Statistics Chapter 8, 10-13

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1

Population

All units of possible interest

2

Sample

The part of the population upon which we actually take measurements

3

Frequency Curves

A "picture" of the population

4

Systematic Frequency Curve

Not skewed, symmetric

5

Left Skewed Frequency Curve

Negatively Skewed

6

Right Skewed Frequency Curve

Positively Skewed

7

Proportion

The PROPORTION of the population with a measurement in a certain range is equal to the AREA under the frequency curve over that range

8

Standardized Scores (Z-Scores)

The number of standard deviations away from the mean an observation is

9

Percentiles

An observation's PERCENTILE (or PERCENTILE RANK) is the percentage of the population that is equal to or less than the observation

10

Measurement Variables

Continuous: every fraction is a possible value
Discrete: only a countable number of values are possible

11

Deterministic Relationships

Perfect
One variables cant be perfectly predicted using the other variables
y= function of x
Ex: x= height is feet
y= height in inches
y=12x

12

Statistical Relationships

Not perfect
The two variables may be related, but perfect prediction is not possible
y= function of x+error
Error: everything that affects y besides x
Ex: x= amount of time spent studying
y= score on exam
What factors affect exam scores other then amount of time studying?

13

Linear Relationships

A relationship of the form, y=a+bx where
a= y-intercept
b= slope

14

Correlation

A measurement of the STRENGTH and DIRECTION of the LINEAR relationship between two measurement variables
r= coefficient of correlation

15

Positive Correlation

r>0
x and y tend to be of the same magnitude

16

Negative Correlation

r<0
x and y tend to be of opposite magnitude

17

No Correlation

r=0
x and y are not linearaly related

18

Perfect Correlation

r=1 or r=-1
All the points fall on a line

19

Regression

A procedure for eliminating the "best" line relating two variables
Linear equation: y=a+bx
To fit the line we need to "guess" the a and b

20

Extrapolation

Using the regression line for prediction at an x-value that is outside of the x-range of the original data, predictions that involve extrapolation are NOT valid

21

Outliers

Points that are far removed from the rest of the data due to error in collecting or entering data, and rare events
Can either strengthen or weaken a correlation

22

Non-Linear Relationships

A correlation of r=0 means that in the sample no LINEAR relationship exists between x and y (even if r is close to 0 a strong, even perfect, non-linear relationship may exist).

23

Risk

Proportion with "the trait"

24

Baseline Risk

Risk of having "the trait" for a group used as the basic for comparison

25

Contingency Tables

A contingency table is a display showing the combinations of categories for two categorical variables and the number of individuals that fall in eahc category

26

Rows

The sides of the table, usually EXPL

27

Columns

The top of the table, usually RESP