Term
| Basic Context for Data (5-6 questions to ask) |
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Definition
| Who, What, When, Where, Why and How? |
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Term
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Definition
| When Data answers questions but does not represent a sumable or manipulatable quantity. Can be represented by a # |
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Definition
| Whenever a variable is in units representing exact amounts of something or some occurrence. |
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Term
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Definition
| A number assigned to each individual case for sorting purposes |
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Term
| Frequency Table/ Relative Frequency Table |
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Definition
| A table with different categories and and total counts or one which represents the proportion of each count as a percent |
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Definition
| Displays distribution of a categorical variable. NOT a quantitative variable |
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Term
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Definition
| A table which represents categories and breaks down the totals into their representative parts. The margins represent the totals |
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Term
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Definition
| When graphing data, make sure each catagory has an area which is proportional to its total in the group |
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Term
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Definition
| Unfair averaging over different groups without the same conditions and quantity |
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Term
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Definition
| Only for quantitative data. Looks like bar graph (only for catagorical data) except that there is no space between bars unless there is a gap in the data. Good for illustrating distribution |
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Term
| Stem and Leaf Displays (and Dotplots) |
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Definition
| Writing the first digit on one side of the table, then listing one following digit for each case in that range. Dotplots replace digits with dots |
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Term
| Three things to mention when describing distribution |
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Definition
Shape: Describe how many modes in data set/ symmetricallity/ outliers?
Center: Median/ Mean
Spread: Average variation/ interquartile range |
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Term
| Unimodal /Bimodal/ Multimodal |
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Definition
| With one hump/ 2 humps/ more than 2 heads |
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Term
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Definition
| Data which is fairly consistent, no modes or trend |
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Term
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Definition
| When there is a Tail (thinner ends of the distribution) one way or the other, the graph is said to be this |
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Term
| Interquartile Range (IQR) |
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Definition
| The upper quartile (75th percentile)- lower quartile (25th percentile) |
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Term
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Definition
The total sum of the difference between each y value and the mean squared divided by (n-1)
It is just before you square root to find the standard deviation |
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Term
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Definition
Take the square root of:
Sum of difference between y and the mean squared/ (n-1) |
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Term
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Definition
| 1. Make boxes with lower, upper quartiles and mean. Add whiskers up to 1.5 times the IQR and add outliars |
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Term
| Z-Score (Standardized Value) |
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Definition
| (y-the mean of y)/ standard deviation. Written z(x) or z(y) |
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Term
| How does standardizing data change data |
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Definition
Shape: Does not change
Center: Makes the mean 0
Spread: The standard deviation becomes 1 |
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Term
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Definition
| The shape of the data's distribution is unimodal and symmetric, then you can apply different things. Make a Picture |
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Term
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Definition
| Within 1 sd positively and negatively of 0 is 68% of data, within 2 is 95% of data, within 3 is 99.7 |
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Term
| Finding Normal Percentiles |
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Definition
| Calculate Z-Score then look to left of table for 1st 2 digits and match with the top of the table to find the corresponding normal percentile |
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Term
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Definition
| The y axis is the x of the corresponding histogram (ex. mpg) and the x axis is each data points Z-score. Should be a diagonal, left-right graph |
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Term
| Things to look for in Scatterplots |
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Definition
Direction: Is it positive or negative
Form: Is it linear? Curved?
Strength: How much does it scatter?
Outliers: Anything that significantly skews the data |
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Term
| Predictor/ Explanatory Variable |
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Definition
| The x-axis which is believed to inform or predict the y value |
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Term
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Definition
| The y axis and variable of interest. This is the variable used in St. dev. etc... |
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Term
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Definition
Measures the strength of the linear association between two quantitative variables.
