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51 Cards in this Set

  • Front
  • Back

IQR


(Inter-Quartile Range)

Measures the range covered by the middle 50%


IQR= Q3 - Q1


Q1: median of lower 50%


Q3: median of top 50%

The Standard Deviation Rule


("The Empirical Rule")

Approx. 68% of observations fall within 1 SD


Approx. 95% of observations fall within 2 SD


Approx. 99.7% of observations fall within 3 SD

The Five Number Summary

(min, Q1, M, Q3, Max)


Use for all cases not reasonably symmetric.

The 1.5 (IQR) Criterion for Outliers

Used to detect outliers. An observation is an outlier if:


Below Q1 - 1.5(IQR)=


Above Q3 + 1.5(IQR)=

Peakedness (Modality)

The number of peaks (modes) the distribution has.

Mean


(denoted by x-bar)

The average of a set of observations


(The sum of the observations divided by the number of observations)

Mode

The most commonly occurring value in a distribution.

The General Addition Rule

For any 2 events A and B,


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




P(A or B)= P(A or B occurs or both)




Disjoint or not

Conditional Probability

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




note that the denominator is always the 2nd event after condition line.

Probability Rule #1

The probability of an event can range anywhere from 0 to 1.

Shape?

Shape?

* Unimodal


*Symmetric


*Normal




Mean is approximately equal to M.

Shape?

Shape?

Skewed Right




Mean > M

Shape?

Shape?

Skewed Left




Mean < M

Tree Diagram

To determine possible outcomes.

Observational Study

Values of the variable(s) of interest are recorded as they naturally occur. No interference by researchers.

Experiment

Instead of assessing the values of the variables as they naturally occur, the researchers interfere and they are the ones who assign explanatory variable to individuals.

Hawthorne Effect

People in an experiment behave differently from how they would normally behave.

Range

Range = Max - min

Q1

median of lower 50%

Q3

median of top 50%

Lurking Variable

A variable not included in the study, but could have a substantial effect on our understanding of the relationship between the two studied variables.

Correlation Coefficient -r

A numerical measure that measure the strength and direction of a linear relationship between 2 quantitative variables.

Simpson's Paradox

When including a lurking variable causes us to rethink the direction of an association.

C -> C

*Categorical Explanatory Variable


*Categorical Response Variable


Display: Two-way Table


Numerical Summary: Conditional Percentages


Desc.: Compare distributions/conditional %

Q -> Q

*Quantitative Explanatory Variable


*Quantitative Reponse Variable


Display: Scatterplot, points= individuals


Desc.: Overall pattern, any outliers




Direction/Form/Strength

C -> Q

* Categorical Explanatory Variable


*Quantitative Response Variable


Display: side-by-side boxplots


Numerical Summ.: Descriptive Stats


Desc.: Difference between distributions.

Response Variable


(Dependent Variable)

The outcome of the study.

Explanatory Variable


(Independent Variable)

The variable that claims to explain, predict or affect the response.

Standard Deviation

The SD is the square root of the Variance.

Median (M)

The midpoint of the distribution.




To find the median:


*Order the data from smallest to largest.




*If n is odd: (n+1)/2


*If n is even: between n/2 and n/2+1

Disjoint Events

Cannot occur at the same time.

Probability of Equally Likely Events

P(A)= number of outcomes in A




Divided by




number of outcomes in S

Sample Space (S)

All possible outcomes.

Law of Large Numbers

States that as the number of trials increases, the relative frequency becomes the actual probability.

Relative Frequency

The relative frequency that an event occurs in a long series of trials.

Probability

A way of quantifying uncertainty/ chance

Sample Survey

Observational study in which individuals report variables' themselves, frequently by giving their opinion.

Simple Random Sampling

Each individual has the same chance of being selected.

Stratified Sampling

Used when our population is naturally divided into sub-populations, called stratum. Choose a random sample from each stratum.

Cluster Sampling

Take a random sample of clusters and use all the individuals within the selected clusters as our sample.

Value of -r

The value of -r falls between -1 and 1.


Closer to 1 = Strong positive relationship


Closer to 0 = Weaker relationship


Closer to -1= Strong negative relationship

Probability Rule #5


The Multiplication Rule of Independent Events

If A and B are two independent events.




P(A and B)= P(A) x P(B)

The General Multiplication Rule

For any two events A and B, independent or not.




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

Law of Total Probability

For total probability of event (B),




P(B)= (P(A)*P(B|A)) + (P(not A)*P(B|not A)

AND

Multiplication

OR

Addition

Probability Rule #4


The Addition Rule for Disjoint Events.

If A and B are disjoint events,




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

Probability Rule #2

The sum of the probabilities of all possible outcomes is 1.

Rule #3


The Complement Rule

P(not A)= 1 - P(A)




The probability that an event does not occur is 1 minus the probability that it does occur.

Probability Table

Condition Tree