Binomial distribution and Hypothesis testing (wk3 3)

Question 1

What is Pascals’s triangle?

Answer 1

-A tree of numbers which help to identify the probability of situations

Question 2

What is a decision tree?

Answer 2

Multiple coin toss can be visualised as a connection of branches, which forms a decision tree

Question 3

What is a binomial distribution (with a coin toss)?

Answer 3

-You can calculate the probability of getting heads from tosses. If you write down the probabilities in each node, you get a probability distribution. For this specific case where there are always two choices, this distribution is called the binomial distribution

Question 4

What is cumulative probability?

Answer 4

-When the number of coin tosses become high, it does not make much sense of using the probability of getting the exact number of heads
-Therefore, it can make much more sense to use the probability that the value falls in a certain range, and this is called the cumulative probability

Question 5

What is two-tailed? (cumulative probability)

Answer 5

Taking the cumulative probability at both ends

Question 6

What is a discrete distribution (through a coin toss)?

Answer 6

The coin tossing is a discrete event i.e. you can count how many times something happened. Binomial distribution is a discrete distribution (i.e. distribution is a bunch of numbers located at each count

Question 7

What is a continuous distribution (through a coin toss)?

Answer 7

You need a continuous distribution to describe a distribution of a continuous variable.

Question 8

What is a normal distribution?

Answer 8

• Binomial distributions have specific shapes, which becomes clearer as the number of tosses increases
• The shape is a continuous distribution, called normal distribution
• Mean and SD describe normal distributions

Question 9

What is a binomial test?

Answer 9

Testing the statistical significance of deviations from a theoretically expected probability of a binary event. Null hypothesis is that the observed data occurred by the expected probability

Question 10

Name and describe the 3 types of binomial test:

Answer 10

• Observed proportion < Expected proportion. Cumulative probability from 0 to observed
• Observed proportion > Expected proportion. Cumulative probability from observed to max.
• Observed proportion (not equal to) Expected proportion. Two-tailed cumulative probability and Same distance from the mean.

Question 11

What is a confidence interval?

Answer 11

Confidence interval -> A range of plausible values associated with a confidence level (usually 95%). In binomial test, this means that you are 95% certain that the true proportion falls within the CI.

Question 12

What is a hypothesis test?

Answer 12

-In statistics, we test the probability that null hypothesis is true (i.e. there is no effect/ relationship)
-You can never prove something is true but can prove something is false
-It is difficult to make a precise research hypothesis

Question 13

What is a null hypothesis?

Answer 13

A hypothesis against the research question, claiming that there is no difference in the result and the only difference observed are just noise/error.

Question 14

What is a research/ alternative hypothesis?

Answer 14

Research/alternative hypothesis -> Opposite to the null hypothesis claiming that there is a difference in the result.

Question 15

What is the process with accepting/ rejecting null hypothesis?

Answer 15

Most of analyses in experimental science are focused on testing whether the obtained data can reject the null hypothesis. The significancy is estimated by the probability that the difference occurred by chance, which is called the p-value. The threshold/ alpha level for the significancy is p<0.05.

Question 16

What is a p-value and confidence interval?

Answer 16

-P-Values -> If the probability is very low we can reject our hypothesis. If the probability is not so low, we cannot reject our hypothesis. These probabilities used to reject hypotheses are called p-values.
P-values -> A probability that your hypothesis is right. A threshold level for the p-value, called alpha-level needs to be defined prior to the analysis. A usual choice is 0.05, i.e.
* If p-value is <0.05 you reject the hypothesis
* If p-value is >0.05 you accept the hypothesis

Question 17

What is an error in stats tests?

Answer 17

Since we are dealing with probability, potential error in the test always exist.

Question 18

What is a type-1 and type-2 error?

Answer 18

1. Type 1 (false-positive) -> The vaccine is not effective but you can conclude it is effective (reject the null hypothesis when it is true)
2. Type 2 (false-negative) -> The vaccine is effective but you can conclude it is not effective (not to reject the null hypothesis when it is false).