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| 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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Definition
| When Data answers questions but does not represent a sumable or manipulatable quantity. Can be represented by a # |
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| Whenever a variable is in units representing exact amounts of something or some occurrence. |
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| A number assigned to each individual case for sorting purposes |
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| 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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| A table which represents categories and breaks down the totals into their representative parts. The margins represent the totals |
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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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| Unfair averaging over different groups without the same conditions and quantity |
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| 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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| 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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| 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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| Unimodal /Bimodal/ Multimodal |
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Definition
| With one hump/ 2 humps/ more than 2 heads |
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Definition
| Data which is fairly consistent, no modes or trend |
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| 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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| Interquartile Range (IQR) |
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Definition
| The upper quartile (75th percentile)- lower quartile (25th percentile) |
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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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Definition
Take the square root of:
Sum of difference between y and the mean squared/ (n-1) |
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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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| 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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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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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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| 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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| 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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| 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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Definition
| The y axis and variable of interest. This is the variable used in St. dev. etc... |
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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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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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Definition
| The explanation of why correlation is misleading and does not prove causation |
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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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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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| 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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| Also know as the least squares line |
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| Linear Regression equation |
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Definition
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| 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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Definition
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Definition
| Gives a positive fraction of the data's variation accounted for by the model |
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| 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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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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Definition
| The extent to which a point influences analysis |
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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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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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Definition
| Try for unimodal, left skewed histograms |
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| 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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Definition
| Negative square root perserves the direction of relationships. Your last bet |
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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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| 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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Definition
| A sample of the entire population, often quite inefficent |
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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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| 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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Definition
| The list of individuals from which the sample is drawn |
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| 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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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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Definition
| When you use a nonrandom, but systematic sample of individuals. For example, selected every 20th person in a population. |
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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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| 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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Definition
| When people or subjects are viewed in their natural environments. Often retrospective studies |
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| 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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Definition
| When you attempt to isolate very simple variables through random assignment of treatments to subjects. Active manipulation by researchers. |
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| 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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Definition
| Pairing subjects because they are similar in ways not under study |
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