Stats Exam 1

Front 1

Design

Back 1

Plan how to obtain the data

Front 2

Description

Back 2

Summarize the data with graphs and numerical summaries

Front 3

Inference

Back 3

Use data from a random and representative sample to draw conclusions about the the population of interest

Front 4

Parameter

Back 4

Numerical summary of a population

Front 5

Statistic

Back 5

Numerical summary of a sample

Front 6

Subjects

Back 6

Persons, animals, or objects in our study/experiment

Front 7

Variables

Back 7

The characteristics that we measure on each subject

Front 8

Population

Back 8

All subjects of interest

Front 9

Sample

Back 9

Subjects for whom we have data

Front 10

Random Sampling

Back 10

Each member of population has the same chance of being included in the sample (representative of the population)

Front 11

Categorical Variables

Back 11

Summarize with counts and percentages

Graphs: bar charts and pie charts

Front 12

Quantitative Variables

Back 12

Takes on numerical values

Graphs: dotplots, histograms, stemplots, and box plots

Measures of center: mean, median, mode

Measures of spread: range, IQR, standard deviation

Front 13

Discrete Quantitative

Back 13

Take only a finite list of possible outcomes, such as a count (ex: year, absences)

Front 14

Discrete Quantitative

Back 14

Take only a finite list of possible outcomes, such as a count (ex: year, absences)

Front 15

Continuous Quantitative

Back 15

Has a an infinite list of possible values that form an interval (ex: exam scores)

Front 16

Dotplot

Back 16

Back (Definition)

Front 17

Stemplot

Back 17

Back (Definition)

Front 18

Histogram

Back 18

Back (Definition)

Front 19

Boxplot

Back 19

Back (Definition)

Front 20

Bar Chart

Back 20

Back (Definition)

Front 21

Pie Chart

Back 21

Back (Definition)

Front 22

Histogram Shapes

Back 22

Back (Definition)

Front 23

Mean

Back 23

The average of all the observations

Front 24

Median

Back 24

Observation “right in the middle” : M

Front 25

Mode

Back 25

Most frequently occurring value

Front 26

Range

Back 26

Range = maximum - minimum

Front 27

Variance

Back 27

-Average squared deviation from the mean: s^2

Front 28

Standard Deviation

Back 28

Square root of the variance: s

Front 29

Empirical Rule

Back 29

In any bell-shaped and symmetric distribution you will find approx:

-68% of the observations within one sdev of the mean

-95% of the observations within 2 sdev of the mean

-99.7% of the observations within 3 sdev of the mean

Front 30

Quartiles

Back 30

Divide the data set into four quarters

Front 31

IQR

Back 31

Measures the spread of the central 50% of the data

IQR = Q3 - Q1

Front 32

IQR

Back 32

Measures the spread of the central 50% of the data

IQR = Q3 - Q1

Front 33

Five number summary

Back 33

Minimum, Q1, median, Q3, maximum

Front 34

Z-Score

Back 34

Fill in….

Front 35

Scatterplot

Back 35

Back (Definition)

Front 36

Explanatory Variable

Back 36

X axis

Front 37

Response Variable

Back 37

Y axis

Front 38

DOTS (Scatterplot)

Back 38

Direction

Outliers

Trend

Strength

Front 39

Correlation

Back 39

-The direction and strength of the straight line in relationship between x and y.

-Represented by r

-r is always between 1 and -1 (no units)

-Interpretation: strong/weak, positive/negative

-Outliers can have strong effect of r

Front 40

Regression Equation

Back 40

y(hat) = a+bx

Front 41

B (slope of regression line)

Back 41

Average change in y for one unit change in x

Front 42

A (slope of regression)

Back 42

Y-intercept: expected value of y when x=0. Only interpret if x=0 makes sense and is close to values of x observed in data

Front 43

Residuals

Back 43

Prediction of errors for each observation

Residuals = y - y(hat)

Front 44

Residuals

Back 44

Prediction of errors for each observation

Residuals = y (observed y) - y(hat) (predicted y)

