Probability, Correlation And Hypothesis Testing

Question 1

Comparative pie charts formula

Answer 1

Question 2

Outliers formula

Answer 2

Question 3

Comparative pie charts

Answer 3

The ratio of the sample size is the same as the ratio of the areas

Question 4

Population mean

Answer 4

Question 5

Sample mean

Answer 5

Question 6

‘Sum of’

Answer 6

Question 7

The sample mean when xi occurs with a frequency fi

Answer 7

Question 8

What is discrete data?

Answer 8

Data that can only take certain values which are often integers but sometimes aren’t , for example shoe size

Question 9

What is continuous data?

Answer 9

Can take any numerical value such as height

Question 10

What is the range?

Answer 10

Highest value - lowest value

Question 11

What is IQR?

Answer 11

Q3 - Q1

Question 12

Standard deviation formulas

Answer 12

Question 13

Variance formulas

Answer 13

Question 14

What is probability?

Answer 14

Question 15

What is a set?

Answer 15

A collection of numbers which cannot have repeats

Question 16

What is a subset?

Answer 16

All the elements in ‘A’ are in ‘S’

Question 17

What is an empty set?

Answer 17

An imaginary set with no elements

Question 18

What is a sample space?

Answer 18

All the possible outcomes of a random experiment

Question 19

Complement of A

Answer 19

A’ (not A)

Question 20

B is a subset of A

Answer 20

If B occurs so does A

Question 21

Mutually exclusive

Answer 21

The occurrence of one event excludes the possibility that any other events could occur (they cannot happen at the same time)
If A and B are exclusive the probability of A or B occurring is the probability of the sum of AUB

P(AUBUC) = P(A) +P(B) +P(C)

Question 22

Independent events

Answer 22

The probability of event A occurring is unaffected by whether or not B occurs
If A and B are independent then P(AnB) = P(A) x P(B)

Question 23

The addition law of probability

Answer 23

Question 24

Multiplication law

Answer 24

Question 25

What is Pearson’s Product Moment Correlation Coefficient

Answer 25

The PMCC is denoted by R and named after Pearson, an applied mathematician who worked on the application of statistics to genetics evolution

Question 26

PMCC formulas

Answer 26

Question 27

Interpreting PMCC values

Answer 27

R = 1 perfect positive correlation R = -1 perfect negative correlation R = 0 no linear correlation

Question 28

What does a measure of correlation indicate?

Answer 28

A relationship between the two values however, it does not indicate a causal relationship

Question 29

Spearman’s correlation coefficient formula

Answer 29

Question 30

Spearman’s

Answer 30

Makes no assumptions about the original data and the original data does not need to be linear

Question 31

PMCC

Answer 31

We can only do a hypothesis test here if the variables are jointly normally distributed

Question 32

H0 and H1

Answer 32

H0: null hypothesis (no correlation) H1: correlation

Question 33

Hypothesis testing

Answer 33

Question 34

What is a regression line?

Answer 34

It should intersect the double mean point and should be linear for bivariate data The equation for the linear regression line is given as: Y = ax + b Where a is the gradient and b is the y intercept X is the independent value and y is the dependent

Question 35

Things to consider when analysing the regression model

Answer 35

How do we interpret the model How can we interpret in context the coefficient of x How can we interpret in context the constant term

Question 36

What is a residual?

Answer 36

An error the model produces when trying to predict a data point It is the distance between the data point and regression line For y on x regression it is only sensible to consider predictions for y

Question 37

How to calculate a residual?

Answer 37

Question 38

What does a positive residual indicate?

Answer 38

Where the model is giving an underprediction

Question 39

What does a negative residual indicate?

Answer 39

An overprediction

Question 40

What should we see when we plot predicted vs actual?

Answer 40

Strong positive correlation

Question 41

What should we see when we plot predicted vs residual?

Answer 41

A uniform distribution clustered around zero with no patterns

Question 42

Anscombe’s quartet

Answer 42

Each data set has the same summary statistics and are clearly different

Question 43

Unstructured statistics

Answer 43

Each data set has the same summary statistics but they are visually different

Question 44

The normal distribution diagram

Answer 44

Question 45

The normal distribution formula

Answer 45

Question 46

What is the z-value?

Answer 46

The number of standard deviations a value is above/below the mean Because the normal distribution is symmetrical we can use the positive z-value to calculate the negative

Question 47

We can only use the z-table when…

Answer 47

The z-value is positive (on the right of the graph) We’re finding the probability to the left of this z-value

Question 48

Changing the direction of the inequality

Answer 48

Changing the sign or direction of the inequality does ‘1-‘ If we do both they cancel out

Question 49

Standardising formula

Answer 49

Question 50

To find the z score?

Answer 50

Question 51

To find the z value for a probability?

Answer 51

Use the z table backwards Find the value on the table and work backwards

Question 52

Central limit theorem

Answer 52

If we continually take samples of the same size and record their corresponding sample means, they themselves will be normally distributed around the known population mean

Question 53

How is the sample mean normally distributed

Answer 53

Question 54

Standard deviation

Answer 54

Question 55

Continuity corrections

Answer 55

We can convert discrete data to continuous

Question 56

Approximating

Answer 56

To approximate a binomial distribution as a normal we can copy over the mean and variance of the binomial We must change the letter as it is a different distribution