Why do we need statistics?

Question 1

What is data?

Answer 1

Observations that have been collected e.g. measurements

Question 2

What is a population?

Answer 2

The COMPLETE collection of subjects studied

Question 3

What is a sample?

Answer 3

A SUBCOLLECTION of subjects from the population

Question 4

What is random sampling?

Answer 4

Sampling so that each subject in the population is EQUALLY likely to be selected

Sample mean will be biased if subjects are not sampled randomly from the population

Question 5

What is replication?

Answer 5

Repeats of the experiments to identify the degree of variation and confidence in results

Question 6

What are the two different types of data?

Answer 6

Quantitative data: Data which can be counted, discrete or continuous e.g. temperature, height, lengths

Qualitative data: Data which can be separated into different categories and are distinguished by some non-numeric characteristics

Question 7

What is the difference between nominal data and ordinal data?

Answer 7

Nominal: CANNOT be ordered e.g. yes or no , different colours, male or female

Ordinal: CAN be ordered e.g. short, medium, tall or none, few, many

Question 8

What is the difference between observational studies and experimental studies?

Answer 8

Observational studies: Just monitoring= Not changing the patients, which allows us to say something about the correlation. There is no attempt to modify the subjects being studied

Experimental: Apply one or more treatments and observe their effect

In general, it is easier to infer causation from experimental study whereas observational studies tend to only reveal correlations

Question 9

What is a parameter?

Answer 9

Measurement describing some characteristic of a POPULATION (what we would ideally like to know)

μ= population mean

Question 10

What is a statistic?

Answer 10

Measurement describing some characteristic of a SAMPLE = Used as an estimate (what we find out from the study)

x̅= Sample mean

Population parameter is estimated by the sample statistic

Question 11

What is a sampling error?

Answer 11

The difference between the statistic and the parameter

Question 12

What are histograms used for?

Answer 12

X axis: Classes of data
Y axis: Frequency of data or portion of the data in the category

Portion: Number of observations in the category/ Total number of observations and the heights of the categories will sum to 1

Indicate variation, can be used to visualise continuous data

Question 13

What are the different ways of measuring the centre of the data?

Answer 13

Mean

Median: Middle value of the data when arranged in order- It is robust from large data that does not fit the trend

Mode: Value that occurs most frequently
Bimodal: Two different values with the same greatest frequency
Multimodal: If more than two values occur with the same greatest frequency

Question 14

What are the different ways of measuring similarity or dissimilarity in the data?

Answer 14

Range: The difference between the smallest and largest value in the data

Sample variance: Measure of squared distance of each data point from the mean

Question 15

How do you measure the sample variance?

Answer 15

FORMULA FOR IT

Add together all the data values - the sample mean and divide by the number of data - 1

s² is a STATISTIC and high values= high dissimilarity in the data

σ² is a PARAMETER = If all members of the population are measured then it is the population variance and you divide by n instead of n - 1

s² can estimate σ²

Question 16

What is the sample standard deviation?

Answer 16

Square root of the sample variance

Sample variance has units different to the data whereas the sample standard deviation has the same units

s= Sample standard deviation 
s²= Sample variance 

σ= Population standard deviation 
σ²= Population variance

Rule of thumb: About 95% of the data should lie within 2 standard deviations from the mean

Question 17

What does statistical inference make use of?

Answer 17

Information from a sample to draw conclusions about the population from which the sample was taken

Problem: Wish to know something about a population of interest, but cannot examine every member of the population

Question 18

How can you increase the likelihood of the sample mean being a better estimate?

Answer 18

1) Increase sample size

2) The variation in observed is low

Question 19

What test statistic would you carry out if a population mean was claimed to be μ and you knew that the population mean is?

Answer 19

t statistic

If the data really were generated from a distribution having mean μ
then the test statistic is consistent with the t-distribution

Expect t to be small (positive or negative)

Question 20

What do parametric and non-parametric test assume?

Answer 20

Parametric: Some aspect of the data has a normal distribution

Non-parametric: Usually do not make such strict assumptions about the shape of the data= Less likely to detect patterns in the data, therefore less likely to reject the null even if it is false