The Statistical Distributions

Question 1

What is the Distribution in Statistics?

Answer 1

A variable’s distribution is related to the possible value that variable can take on and the relative frequency (or probability) of their occurence

Question 2

What are the 2 main types of distributions?

Answer 2

Empirical and Statistical

Question 3

Empirical Distribution

Answer 3

Actual values observed

Question 4

Statistical Distribution

Answer 4

Theoretical probability distribution that describes how a variable is expected to behave

Question 5

What does a Normal Distribution include?

Answer 5

z- and t- Distribution

Question 6

What are the properties of a Normal Curve?

Answer 6

M/M/M all have the same value
Curve is symmetric around the mean, no skew

Question 7

What are the percent values what fall within SD of a normal curve?

Answer 7

68% 1SD
95% 2SD
99.8% 3SD

Question 8

What is the Z-Distribution Mean and SD?

Answer 8

Mean = 0
SD = 1

Question 9

What is the Z-Score?

Answer 9

Describes the deviation of an observation from the mean in terms of ‘standard units’ from zero

Question 10

Why use a z-score?

Answer 10

Transform all normal distributions so that they are all in the small scale, a way to express raw score in terms of SD units

Question 11

How to calculate a Z-Score?

Answer 11

(raw point - mean) / SD = z

Question 12

The raw score mean equals what in the z-score?

Answer 12

0

Question 13

What is the t-Distribution?

Answer 13

Modification of the z-distribution when the sample size is relatively small (n<30) an when the population SD is not known

Question 14

What does the t-distribution looks like when the sample size is small?

Answer 14

t-distribution is flatter with thicker tails than the z-distribution

Question 15

What is the key takeaway from t-distribution?

Answer 15

T-test assumes the variables come from a normal distribution

Question 16

A t-distribution on a graph looks like what?

Answer 16

The peak is smaller, the tails are thicker

Question 17

What is the Central Limit Theorem?

Answer 17

1. The mean of all sample means will equal the population mean
2. The standard deviation of the sample mean is equal to the standard error of the mean
3. As the sample size increases, the distribution of the sample mean approaches the normal distribution (regardless of the underlying distribution of the variable)

Question 18

Standard Deviation of ALL Sample Means = Standard Error of Mean

Answer 18

More samples = the sample mean will be more similar to the population mean

Question 19

What is does Repeated Sampling do?

Answer 19

Repeating a study with a different sample many times over will result in findings approaching the true population values