r= The sum of z(x) times z(y) / (n-1) |
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Term
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Definition
Quantitative Variables Condition: Make sure data isn't categorical
Straight Enough Condition: It is subjective, but make sure the data isn't clearly non-linear
Outlier Condition: Make sure outliers are not present as they can distory the correlation dramatically
Check these conditions with a scatter plot |
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Term
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Definition
| The explanation of why correlation is misleading and does not prove causation |
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Term
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Definition
| Designed to assess how close the relationship between two variables is to being monotone. A monotone relationship is how consistently they increase or decrease, not necessarily linearly. A value of -1 means constant decreasing, 1 means constant increase. Its a nonparametric value |
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Term
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Definition
| Is less sensitive to outliers. Gives a rank (starting with 1, 2,3 etc....) to each x value. Also between -1 and 1. It is a nonparametric value. |
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Term
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Definition
| The difference of the y value of a coordinate and the predicted y value of a linear regression (also refered to as y(hat). |
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Term
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Definition
| Also know as the least squares line |
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Term
| Linear Regression equation |
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Definition
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Term
| b1 (The slope of linear regression) equation |
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Definition
r (sy/sx)
or
the correlation x times (standard deviation of y/ stand. dev. of x) |
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Term
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Definition
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Term
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Definition
| Gives a positive fraction of the data's variation accounted for by the model |
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Term
| Does the Plot Thinken? Condition |
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Definition
| When you plot the residuals against the model, there should be no discernable pattern. If there is, your model isn't ideal |
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Term
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Definition
| You can't simply rearrange regresion line equations unless correlation is 1.0. You must do the b1 and b0 formulas again |
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Term
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Definition
| The extent to which a point influences analysis |
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Term
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Definition
| Distinguishable traits of the data that can allow you to fit different regression lines to different segments of information (male/female etc...) |
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Term
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Definition
1. Make the distribution of a variable more symmetric
2. Make the spread of several groups (as seen in side-by-side boxplots) more alike, even if their centers differ (often achieved with logs)
3. Make the form of a scatterplot more nearly linear
4. Make the scatter in a scatterplot spread out evenly rather than thickening at one end |
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Term
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Definition
| Try for unimodal, left skewed histograms |
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Term
| Ladder of Powers: "0" aka Logs |
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Definition
| This is the go to. You can't have negative or 0 numbers, so add small constants to all data to avoid mistakes. Try logging y, then logging x, and if all else fails log both. |
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Term
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Definition
| Negative square root perserves the direction of relationships. Your last bet |
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Term
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Definition
| Positive or negative, depending on which way you want the data to go. Ratios of 2 quantities benefit the most. |
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Term
| Sample Strategies and Ideals to keep in mind: |
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Definition
1: Examine a Part of the Whole: Try to avoid bias by representing all parts of the population equally proportional to their representation in the whole
2: Randomize: When in doubt, make sure there is nothing that could be associated with what your sample
3: Its the Sample Size: The fraction of the population doesn't matter, just the actual sample size (2,000 is a good number). |
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Term
| Sample Strategies and Ideals to keep in mind: |
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Definition
1: Examine a Part of the Whole: Try to avoid bias by representing all parts of the population equally proportional to their representation in the whole
2: Randomize: When in doubt, make sure there is nothing that could be associated with what your sample
3: Its the Sample Size: The fraction of the population doesn't matter, just the actual sample size (2,000 is a good number). |
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Term
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Definition
| A sample of the entire population, often quite inefficent |
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Term
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Definition
Parameters are real information about the world that we are trying to get at, often in vain.
Statistics are anything we calculate from data |
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Term
| Simple Random Sample (SRS) |
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Definition
| A method by which any combination of samples could be selected. The basis for comparison with all other statistical methods |
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Term
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Definition
| The list of individuals from which the sample is drawn |
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Term
| Stratified Random Sampling |
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Definition
| Dividing the population into distinct strata of samples, and using a simple random sample within each strata. |
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Term
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Definition
| Taking a representative cluster of the population which expresses the population as a whole. If it doesn't represent the population as a whole it will be bias. Can also be a piece of multistage samples |
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Term
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Definition
| When you use a nonrandom, but systematic sample of individuals. For example, selected every 20th person in a population. |
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Term
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Definition
| A trial run of a survey before it is employed in a larger group at higher cost. Gives you a chance to recognize flaws in your design |
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Term
| Sampling Technique Errors |
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Definition
Voluntary Response Sample: Because it is self-selective, it is inherently bias
Convenience Sampling: Does not usually make unbiased information |
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Term
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Definition
Nonrespondants: Its always a good investment to limit the amount of Nonrespondants, because their lack of incorporation can shift data
Response Bias: Anything in the survey which influences response (wording of a question, the environment its taken in) |
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Term
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Definition
| When people or subjects are viewed in their natural environments. Often retrospective studies |
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Term
| Prospective v. Retrospective Studies |
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Definition
| Prospective studies follow randomly picked individuals and watch them for a given amount of time, generally favored over retrospective options |
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Term
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Definition
| When you attempt to isolate very simple variables through random assignment of treatments to subjects. Active manipulation by researchers. |
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Term
| The 4 Principles of Experimental Design |
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Definition
1. Control: Control sources of variation other than what we are testing
2. Randomization: Equalizes the effects of unforseen or uncontrollable sources of variation
3. Replicate: Results have to be replicated in slightly altered situations to show no bias
4. Block: Sometimes attributes affect outcomes of an experiment, so grouping different blocks together is more accurate |
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Term
| The 4 Principles of Experimental Design |
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Definition
1. Control: Control sources of variation other than what we are testing
2. Randomization: Equalizes the effects of unforseen or uncontrollable sources of variation
3. Replicate: Results have to be replicated in slightly altered situations to show no bias
4. Block: Sometimes attributes affect outcomes of an experiment, so grouping different blocks together is more accurate |
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Term
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Definition
| Limiting the effect knowledge can influence the experiment, by keeping key catagorical variables a secret from the subject and from the researcher. An experiment is "double blind" when even those who interprete the data are unaware of its identity. |
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Term
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Definition
| Pairing subjects because they are similar in ways not under study |
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Term
| Discrete v. Continuous Random Variables |
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Definition
| Discrete random variables are randomly selected from a set of outcomes which can be listed, while continuous random variables cannot be listed, they are infinite |
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Term
| Expected Value of a discrete random variable |
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Definition
| Multiple each possible outcome by its probability and add them all together |
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Term
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Definition
The difference between observed and expected (mean), squared and multiplied by liklihood of it happening + the same process for all different outcomes
For an insurance policy, if average cost is $20 per policy, with a payout of 10,000 and a likihood of having to pay out of 1/1,000, then
(10,000-20)^2*(1,000) |
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Term
| Calculate S.D. (given variance) |
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Definition
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Term
| Adding/subtracting rules for SD and variance |
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Definition
-The variance of the sum of two independent random variables is the sum of their individual variances NOT S.D.
