Week 1: Ingredients for Statistics

Question 1

What are descriptive statistics?

Answer 1

Statistics that describe your data

Question 2

What are inferential statistics?

Answer 2

Statistics that infer beyond your data and make decisions.

Question 3

What do inferential statistics involve?

Answer 3

They involve making inferences about populations based on information from samples (as compared to descriptive statistics, which merely summarize known information)

Question 4

What is the BIG picture?

Answer 4

Population -> Sampling -> Sample -> Statistic Inference -> Population

Question 5

What is a simple random sample?

Answer 5

When each unit of the population has the same chance of being selected, regardless of the other units chosen for the sample.

Question 6

Three comparisons between random and non random sampling?

Answer 6

• Random samples have averages that are centred around the correct number
• Non-random samples may suffer from sampling bias, and averages may not be centred around the correct number
• Only random samples can truly be trusted when making generalisations to the population.

Question 7

What are population parameters?

Answer 7

A quantity or statistical measure that, for a given population, is fixed and that is used as the value of a variable in some general distribution or frequency function to make it descriptive of that population… A score from entire population such as the mean. They are usually unknown.

Question 8

What letters do population parameters have?

Answer 8

Usually have greek letters.

Question 9

What are statistics?

Answer 9

Statistics are figures from known data. They are scores of the sample only

Question 10

What letters do statistics have?

Answer 10

They usually have roman letters.

Question 11

What are point estimates?

Answer 11

They are single figure estimates of an unknown number. They will not match the population parameters exactly, but they are our bets guess given the data.

Question 12

Example of how point estimates come about?

Answer 12

Using a single number (sample mean) to estimate another single number (population mean).

Question 13

What do we use as a point estimate?

Answer 13

We use the statistic from a sample as a point estimate for a population parameter.

Question 14

For a given sample statistic, what are plausible values for the population parameter? How much uncertainty surrounds the sample statistic?

Answer 14

It depends on how much the statistic varies from sample to sample.

Question 15

What is the sampling distribution?

Answer 15

A hypothetical distribution. It is a probability distribution of a statistic obtained through a large number of samples drawn from a specific population.

Question 16

How do we get a sampling distribution?

Answer 16

We select an infinite number of samples from a population and calculate a particular statistic (eg a mean) for each one. When we plot all these calculated statistics as a frequency histogram, we have a sampling distribution.

Question 17

What does a sampling distribution show us?

Answer 17

A sampling distribution shows us how the sample statistic varies from sample to sample.

Question 18

What is the central limit theorem (what does it state)?

Answer 18

The central limit theorem states that as the size of the samples we select increases, the nearer to the population mean will be the mean of these sample means and the closer to normal will be the distribution of the sample means. Eg, For random samples with a sufficiently large sample size, the distribution of sample statistics for a mean or a proportion is normally distributed.

Question 19

What is the standard error?

Answer 19

The standard error of a statistic (SE) is the standard deviation of the sample statistic.

Question 20

What does the standard error measure?

Answer 20

The standard error measures how much the statistic varies from sample to sample

Question 21

What can the standard error be calculated as?

Answer 21

The standard error can be calculated as the standard deviation of the sampling distribution

Question 22

What is the standard error formula?

Answer 22

(Write this out, it’s in condensed notes)

Question 23

What is probability?

Answer 23

Expected relative frequency of a particular outcome.

Question 24

What is outcome?

Answer 24

The results of an experiment

Question 25

What is the formula for probability?

Answer 25

Probability equals the possible successful outcomes divided by all possible outcomes.

Question 26

What are the two interpretations of probability?

Answer 26

Long-run relative frequency interpretation and subject interpretation.

Question 27

What is the outcome, frequency, relative frequency, expected relative frequency and probability of long-run relative frequency interpretation?

Answer 27

• Outcome: Result of an experiment or event
• Frequency: How many times something occurs
• Relative frequency: Number of times something actually occurs relative to the number of times it could have occurred.
• Expected relative frequency: what you expect to get, in the long run, if the experiment was repeated many times
• Probability: is the likelihood of a particular outcome

Question 28

What is the expression and probability for subject interpretation?

Answer 28

• Expression of one’s certainty that a particular outcome will occur
• Probability is the confidence of a particular outcome

Question 29

When representing probability what are the range of probabilities?

Answer 29

• Proportion: from 0 to 1
• Percentages: from 0% to 100%
• Fraction, e.g. 1/36

Question 30

When representing probability what are the probabilities as symbols?

Answer 30

• p

* p

Question 31

What is the normal distribution?

Answer 31

A probability distribution