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1

Discrete Uniform

'N' Possible values, each with equal probability

2

Continuous Random Variable

Can be any real number

3

Law of small numbers

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

4

Law of large numbers

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

5

Pearson's Chi-square test

Test of independence

Test of Homogeny

Cannot be one-sided

6

Fisher's exact test

Test of Independence

Test of Homogeny

Can be One or Two-sided

7

Binomial

Used when sample size and prevalence are given

8

Popper's theory of falcification

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

9

Wilcoxans rank sum test

Testing the orders (ranks) of the observed values

10

T-test

Difference of the averages

Assume normal distribution

11

Standard error of Mean =

σ/√n

σ = Standard Deviation

n = Number of Values

12

Interval Estimate =

Confidence interval

Contains the unknown quantity with high probability (95%)

13

Two sample t-test

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

14

Paired sample t-test

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

Difference between the pairs must be normally distributed

15

Levene Test

Variances of several populations

Independent Samples

Hclaims each population variance is the same

16

Mood's Median

Median of several populations

Hcan be one or two sided in case of two samples

Must be continuous

17

Which hypothesis can never be rejected?

The Alternative Hypothesis

18

What can be the alternative hypothesis for a correlation test?

Correlation doesn't = 0

19

The question 'Is there a difference between...' leads to a...

Two-sided test

20

ANCOVA

Corresponds ot the notation:

X5, X4, X3, X2, X1 → Y

21

Two types of conditional probability

Sensivitiy - % Sick individuals diagnosed

Specificity - % Healthy individuals diagnosed

22

Bocyes Theorem

Calculation method for inverse conditional probabilities

23

Point Estimate

Single number calculated from the sample

24

Ordinal Scale

When the data being collected is qualitative but can be ranked

 

25

Ratio Scale

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

26

Interval Scale

Allows calculation of the degree of difference between items, but not the ratio

e.g degrees Celcius

27

ANOVA

Used to investigate a hypothesis with the mean values of several populations

Measures equality of means in 4 groups

Hclaims each population mean is the same

28

F-test

Investigates the hypothesis about the relationship of two population variances based on two independent samples

Used for multiple sample problems

Hclaims each population variance as the same

29

Compare two side samples and one side samples

Two sided samples are symmetrical

One sided have a definitive direction

30

Type 1 error

Rejection of a true null hypothesis

False-Positive finding

31

Type 2 error

Retaining a false null hypothesis

False-negative finding

32

Power of the statistical test

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

33

Chi-Square test

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

 

34

Give the formula for the Chi-square test

35

A & B are independent if...

P(A)P(B) = P(A∩B)

Their joint probability equals the product of their probababilities

36

Give the formula for conditional probability

P(A) = P(A|B)

37

Explain the addition rule

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

38

Nominal Scale

When data is collected qualitatively

e.g Eye colour, nationality

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)?

95%

40

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

A and B are mutually exclusive

41

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

A and B are not mutually exclusive

42

Normal distribution is...

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

43

Standard deviation is...

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

44

Give the formula for standard deviation

45

Variance is...

Standard Deviation squared

46

Which scale is typical for a correlation coefficient?

-1 < X < 1

47

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

ANOVA

48

Which test is appropriate for only large samples?

Chi-square test

49

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

Descriptive Statistics

50

Inductive statistics

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

51

Descriptive Statistics

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

52

Describe odds ratio

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)

53

Explain relative frequency

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

54

Formula to calculate relative frequency

RF = K/N

K = Number of observed events

N = Number of trials

55

Conditions of applicability of ANOVA

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

56

What is the critical value?

The value obtained if chance alone contributed to the outcome

57

What is the Observed Value?

The value collected experimentally

58

What is the p value?

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