-If random variables are independent, the variance of their sum or difference is always the sum of the variances. |
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Term
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Definition
| The mean of the sum/ difference of two random variables is the sum/difference of their means |
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Term
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Definition
| Difference between Expected value and observed (or theoretically observed) value over S.D., then use z-score technology/table |
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Term
| Definition of and Calculating Covariance |
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Definition
Measures how X and Y vary together. When two things correlated (i.e. X above its mean and y above its mean) they will have positive covariance.
Covariance (X,Y)= E((X-u)(Y-v))
In other words, the difference of individual data point and mean of x and y times one another. |
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Term
| Geometric probability model for Bernoulli trials |
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Definition
p= probabilty of success
X=number of trials until first success
P(x)=p*(1-p)^x-1
In other words, the probabilty of success with only x trials equals the individual probability of success times the probability of failure to the x-1 degree. |
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Term
| Expected number of trials for geometric probability model for Bernoulli trials |
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Definition
E(X)=1/p
1/ the probabilty of an accurance equals how many times you would expect to have to run the experiment before a success. |
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Term
| Standard deviation geometric probability model for Bernoulli trials |
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Definition
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Term
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Definition
| Random events labeled x are not algebraically manipulatable, X(1)+X(2)+X(3) cannot be simplified. Insuring 3 people for 10,000 each is not the same as insuring one for 30,000 |
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Term
| If shifting a data set by a constant, describe effect on s.d., variance and mean |
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Definition
The mean of the data fluctuates the same way the change influenced.
Variance and Standard Deviation are completely unaffected by addition/subtraction of a constant |
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Term
| Multiplying data by a constant |
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Definition
Multiplying data by a constant shifts the mean that same amount
The variance of the constant is multipied by the square of the constant.
If we multiply X by a, then E(x*a)=a*E(x)
Var (x*a)= a^2Var(x) |
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Term
Probabilty of certain outcome given
-x successes and
-n trials |
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Definition
The number of possible outcomes giving x successes in n trials* p^x * (1-p)^n-x
The probability is the number of possible outcomes times the probability of individual success to the number of successes and the probability of failure to the number of failures. |
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Term
| Standard deviation of a binomial model |
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Definition
square root (n*p*(1-p))
or the number of outcomes times the probability of success times the probability of failure |
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Term
| Estimate binomial probability for large sample size using the normal method |
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Definition
The difference of the mean and the observed (or necessary) number of successes over the standard deviation
n*p- observed/ sq. rt. (np(1-p)) |
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Term
| To estimate the probability you will get your first success on a certain trial, use... |
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Definition
Geometric trial
P(x)= (p)(1-p)^(x-1) |
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Term
| To estimate the probability you'll get a certain number of success in a specified number of independant trials, use... |
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Definition
the Binomial method
nCx= n!/(x!)(n-x)!
nCx ("n choose x")*(p^x)*(1-p)^n-x
Number of possibilities * probability of success to the number of successes*probability of faliure to the number of needed failures |
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Term
| To estimate probability involving (large) quantitative variables, use |
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Definition
The normal model
exp. mean- observed/ sd. sq. rt. [np(1-p)] |
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Term
| Sampling distribution model |
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Definition
| allows us to quantify variation between samples and talk about how likely it is that we'd observe a sample proportion in any particular interval |
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Term
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Definition
sq. rt. [P(1-P)/n]
square root of probabilty of success * failure/ number of cases |
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Term
| Assumptions and Conditions for normal model usage in proportions |
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Definition
Independance assumption: each sample is indep.
