Five Number Summary
Minimum, Q1, Median, Q3, Maximum
IQR and Outliers
IQR: Q3-Q1 |
Low Outlier: (Q1)(1.5 IQR) |
High Outlier: (Q3)(1.5 IQR) |
Histograms
Regular: equal spacing, used to determine shape |
Relative: divide # by n to get % |
Cumulative: ≤, last bar = n, never for shape |
Cumulative: percentage based, 50% is median |
relative location= (# of values below)/n
Transformations
Linear: affects center not spread |
Adds to sample mean (x), M, Q1, Q3, IQR |
Multiplication: affects center and spread |
Multiplies to mean (x), M, Q1, Q3, IQR, and sigma |
"Describe the distribution"
Center: Mean or median |
Spread; Standard deviation, IQR or range |
Shape: Symmetric or skewed |
Density Curves
-Always on or above x-axis
-Area = 1
-Has mean and median
-Infinite tails
-Singular point has NO AREA |
Median: equal areas point (point that divides curve in half)
Mean: balance point (where curve would balance if solid)
Symmetric curve: Mean = Median
"Describe the relationship" (Scatter plot)
Direction: +/- or neither (analyzed from L to R) |
Form: linear or not |
Strength: how correlated (see below) |
Very strong: 100-91
Strong: 90-85
Moderately strong: 84-75
Moderately weak: 74-70
Weak: 70 and below
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Residual Plots
Exhibits randomness, then a line is a good model for the data |
Exhibits a pattern, then a line is NOT a good model for the data |
Coefficents
R2 (Coefficient of determination): represents the percentage of the change in the y-variable that can be attributed to its relationship with the x-variable |
Ex: r-squared for the regression between x and y is .73, we can say that x accounts for 73% of the variation in y |
R (Correlation coefficient): strength of linear line on scale of -1≤0≤1 |
-1: perfectly linear (negative slope)
0: literally sucks
1: perfectly linear (positive slope)
Correlation
X and Y variable assignment doesn't matter |
Quantitative values only |
Non-resistant (affected by outliers) |
Scatterplot Vocab
X-variable: explanatory/independent variable (cause) |
Y-variable: response/dependent variable (effect) |
Extrapolation: predicting outcome outside of the domain |
Interpolation: predicting inside the domain [lowest X, highest X] |
Sampling Methods
Simple random sample (SRS): every group of objects has equal probability of being selected |
Ex: Hat method, calc, table of random digits* |
Stratified random sample: sample from each subgroup (good for comparison) |
Cluster sample: pick a few subgroups to sample and sample entire subgroup |
Systematic Random Sampling: select a sample using a system (like every 3rd) |
*ignore number if not in sample, skip if repeat
Bad Sampling
Voluntary response: incomplete data (extremes) |
Convenience: chooses easiest individuals to reach |
Under-coverage: people aren't reached or accessible |
Bad surveying
Non-response: not providing data or talking to you |
Response: lying |
Poor wording: leans toward bias answer |
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Principles of Experimental Design
Comparison: Use design that compares two or more treatments |
Random Assignment: Use chance to assign experimental units to treatments (balances effects of other variables) |
Control: Keep other variables that might affect the response the same for all groups |
Replication: Use enough experimental units in each group so that any differences in the effects of the treatments can be distinguished from chance differences between the groups |
Completely randomized:
-The treatments are assigned to all the experimental units completely by chance
-Control group: that receives an inactive treatment or an existing baseline treatment
-Placebo effect: response to a dummy treatment
-Double-blind experiment: neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received
Experimental Design
Matched pairs:
-Randomized blocked experiment in which each block consists of a matching pair of similar experimental units
-Chance is used to determine which unit in each pair gets each treatment
Law of Large Numbers
As n becomes large the sample mean approaches the population mean |
Binomials
1. Each observation falls into one of just two categories –“success” or “failure” |
2. The procedure has a fixed number of trials – (n) |
3. The observations must be independent – result of one does not affect another |
4. The probability of success (p) remains the same for each observation |
Geometric
(1-3 same as binomial) |
4. The variable of interest is the number of trials required to obtain the first success* |
*Geometric is also called a “waiting-time” distribution
Error
Type I: Rejecting the Ho when it is actually true (a false positive); probability = alpha |
Type II: Accepting the Ho when it is actually false (a false negative) |
Central Limit Theorem
As n becomes very large the sampling distribution for sample mean (x bar) is approximately normal
(n≥30)
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