Distributions and scores

Question 1

Z-score

Answer 1

z = (x – μ) / σ

Question 2

z = (x – μ) / σ

Answer 2

z-score, where:
X = standartized value
μ = the mean
σ = standard deviation

Question 3

Bell curve

Answer 3

graphic representation of a normal distribution

Question 4

Empirical rule

Answer 4

The empirical rule, or the 68-95-99.7 rule, tells you where most of the values lie in a normal distribution:

Around 68% of values are within 1 standard deviation of the mean.
Around 95% of values are within 2 standard deviations of the mean.
Around 99.7% of values are within 3 standard deviations of the mean.

Question 5

the 68-95-99.7 rule

Answer 5

aka the empirical rule:
Around 68% of values are within 1 standard deviation of the mean.
Around 95% of values are within 2 standard deviations of the mean.
Around 99.7% of values are within 3 standard deviations of the mean.

Question 6

t-score formula

Answer 6

Where
x̄ = sample mean
μ0 = population mean
s = sample standard deviation
n = sample size

Question 7

2 conditions of when T score is chosen over Z score

Answer 7

1. small sample size (e.g. under 30 samples)
2. when sigma is unknown (standard deviation)

Question 8

levels of freedom

Answer 8

n - 1

the number of independent pieces of information that went into calculating the estimate;

the number of values that are free to vary in a data set

Question 9

What is standard deviation equal to on a normal distribution?

Answer 9

1

Question 10

How does t-score change as n increases?

Answer 10

t-score goes up too

Question 11

What does a Z-score of 0 say?

Answer 11

the value is right in the middle, in the mean

Question 12

what does a Z-score of 1 say?

Answer 12

exactly one standard deviation above the mean

Question 13

where are the negative Z-scores, respective to the mean?

Answer 13

to the left from it

Question 14

where are the positive Z-scores, respective to the mean?

Answer 14

to the right from it

Question 15

formula to covert Z-score to T-score

Answer 15

T = (Z x 10) + 50.

Question 16

Confidence levels: what does a 95% confidence level mean?

Answer 16

What a 95 percent confidence level is saying is that if the poll or survey were repeated over and over again, the results would match the results from the actual population 95 percent of the time.

Question 17

confidence interval graph

Answer 17

Question 18

confidence coefficient

Answer 18

The confidence coefficient is the confidence level stated as a proportion, rather than as a percentage. For example, if you had a confidence level of 99%, the confidence coefficient would be .99.

The following table lists confidence coefficients and the equivalent confidence levels.

Confidence coefficient (1 – α)Confidence level (1 – α * 100%)0.9090 %0.9595 %0.9999 %

Question 19

Chi-square analysis: type of data it is best applied on?

Answer 19

nominal

Question 20

Chi-square statistic: essence

Answer 20

A chi-square (χ²) statistic is a test that measures how a model compares to actual observed data. The data used in calculating a chi-square statistic must be random, raw, mutually exclusive, drawn from independent variables, and drawn from a large enough sample.

Question 21

Chi-square statistic: depends on three things

Answer 21

χ² depends on:

1. the size of the difference between actual and observed values
2. the degrees of freedom
3. the samples size.

Question 22

what can a Chi-square statistic be used to test?

Answer 22

• χ² can be used to test whether two variables are related or independent from one another.
• to test the goodness-of-fit between an observed distribution and a theoretical distribution of frequencies.

Question 23

Formula of the Chi-square statistic

Answer 23

Question 24

What is Chi-square statistic test for independence?

Answer 24

A χ² test for independence can tell us how likely it is that random chance can explain any observed difference between the actual frequencies in the data and these theoretical expectations.

Question 25

What is Chi-square statistic: Goodness-of-fit?

Answer 25

χ² provides a way to test how well a sample of data matches the (known or assumed) characteristics of the larger population that the sample is intended to represent. If the sample data do not fit the expected properties of the population that we are interested in, then we would not want to use this sample to draw conclusions about the larger population.

Question 26

null-Hypothesis

Answer 26

what we want to NULLIFY, to disprove

Question 27

alternative Hypothesis

Answer 27

what we believe we can prove