Statistics 3

Question 1

Define probability

Answer 1

A quantitative description of the likelihood of an event occurring within dataset

Question 2

What are the three ways of calculating probability?

Answer 2

Subjective: Judgement based on individual opinion and experiences
Theoretical: Calculation based on reasoning using knowledge of the specific dataset characteristics
Experimental: Measurement of an observation

Question 3

What is sample space?

Answer 3

All the outcomes that could occur within a distribution

Question 4

What does it mean if events are mutually exclusive?

Answer 4

Zero probability of two events occurring together (e.g. on a dice there is no way of getting a 5 and a 3)

Question 5

What does it mean if events are independent?

Answer 5

Events that have no influence on each other

Question 6

What should you typically assume about events?

Answer 6

That they are independent but not always

Question 7

In a normal distribution what does the area under a curve represent?

Answer 7

the probability of different events occurring within the dataset

Question 8

In a normal distribution what does the curve represent and what is underneath?

Answer 8

the probability density function and underneath are all the associated probabilities

Question 9

Why cant you compare different normal distributions?

Answer 9

Because they typically have different means and standard deviations

Question 10

What do you need to do to compare different normal distributions?

Answer 10

Standardisation

Question 11

What is the standardization formula?

Answer 11

X-u/ standard deviation

Question 12

What does the standardization formula do to the mean and standard deviation of normal distributions?

Answer 12

Mean: makes it 0

Standard deviation: makes it 1

Question 13

What happens as you move away/to from the mean?

Answer 13

there is losses or gains in the mass of the dataset which is captured which then affects probability

Question 14

What is hypothesis testing?

Answer 14

Testing to see whether the hypothesis around outcomes of a dataset are statistically significant or not

Question 15

What is the initial hypothesis called and how is it phrased?

Answer 15

Null hypothesis always negatively phrased.

Question 16

What is the alternative hypothesis and when is it formed?

Answer 16

The alternative to the null that is formed as the test has been carried out and after the null hypothesis has been rejected or accepted based on the test

Question 17

What are 3 examples of null hypothesis? No statistically significant…

Answer 17

difference between sample and population
difference between samples a, b, c
relationship between variables a, b, c

Question 18

How is the significance threshold determined?

Answer 18

By you - you decide what is a suitable level for a probability to confidently not have occurred due to chance

Question 19

What are 4 typical levels of significance?

Answer 19

90%, 95%, 99%, 99.9%.

Question 20

What does the result mean in regards to the statistical significance threshold?

Answer 20

If the result falls outside of the significance threshold then it did occur due to chance, but if it does surpass then you can be confident that it did not occur due to chance and it is indeed a statistically significant result

Question 21

Why is it crucial to test for normality in a distribution?

Answer 21

To determine whether to carry out parametric or non-parametric data analysis

Question 22

What are the three ways of determining normality in a distribution?

Answer 22

Observation
Q-Q plot
K-S test

Question 23

What is the q-q plot?

Answer 23

Determining whether there is an even scatter of data that is also closely centred around the drawn straight line

Question 24

What is the K-S test?

Answer 24

Observational with empirical analysis of whether a distribution is normally distributed

Question 25

What does the K-S test involve?

Answer 25

Comparing the measured/observed distribution against a theorised normal distribution of that dataset.

Question 26

What does it mean visually if the observed distribution resembles that of the theorised distribution?

Answer 26

that it is probably normally distributed

Question 27

Why is the K-S similar to hypothesis testing?

Answer 27

Because you accept the null or alternative hypothesis

Question 28

What is the null hypothesis and alternative hypothesis for a k-s test?

Answer 28

Null: there is no statistically significant difference between the observed dataset and the theorised dataset i.e. it resembles the normal distribution
Alternative: there is statistical significant difference i.e. it does not resemble the normal distribution

Question 29

How do you analyse a K-S test in SPSS?

Answer 29

Analyse > non-parametric tests > legacy dialogs > one sample K-S > tick “normal” box

Question 30

What is the product of the K-S test on SPSS?

Answer 30

Table - the column titled “sig.” tells you what the level of significance is and therefore enables you to determine whether to accept the null or alternative hypothesis

Question 31

What is the importance of the “statistic” column in the SPSS table produced for K-S?

Answer 31

Nothing