Statistics for Dummies

Question 1

What % constitutes a high response rate to a survey?

the number of respondents divided by the number of surveys sent

Answer 1

70%
———-

Some statisticians will settle for nothing less.

Rarely does it get that high, but the lower the response rate the less credible the results

A 20% (say) rate could easily mean that more people in the population feel differently than the respondents.

Question 2

In the research statistics process, there are 6 main steps. Starting with:
1) what is the question to be answered?
2) design a study
3) determine the group of people to be studied
…
What are the next 3?

Answer 2

4) collect the data
5) organise, summarise and analyse the data
6) draw conclusions from the summaries and graphs to answer the question

Question 3

What is a ‘Parameter’?

Answer 3

Usually we only have a statistic from a sample, which is then said to ‘estimate the parameter

Question 4

What is a ‘Statistic’?

Answer 4

data from a population is a ‘census’, and data summarised to a stat from a census is called a ‘parameter’ because it refers to the population.

Question 5

What are ‘Categorical Data’?

Answer 5

Sometimes categories are recorded using numbers, like 1 for male and 2 for female but they don’t have any specific meaning

Question 6

What are ‘Numerical Data’?

Answer 6

Also referred to as Quantitative or measurement data.

Examples: Height, Weight, IQ, Blood pressure

Question 7

What is a ‘standard score’

Answer 7

Like +2 or -1

Question 8

What is the ‘central limit theorem?

Answer 8

The ‘crown jewel’ of all statistics’

Question 9

What are Z-Values

Answer 9

The distribution is then called a ‘standard normal distribution’ or ‘Z-Distribution’

Question 10

What is a ‘Standard Normal Distribution’

Answer 10

It is the Z-Distribution

Useful for determining percentiles, and what data fall between two values

Question 11

What is a ‘Z Distribution’?

Answer 11

It is the ‘Standard Normal Distribution’

Useful for determining percentiles, and what data fall between two values

Question 12

a single sentence that describes an ‘Experiment’

Answer 12

And often their environment.

The purpose is to pinpoint a cause-and-effect relationship between two variables (drug vs health or placebo vs health)

Question 13

What is a ‘blind experiment’

Answer 13

Where bias is controlled because the subjects do not know if they are in the control group or the treatment group

Question 14

What is a ‘double blind experiment’?

Answer 14

Where bias is controlled on the part of both patients and researchers because none of them know

Question 15

What is the purpose of sample statistics

Answer 15

To produce an ‘estimate’ of a population parameter

Question 16

Explain a 10% Probability vs. ‘9 to 1 odds’

Answer 16

If a horse has a 1 in 10 chance of winning then it is 1/10 so 0.10 = 10%

But bookies use 9/10 vs 1/10. So the 10’s cancel out leaving 9/1 or ‘9 to 1’

Question 17

Describe the ‘law of averages’

Answer 17

In the long term, results will average out to their expected value. In the short term no one knows what will happen.

Question 18

In hypothesis testing, a ‘statistically significant result’ is related to chance in what way?

Answer 18

it means a result with a small probability of happening by chance

Question 19

What is the range for a p-value?

Answer 19

Between 0 and 1
——

a small p-value indicates strong evidence AGAINST the null hypothesis

Question 20

What does a small p-value indicate?

Answer 20

strong evidence AGAINST the null hypothesis
———

p-values are between 0 and 1

Question 21

On a distribution graph or a histogram, if a long tail of data is on the right, which way is the data skewed?

Answer 21

skewed to the right

Question 22

On a distribution graph or a histogram, if a long tail of data is on the left, which way is the data skewed?

Answer 22

skewed to the left

Question 23

Does a histogram deal with numerical or categorical data?

Answer 23

You need to decide your own groups to put the numbers into

Question 24

What does the empirical rule state?

Answer 24

In a normally distributed data set, about 68% of values are within 1 SD of the mean, 95% within two standard deviations and about 99.7% within three SD
——-
Following from Chebyshev’s inequality, it seems that even in non normal sets, about 89% of values lie within 3 SDs

Question 25

How do you calculate a percentile? E.g 90th percentile of n values?

Answer 25

Order the data ascending. Multiply n x kth percentile desired. Round UP the result to nearest whole number. That number in the n set represents the kth percentile
——

Eg n is 1,2,3,4,5,6,7,8,9,10,11

Kth sought is 90%

11 * .9 = 9.9

Round up = 10

So 10 is at the 90th percentile

Question 26

Is probability calculation effective in predicting short term behaviour?

Answer 26

No, it is effective when predicting long term behaviour

Question 27

If only two outcomes are possible, what are the chances of one of them occurring?

Answer 27

It’s not necessarily 50/50.

The chances are based on the probability of the particular event, not because there are only two outcomes (otherwise every penalty goal attempt would be 50/50

Question 28

Is probability calculation effective in predicting short term behaviour?

Answer 28

No, it is effective when predicting long term behaviour

Question 29

If only two outcomes are possible, what are the chances of one of them occurring?

Answer 29

It’s not necessarily 50/50.

The chances are based on the probability of the particular event, not because there are only two outcomes (otherwise every penalty goal attempt would be 50/50

Question 30

Any probability is a number between what and what..?

Answer 30

0 means impossible
1 means certain

Question 31

All of the probabilities for all possible outcomes must add up to..?

Answer 31

the probability that an outcome does NOT happen is 1 minus the probability that the outcome DOES happen

Question 32

in probability, what is an event a combination of..?

Answer 32

equal to the sum of the probabilities of the individual outcomes that make up the event

Question 33

What is a ‘confidence interval’

Answer 33

A statistic, plus or minus a margin of error

Question 34

How can you roughly work out the sample size needed to achieve a particular desired margin of error ?

Answer 34

1 / √n * 100 gives the + or - error so * 2 gives the margin.

In reverse pick your margin of error , say 5% / 2 = 2.5% / 100 = 0.025

(1/0.025)^2 = 1600 is the rough estimate of sample size needed for a +/- 2.5% margin

Presumably assuming normally distributed population and no bias in the sample