Front 45

Least Squares Method

Back 45

Finds the line that minimizes the sum of the squared residuals

Front 46

R^2

Back 46

R^2= (r)^2

Proportion of the variability in y that is explained by the regression on x

Front 47

Cautions

Back 47

Influential Outlier: points that have an x value far away from the rest

Correlation (or Association): does not imply causation

Extrapolation: extend the application to an unknown situation by assuming that existing trends will continue or similar methods will be applicable

Simpson’s Paradox: a lurking variable can reverse the association between two categorical variables in a contingency table

Front 48

Contingency Tables

Back 48

-Both explanatory and response variables are categorical

-Display counts (frequencies) on the table

-Compute % to determine association

Front 49

Experiments

Back 49

The researcher assigns subjects to certain experimental treatments

Front 50

Experiments

Back 50

The researcher assigns subjects to certain experimental treatments

Front 51

Observational studies

Back 51

Researcher does nothing to subjects but observe x and y

Front 52

Experimental unit

Back 52

Subjects involved in the experiment

Front 53

Experimental unit

Back 53

Subjects involved in the experiment

Front 54

Treatments

Back 54

Experimental conditions given to the subjects

Front 55

Random Phenomenon

Back 55

Distinct predictable pattern after many outcomes

Front 56

Probability

Back 56

Long-run relative frequency

Front 57

Independent Trials

Back 57

The outcome of one trial is not affected by the outcome of another

Front 58

Sample Space

Back 58

The set of all possible outcomes

Front 59

Event

Back 59

An outcome or group of outcomes, a subject of the sample space

Front 60

Biased samples

Back 60

Systematically favor certain outcomes, not representative of the population of interest

Front 61

Margin of error

Back 61

1/square root of n

Front 62

Placebo

Back 62

Dummy treatment

Front 63

Placebo

Back 63

Dummy treatment

Front 64

Blind study

Back 64

Subjects do not know if they receive treatment or placebo

Front 65

Blind study

Back 65

Subjects do not know if they receive treatment or placebo

Front 66

Double blind study

Back 66

Neither the subject or those in contact with the subject know who gets the treatment or placebo

Front 67

Randomization

Back 67

Use mechanical method to select subjects and assign them to treatments

Front 68

Randomization

Back 68

Use mechanical method to select subjects and assign them to treatments

Front 69

Replication

Back 69

Number of experimental units that get each treatment

Front 70

Cross-sectional studies

Back 70

Sample surveys that just want to take a snapshot of the population at the current time

Front 71

Case-control studies

Back 71

Retrospective studies (backward looking) in which we match each case (positive outcome) with a control (negative outcome) and then ask questions about the explanatory variable

Front 72

Prospective studies

Back 72

Forward looking and follow subjects into the future

Front 73

Complement of an event

Back 73

The rest of the sample place, written as A^c

P(A^c)=1-P(A)

Front 74

Disjoint events A and B

Back 74

P(A or B)= P(A) + P(B)

Front 75

Conditional probability

Back 75

P(A|B) = P(A and B) / P(B)

Front 76

Independent events A and B

Back 76

If two events are independent, knowledge about one event tells us nothing about the other event

Definition: P(A|B) = P(A)

Multiplication rule: P(A and B) = P (A) x P(B)

Front 77

Discrete Random Variables

Back 77

Finite number of possible values

Prob distribution: list, graph or formula with all possible values of X and their probabilities

Population mean: u=sum of xP(x)

Front 78

Continuous Random Variables

Back 78

-Infinite number of possible values

-Probabilities are areas under a density curve (smooth) with a total area of 1

-Assign probabilities to intervals, not individual values of X

Front 79

Normal Probability Distributions

Back 79

- Bell-shaped curves, indexed by their mean and standard deviation

-Follows empirical rule

Front 80

Binomial distribution

Back 80

-Each of n trials can have two possible outcomes: success or failure

-Probability of success for each trial is the same: p (independent events)

-Binomial Random Variable X counts the number of successes

Mean: u(mu)=np

Standard deviation: square root of np(1-p)

Hint 80

Front 81

Binomial distribution

Back 81

-Each of n trials can have two possible outcomes: success or failure

-Probability of success for each trial is the same: p (independent events)

-Binomial Random Variable X counts the number of successes

Mean: u(mu)=np

Standard deviation: square root of np(1-p)

Front 82

P(at least one)

Back 82

1-P(none)