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49 Cards in this Set
- Front
- Back
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3 Useful features of ration data
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-shape of distribution
-central, average, or typical value (mean, median, mode) -variability |
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Histograms (steps)
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Display the shape of distributions
1. Divide data set into intervals, equal width 2. Count # of cases per bin 3. Bar height= # of cases within that bin |
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Outliers
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Unusual cases
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Skewed to right/left/symmetric
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fewer values on right vs. fewer values on left
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Bimodal
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2 peaks
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Unimodal
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1 peak
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Mode
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The most common value
- can also be used for ordinal or nominal data |
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Mode strengths
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East to understand & calculate
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Mode weaknesses
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-Not practical for a large # of categories
-Does not provide a lot of information |
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Mean
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The average, center of gravity as a distribution
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Mean formula
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M=Exi/N
m:mean E=sum of Xi N=total # of cases |
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Strengths of mean
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Simple to calculate & can tell you a lot about a distribution
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Median
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The value of the score that divides the date in half
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Median strengths
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Less sensitive to outliers than the mean
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Range
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Difference between minimum value and maximum value
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Range strengths
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Easy to calculate & understand
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Range weaknesses
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Only depends on large & small values
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Interquartile Range
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Difference between the upper & lower quartiles
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Strengths of IQ range
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Less influenced by largest & smallest values than the range
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Weakness of IQ range
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Hard to calculate & explain
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Standard deviation (steps)
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Average distance from the mean
1. calculate mean 2. Find deviation from mean for each value 3. Square these deviations 4. Sum squared deviations 5. Divide by n-1 6. Take square root of variance |
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Variance
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The standard deviation squared
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Variance formula
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S^2=E(Xi-M)^2/N-1
Xi: case value M: mean of cases E: sum of (Xi-M)2 N: total # of cases |
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Standard deviation
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s=Square root of s^2
(square root of the variance) |
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Frequency curve
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Taking a smooth curve along the top of a histogram to represent the data
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Normal curve
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A distribution whose frequency is bell shaped
- allows us to easily estimate the proportion of people within any given interval on the curve - we can also calculate what value corresponds to a given percentile and vice versa |
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Standardized score (z-score) (formula)
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# of standard deviations the observed value falls from the mean
Z score= (X-M)/S X: value M: mean S: standard deviation |
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Positive standardized score
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Means a score is above the mean
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Negative standardized score
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Means a score is below the mean
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Standard normal curve
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normal curve with a mean of 0 and SD of 1
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Empirical rule
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- 68% of values fall within 1 SD from the mean
- 95% of values fall within 2 SD from the mean - 99.7% of values fall within 3 SD from the mean |
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To find an observed percentile:
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1. Look up observed percentile & find corresponding standardized score
2. compute the observed value =mean- standardized score * standard deviation |
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Reasons to use graphs
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-Can convey a story relatively quickly
-They can also reveal things that would be difficult to see by looking at raw numbers -They can obscure meaning |
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Common problems with graphs
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-Labels
-Range of values displayed -Clutter |
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Graphs used for categorical data
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Pie chart
Bar graph Pictogram |
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Graphs for ratio data
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Histograms
Stem-and-leaf plots Line graphs Scatterplots |
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Pie chart
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Shows the percentage of cases in each category
-usually display 1 categorical variable |
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Bar graphs
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Also show the percentage of cases in each category, but can show more than 1 variable
-height of bar=percentage of cases in each category -sometimes designed to show percentages within a given category as well (all bars same height, split into 2 different categories) |
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Pictogram
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Like a bar chart, but uses a picture instead of a bar
-used in magazine articles, can be misleading |
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Why can pictograms be misleading?
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-should be avoided b/c they can be confusing
-height of bars represents value, but eye can be fooled into thinking area of figure represents the relevant value -can be hard to read |
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Line graphs
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Display lines indicating changes over time
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Scatter plots
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Display the relationship of 2 measurement variables
-show one "dot" for each pair of values for the 2 measurement variables |
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Well designed pictures
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-data should stand out clearly
-clear labeling: tile, source of data, axes or categories |
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Deterministic relationships
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1 variable perfectly predicts another
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Statistical (probabilistic) relationships
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There is a relationship but it is not precise
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Correlation
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positive, negative, no relationship
-express relationships with a single # |
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Correlation coefficient (Pearson Product-Moment correlation)
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Measures strength of relationship between 2 measurement variables
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Pearson product-moment correlation
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Range between -1 and 1
-correlation of 1= perfect linear relationships -0= no linear relationship |
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Correlation coefficient
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Calculated based on the formula for z-scores
r=EZxZy/n |
