

Question 18

What is a confidence interval?

Answer 18

A confidence interval describes the amount of uncertainty associated with a sample estimate of a population parameter. It describes the margin of error either side of our point estimate.

Question 19

What is a type 1 error?

Answer 19

A false positive - falsely rejecting a null hypothesis. ‘optimist’

Question 20

What is a type 2 error?

Answer 20

A false negative - falsely accepting a null hypothesis. ‘pessimist’

Question 21

What does a p-value represent?

Answer 21

They evaluate how well the sample data support the null hypothesis. High p = data are likely with a true null. Low p = data are unlikely with a true null.

Question 22

In estimation statistics what measures of interest are there?

Answer 22

mean, prevalence of a disease (proportion), regression line, RR, OR

Question 23

What are the two categories of estimation?

Answer 23

Point: single value statistic e.g. estimated mean or proportion.
Interval: defined by two numbers, between which the population parameter is estimated to lie, with a high degree of probability. i.e. confidence intervals