Final Exam

Question 1

Discrete Uniform

Answer 1

‘N’ Possible values, each with equal probability

Question 2

Continuous Random Variable

Answer 2

Can be any real number

Question 3

Law of small numbers

Answer 3

Number of observations ‘N’ is large and probability ‘P’ is small.

Distribution is dependent on the mean

λ=N×P

Poisson distribution with parameter λ

Question 4

Law of large numbers

Answer 4

When the number of events ‘N’ increases, the relative freqency better estimates the theoretical probability of an event

Question 5

Pearson’s Chi-square test

Answer 5

Test of independence

Test of Homogeny

Cannot be one-sided

Question 6

Fisher’s exact test

Answer 6

Test of Independence

Test of Homogeny

Can be One or Two-sided

Question 7

Binomial

Answer 7

Used when sample size and prevalence are given

Question 8

Popper’s theory of falcification

Answer 8

A theory can be considered scientific, only if it can be experimentally disproved

Question 9

Wilcoxans rank sum test

Answer 9

Testing the orders (ranks) of the observed values

Question 10

T-test

Answer 10

Difference of the averages

Assume normal distribution

Question 11

Standard error of Mean =

Answer 11

σ/√n

• σ = Standard Deviation*
• n = Number of Values*

Question 12

Interval Estimate =

Answer 12

Confidence interval

Contains the unknown quantity with high probability (95%)

Question 13

Two sample t-test

Answer 13

Investigates a hypothesis about a relationship between two populations with two samples independent from each population

Question 14

Paired sample t-test

Answer 14

Same as two-sample t test only with paired samples between the groups

Difference between the pairs must be normally distributed

Question 15

Levene Test

Answer 15

Variances of several populations

Independent Samples

H₀ claims each population variance is the same

Question 16

Mood’s Median

Answer 16

Median of several populations

H₀ can be one or two sided in case of two samples

Must be continuous

Question 17

Which hypothesis can never be rejected?

Answer 17

The Alternative Hypothesis

Question 18

What can be the alternative hypothesis for a correlation test?

Answer 18

Correlation doesn’t = 0

Question 19

The question ‘Is there a difference between…’ leads to a…

Answer 19

Two-sided test

Question 20

ANCOVA

Answer 20

Corresponds ot the notation:

X5, X4, X3, X2, X1 → Y

Question 21

Two types of conditional probability

Answer 21

Sensivitiy - % Sick individuals diagnosed

Specificity - % Healthy individuals diagnosed

Question 22

Bocyes Theorem

Answer 22

Calculation method for inverse conditional probabilities

Question 23

Point Estimate

Answer 23

Single number calculated from the sample

Question 24

Ordinal Scale

Answer 24

When the data being collected is qualitative but can be ranked

Question 25

Ratio Scale

Answer 25

Used when the data is relative to a predetermined value such as length or mass

Question 26

Interval Scale

Answer 26

Allows calculation of the degree of difference between items, but not the ratio ## Footnote *e.g degrees Celcius*

Question 27

ANOVA

Answer 27

Used to investigate a hypothesis with the **mean values** of **several populations** Measures **equality** of means in 4 groups H₀ claims each population mean is the same

Question 28

F-test

Answer 28

Investigates the hypothesis about the relationship of two population variances based on two independent samples Used for multiple sample problems H₀ claims each population variance as the same

Question 29

Compare **two side** samples and **one side** samples

Answer 29

Two sided samples are symmetrical One sided have a definitive direction

Question 30

Type 1 error

Answer 30

Rejection of a true null hypothesis ## Footnote *False-Positive finding*

Question 31

Type 2 error

Answer 31

Retaining a false null hypothesis ## Footnote *False-negative finding*

Question 32

Power of the statistical test

Answer 32

Gives probability of rejecting the null hypothesis where the alternative hypothesis is true

Question 33

Chi-Square test

Answer 33

Used for Large Samples Used to compare expected and observed values E.g Flip a coin 100× Expected values - H:50 T:50 Observed Values - H:54 T:46

Question 34

Give the formula for the Chi-square test

Answer 34

Question 35

A & B are independent if...

Answer 35

P(A)P(B) = P(A∩B) ## Footnote *Their joint probability equals the product of their probababilities*

Question 36

Give the formula for conditional probability

Answer 36

P(A) = P(A|B)

Question 37

Explain the addition rule

Answer 37

A die is rolled, what is the probability of getting a 2 or a 5? 1. P(A or B) = P(A) + P(B) 2. P(A) = 1/6......P(B) = 1/6 3. P(A or B) = 1/3

Question 38

Nominal Scale

Answer 38

When data is collected qualitatively ## Footnote *e.g Eye colour, nationality*

Question 39

What is the approximate probability that the value of a normally distributed random vatiavle is vetween (mean-2 standard deviation) and (mean+2 standard deviation)?

Answer 39

95%

Question 40

The relationship **P(A+B)=P(A)+P(B)** is true if...

Answer 40

A and B are mutually exclusive

Question 41

The relationship **P(A+B)=P(A)+P(B)-P(A×B)** is true if...

Answer 41

A and B are not mutually exclusive

Question 42

Normal distribution is...

Answer 42

A function that represents a distribution of many random variables as a symmetrical bell shaped graph

Question 43

Standard deviation is...

Answer 43

A quantity calculated to indicate the deviation of a group as a whole

Question 44

Give the formula for standard deviation

Answer 44

Question 45

Variance is...

Answer 45

Standard Deviation squared

Question 46

Which scale is typical for a correlation coefficient?

Answer 46

-1 \< X \< 1

Question 47

Which test should be used if the equality of means in four groups (many) is to be analysed?

Answer 47

ANOVA

Question 48

Which test is appropriate for only large samples?

Answer 48

Chi-square test

Question 49

Which part of statistics does the chi-square test belong to?

Answer 49

Descriptive Statistics

Question 50

Inductive statistics

Answer 50

Dealing with generalisations, predictions, estimations and decisions from the initial data

Question 51

Descriptive Statistics

Answer 51

The use of clear and concise numbers to describe a set of known data

Question 52

Describe odds ratio

Answer 52

The ratio of odds between two groups * e.g. Odds of colourblindness in women **4:48*** * Odds of colourblindness in men **1:47*** (4/48)/(1/47) = 3.91 (Men 4x more likely than women)

Question 53

Explain relative frequency

Answer 53

If a team plays 12 games of football and wins 9, relative frequency of winning is 3/4

Question 54

Formula to calculate relative frequency

Answer 54

RF = K/N ## Footnote * K = Number of observed events* * N = Number of trials*

Question 55

Conditions of applicability of ANOVA

Answer 55

Normally distributed variables for each group, Variances should be equal in each group

Question 56

What is the critical value?

Answer 56

The value obtained if chance alone contributed to the outcome

Question 57

What is the Observed Value?

Answer 57

The value collected experimentally

Question 58

What is the p value?

Answer 58

Probability of finding the observed result when the null hypothesis is true