Week 19

Question 1

What are three types of values?

Answer 1

Categorical - value comes from one of n non-numeric categories, e.g. favourite colour

Numerical - numerical values (no shit), e.g. height of student

Ordinal - one of n numerical categories, e.g. number of stars rating

Question 2

What are mean, median and mode known as?

Answer 2

Measures of central tendency

Question 3

What are descriptive statistics?

Answer 3

Describe/summarize the data e.g. compute an average. But don’t extrapolate

Question 4

What are measures of variability?

Answer 4

Measure how spread out the data is around the mean

Question 5

What are inferential statistics?

Answer 5

Statistics which make conclusions that go beyond the sample data

Question 6

What are the two interpretations of probability?

Answer 6

Relative frequency: how often something happens on average

Degree of belief: subjective opinion of some individual regarding how certain an event is to occur (not really repeatable experiment)

Question 7

What is the sample space and event?

Answer 7

Sample/outcome space: Set of all possible outcomes (e.g. {1,2,3,4,5,6} for rolling a die)

Event: subset of sample space (e.g. event E of getting a value less than 4: E={1,2,3}

Question 8

How is a random variable used with probability?

Answer 8

Takes unique value for each event. E.g. experiment where 3 coins are tossed:

Y = number of heads

Range is 0-3

Y=0 corresponds to {TTT}

Question 9

What are the two types of random variables?

Answer 9

Discrete: Takes countable values, e.g. number of heads

Continuous: real value e.g. 1.534

Question 10

What is a discrete probability distribution?

Answer 10

P(X=x) gives probabilities for each possible value of x

Question 11

What is a continuous probability distribution?

Answer 11

Defined by probability density function giving the probability X is in a certain range,

Question 12

With normal distributions,

__% of the data is within the first standard deviation from the mean

__% is within two stddev

__% is within three stddev

Answer 12

68%

95%

99.7%

Question 13

What is a standard normal distribution?

Answer 13

When mean = 0 and stddev = 1

Question 14

How can a normal distribution X be converted to a Z distribution

Answer 14

Z = (X - mean) / stddev

Question 15

What is the difference between population and sample?

Answer 15

Population is a universe of individuals you’re interested in (e.g. all people in Colchester, infinite number of coin flips)

Sample is a subset of a population that should be representative (e.g. 100 coin flips, 100 people from Colchester)

Question 16

Difference between true mean and true s.d. and sample mean and sample s.d.

Answer 16

True = performed on population

Sample = performed on sample

Question 17

What is the primary concern with using sample statistics?

Answer 17

Variability - hard to get a representative sample

Question 18

What is the sampling distribution?

Answer 18

Taking a very large number of samples of size N, and plotting the sample statistic.

Then, random variable is the sample statistic, not actual values

Question 19

What is the standard error?

Answer 19

The standard deviation of the sampling distribution

Aka, the uncertainty of the sample means. If I take different samples, how much do the means vary

Question 20

What happens to the standard error as the sample size increases

Answer 20

Standard error decreases

Question 21

How can you approximate the standard error from sample standard deviation?

Answer 21

s / sqrt(N)

where s = sample stddev, N = number of samples

Question 22

What does the central limit theorem say?

Answer 22

As N becomes large the sampling distribution can be approximated by a normal distribution

~30+ samples reveal a normal dist

Question 23

What are the implications of the central limit theorem?

Answer 23

Get one sample

Compute sample mean

Get probability of the sample mean under the sampling distribution

• Can get this probability without doing the sampling many times

Question 24

What is the Z test?

Answer 24

Collect N samples, compute sample mean and standard error

z = (sample mean - mean) / standard error

Reject null hypothesis if z value < -1.96 or > 1.96

This represents 95% (1.96 standard deviations from mean)

Question 25

What is the p value?

Answer 25

The probability beneath which you reject the null hypotheses

Look up the p value on a table, e.g. for 2 tailed hypothese, p<0.05 = 0.42

Question 26

What is a common use of the z test?

Answer 26

Check if a sample mean is close to the population mean

Question 27

What is a paired t-test?

Answer 27

Compares two population means where you have two samples in which observations in one sample can be paired with observations in the other sample

e.g. student’s scores before and after a module or course

Question 28

Between-group testing is a form of ___________ testing

Answer 28

Non-paired

Question 29

What is involved in between-group testing?

Answer 29

An experiment with two or more group that each have different testing conditions

E.g. control group and test group

Question 30

Repeated-measures design is also known as

and is a form of ________ testing

Answer 30

within group design

paired testing

Question 31

What is repeated-measures testing?

Answer 31

Using the same subjects with every branch of research

i.e. a longitudinal study where each testing condition is done at some point for each subject

Question 32

What are the advantages and disadvantages of between groups design?

Answer 32

Advantages: multiple variables can be tested at the same time

Can save time

Disadvantages: potential scale can be impractical due to limited resources

selection of subjects may not be representative