Week 3

Question 1

Probability sum?

Answer 1

Number of sequences with specific outcome / number of all possible sequences

Question 2

What is probability used for ?

Answer 2

To quantify how likely a set of data was obtained by pure chance

Question 3

What is binomial distribution?

Answer 3

When there is only two choices in a probability

Question 4

How is binomial distribution measured ?

Answer 4

Using Pascal’s triangle
Counting the layers = number of tests
Adding the numbers on the layer = possible sequences
And then counting the number of sequences with wanted data

Question 5

What is cumulative probability?

Answer 5

Probability of observing a number of successes that is less than or equal to a specific number ( value falls within a range )

This is due to the number of tests the probability of it being specific are very low/zero

Question 6

Binomial distribution sum? What does each mean part mean? Example?

Answer 6

Bi(k | n, q) =
number of sequences with k /
number of all possible sequences

K= specific combination/result
N=amount of tests

Example = Bi( 3 | 4, 0.5 ) = 4 / 16 = 0.25
3 = heads (in H or T) 4 = number of tosses
.5 chance of getting H 16 = possible sequences

Question 7

Cumulative probability sum? Which does each bit mean?

Answer 7

Bi ( /? ≤ k ≤ ? | n, q)

k= within certain value
n= tests done
q= probability of getting specific eg 50/50 = 0.5q

Question 8

Difference between discrete and continuous (event) distribution?

Answer 8

Discrete events are when you can count the number of times something happened, continuous is a variable that can change such as weight

Binomial is discrete

Question 9

What is probability density in continuous distribution?

Answer 9

As in continuous distribution a variable can change, the chance of it being specific such as exactly 60kg is 0. Therefore the probability is the area under the range given such as between 50-60kg but because it is continuous it must be referred to as probability density and not just probability

Question 10

What is probability density in continuous distribution?

Answer 10

As in continuous distribution a variable can change, the chance of it being specific such as exactly 60kg is 0. Therefore the probability is the area under the range given such as between 50-60kg but because it is continuous it must be referred to as probability density and not just probability

Question 11

What is the continuous distribution also known as and what two types of numbers can describe it?

Answer 11

Normal distribution - Most fundamental

It can be described using only the Mean and SD

Question 12

What is two tailed probability ?

Answer 12

Checking how far data deviated from the mean, therefore taking cumulative probability from both ends

Question 13

What is a Statistical test?

Answer 13

We need to assess whether a given scientific claim/hypotheses is valid or not and the probability of it being valid or due to chance.

Question 14

What is a p-value?

Answer 14

Probabilities used to reject hypotheses. If it is very low the hypothesis is rejected, if it is higher it cannot be rejected.

Question 15

What is an alpha level?

Answer 15

A threshold p-value made prior on whether to reject or not, it is commonly 0.05.

If it less than 0.05 it is significant and he null is rejected and an alternative is accepted, If it is above then it is accepted

Question 16

What is a null hypothesis ? Example?

Answer 16

A hypothesis against the research question usually claiming there is no significant difference between a result and its relationship with something.

Eg the vaccine has no effect on infection rate

Question 17

What are the 2 errors in stats tests? With examples?

Answer 17

Type 1 : False positive - Rejecting the null hypothesis when its true eg vaccine is not effective but i conclude it is
Type 2 : False negative - Don’t reject/accepting the null when its false eg vaccine is effective but i conclude it isn’t

Question 18

What is the binomial test/ When is it used?

Answer 18

The binomial test checks whether the observed proportion of successes in your data, of two single categorical variables such as heads/tails, is significantly different from the expected (or hypothesized) proportion.

If the test result is statistically significant, it suggests that the observed proportion is likely different from the expected proportion.

Question 19

What are confidence intervals?

Answer 19

A range of plausible values associated with confidence level, meaning you are 95% sure that the true proportion fall within this range.

Question 20

What are confidence intervals?

Answer 20

A range of plausible values associated with confidence level, meaning you are 95% sure that the true proportion fall within this range.

Question 21

How to determine whether to do a one or two tailed test?

Answer 21

One tailed is for a specific direction, if the result is either greater or less than hypothesised value.

If you want to test any difference with no specific direction or check for deviation used two tailed.

Question 22

What is binomial probability?

Answer 22

Evaluating the probability of observing a specific number of successes in a fixed number of trials with a hypothesised probability of success

Question 23

What is hypothesis testing?

Answer 23

Procedure used to evaluate claims on data

1) Make hypotheses
- Null = No difference
- Alternative = difference

2) Make significance level - probability of rejecting null if results are positive/allow for it - usually 0.05

3) Test statistics - use appropriate test, t-test, chi-squared etc. to determine how far from the null.

4) P-value - determines whether results are due too chance / inconsistent or not, then make a decision based off value.

5) Conclusion and Summary

Question 24

How to calculate expected number of successes in binomial distribution ?

Answer 24

Number of trials x probability of success rate