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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% |
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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 |
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The Five Number Summary |
(min, Q1, M, Q3, Max) Use for all cases not reasonably symmetric. |
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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)= |
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Peakedness (Modality) |
The number of peaks (modes) the distribution has. |
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Mean (denoted by x-bar) |
The average of a set of observations (The sum of the observations divided by the number of observations) |
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Mode |
The most commonly occurring value in a distribution. |
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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 |
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Conditional Probability |
P(B|A)= P(A and B)/ P(A) note that the denominator is always the 2nd event after condition line. |
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Probability Rule #1 |
The probability of an event can range anywhere from 0 to 1. |
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Shape? |
* Unimodal *Symmetric *Normal Mean is approximately equal to M. |
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Shape? |
Skewed Right Mean > M |
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Shape? |
Skewed Left Mean < M |
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Tree Diagram |
To determine possible outcomes. |
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Observational Study |
Values of the variable(s) of interest are recorded as they naturally occur. No interference by researchers. |
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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. |
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Hawthorne Effect |
People in an experiment behave differently from how they would normally behave. |
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Range |
Range = Max - min |
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Q1 |
median of lower 50% |
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Q3 |
median of top 50% |
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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. |
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Correlation Coefficient -r |
A numerical measure that measure the strength and direction of a linear relationship between 2 quantitative variables. |
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Simpson's Paradox |
When including a lurking variable causes us to rethink the direction of an association. |
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C -> C |
*Categorical Explanatory Variable *Categorical Response Variable Display: Two-way Table Numerical Summary: Conditional Percentages Desc.: Compare distributions/conditional % |
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Q -> Q |
*Quantitative Explanatory Variable *Quantitative Reponse Variable Display: Scatterplot, points= individuals Desc.: Overall pattern, any outliers Direction/Form/Strength |
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C -> Q |
* Categorical Explanatory Variable *Quantitative Response Variable Display: side-by-side boxplots Numerical Summ.: Descriptive Stats Desc.: Difference between distributions. |
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Response Variable (Dependent Variable) |
The outcome of the study. |
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Explanatory Variable (Independent Variable) |
The variable that claims to explain, predict or affect the response. |
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Standard Deviation |
The SD is the square root of the Variance. |
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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 |
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Disjoint Events |
Cannot occur at the same time. |
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Probability of Equally Likely Events |
P(A)= number of outcomes in A Divided by number of outcomes in S |
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Sample Space (S) |
All possible outcomes. |
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Law of Large Numbers |
States that as the number of trials increases, the relative frequency becomes the actual probability. |
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Relative Frequency |
The relative frequency that an event occurs in a long series of trials. |
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Probability |
A way of quantifying uncertainty/ chance |
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Sample Survey |
Observational study in which individuals report variables' themselves, frequently by giving their opinion. |
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Simple Random Sampling |
Each individual has the same chance of being selected. |
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Stratified Sampling |
Used when our population is naturally divided into sub-populations, called stratum. Choose a random sample from each stratum. |
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Cluster Sampling |
Take a random sample of clusters and use all the individuals within the selected clusters as our sample. |
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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 |
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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) |
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The General Multiplication Rule |
For any two events A and B, independent or not. P(A and B)= P(A) x P(B|A) |
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Law of Total Probability |
For total probability of event (B), P(B)= (P(A)*P(B|A)) + (P(not A)*P(B|not A) |
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AND |
Multiplication |
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OR |
Addition |
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Probability Rule #4 The Addition Rule for Disjoint Events. |
If A and B are disjoint events, P(A or B)= P(A) + P(B) |
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Probability Rule #2 |
The sum of the probabilities of all possible outcomes is 1. |
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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. |
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Probability Table |
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Condition Tree |
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