Sample size assumption: enough "n"s
Randomization Condition: Subjects randomly assigned to treatments
10% condition: sample size must be no larger than 10% of population
Success/Failure condition: Sample size has to be big enough to have 10 successes and 10 failures |
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Term
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Definition
| The mean of a random sample is a random variable whose sampling distribution can be approximated by a normal model. The larger the sample, the better the approximation will be. |
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Term
| Sampling distribution model for a mean (CLT) |
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Definition
If you take a sample out of a known population, the standard deviation for that sample is smaller than one random instance. Your new sample (new mean) is always smaller than standard deviation of each sample point. It is represented universally as
SD(y bar, or the sample)=SD(population)/(sq. rt. [n]) --> the sample size |
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Term
| Z score calculation for sampling distribution for the mean |
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Definition
Book def: y(bar)-mu/SD(y bar)
given difference that we are testing (in question) - parameter(what we are given as true)/ new standard deviation (SD of population/ sq. rt.[n] |
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Term
| Standard deviation of a sampleing distribution |
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Definition
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Term
| Estimating the standard deviation of a sampling distribution if parameter is unknown |
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Definition
| Is called Standard Error, found with the same formula substituting p(hat) for p. |
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Term
| Given p and n, find margin of error w/ 95% confidence interval |
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Definition
Calculate SE = sq. rt. [(p*(1-p))/n]
Multiply standard error times z*(1.96) to get margin of error |
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Term
| To find sample size to get the confidence interval for a proportion you want |
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Definition
| Use p=.5 and the Margin of error you want (often 0.03) and work backwards until you solve for n |
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Term
| Null v. Alternative Hypotheses |
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Definition
| We assume the null hypothosis is true, alternative hypothesis is something we consider plausible should the null be overturned |
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Term
| Conditions for Hypothesis testing (4) |
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Definition
Independence Assumption
Randomization Condition
10% Condition
10 Success/Failure Condition |
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Term
| Calculating Margin of Error |
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Definition
ME= z* x SE(p)
Where SE= sq rt [(p)(1-p)/n] |
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Term
| Errors in Hypothesis Testing (2) |
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Definition
Type 1: The null hypothesis is true, but we mistakenly reject it
Type 2: The null hypothesis is false, but we fail to reject it |
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Term
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Definition
| The probability that it correctly rejects a false null hypothesis. If B is the probability that a test fails to reject a false hypothesis (Type 2 error), 1-B is the power of the test. |
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Term
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Definition
| The distance between the null hypothesis value and the truth the effect size. This can be estimated with the observed mean |
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Term
| Assumptions and Conditions for comparing proportions |
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Definition
Independence Assumption
Randomization Condition
10% condition if sampled w/o replacement
Success/failure condition
Independant Groups Assumption: Two groups comparing must be independent of each other |
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Term
| Two-proportion z-interval |
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Definition
p(1)-p(2) +/- (z*)(SE {p(1)-p(2)})
(SE {p(1)-p(2)})= sq rt[(p)(1-p)/n + (p)(1-p)/n] for both p(1) and p(2), using appropriate "n"s as well |
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Term
| Pooling proportions (not means!) |
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Definition
Add # of successes and divid by sum of trials, but when calculating SE,
SE {p(pooled)})= sq rt[(p)(1-p)/n(1) + (p)(1-p)/n(2)] for both p(1) and p(2), noting that although the p and q values are pooled, the n value is NOT, and remains distinct for both calculations. |
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Term
| Calculating degrees of freedom |
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Definition
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Term
| One-sample t-interval for the mean |
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Definition
y(bar) +/- (t*)(SE[estimated from y])
SE= s/ sq rt[n] |
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Term
| Getting the standardized sample mean t |
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Definition
[y(bar)-mu]/ SE(y bar)
In other words, the mean from the data, the parameter mean divided by estimated Standard Deviation (s/sq. rt. [n]) |
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Term
| Assumptions and conditions for t test |
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Definition
Independance asumption
Randomization condition
10% condition
Nearly normal condition- unimodal, symmetric distribution. You can use histograms or normal probabilty plot |
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Term
| Bonus assumptions for Counts |
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Definition
Counted Data Condition- There must be counts in each cell, not %s or anything else
Expected Cell Frequency Condition- There must be at least 5 counts in each bar of the table |
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Term
Basic 4 Assumptions and Conditions
+ 3 test specific assumptions/ conditions |
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Definition
1. Independance
2. Randomization
3. 10% condition
4. Success/failure condition
AND
5. Independence of groups- The two groups we are comparing have to be independent of each other
6. Nearly normal condition
7. Paired data assumption |
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