Term
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Definition
| a statistical technique that is used to measure and describe a linear relationship between two variables. It shows 3 characteristics of the relationship: direction (+ or -), form (linear or non-linear), and degree (from +1.0 to -1.0). |
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Term
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Definition
| most common correlation; measures the degree and direction of linear relationship between 2 variables; requires interval or ratio data sets |
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Term
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Definition
- used when both variables are on ordinal scales
- used for determining consistent but non-linear relationship
- still tells strength and direction
of relationship
- calculated just like Pearson but
with the ranks of data |
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Term
| Point-biserial Correlation |
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Definition
- 1st variable is interval or ratio
- 2nd variable is dichotomous; assign 0 and 1 to represent
ex. male vs female; repub. vs. dem.
- calculate as Pearson r |
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Term
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Definition
| consist of a series of ordered categories that are all intervals of exactly the same size. With an interval scale, equal differences between numbers on the scale reflect equal differences in magnitude. However, ratios of magnitudes are not meaningful. |
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Term
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Definition
| an interval scale with the additional feature of an absolute zero point. With a ratio scale, ratios of numbers do reflect ratios of magnitude. |
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Term
| How is Pearson's r related to z scores? |
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Definition
The Pearson correlation measures the relationship between an individual's location in the X distribution and his or her location in the Y distribution. Z scores provide a precise way to identify the location of an individual score within a distribution. Because the Pearson correlation measures the relationship between specific locations (z scores) the Pearson formula can be expressed in terms of z scores:
r = sigma zxzy / n |
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Term
| coefficient of determination, r^2 |
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Definition
- introduced as effect size for ANOVAs
- now it is a proportion of variability in data explained by relationship between x and y
- used for prediction
- measure of the gain in accuracy
obtained from using correlation to
predict x from y |
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Term
| Interpretation of Pearson's r |
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Definition
- no causation
- outliers: extreme points influence correlation
- be mindful of restricted range
- sample scores may not include
extremes and can only comment on
correlation of sample scores
- make sure to get wide range of data
in sample |
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Term
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Definition
| predict an unknown value of X from a known value of Y or the converse |
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Term
| What’s linear regression used for? |
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Definition
- Predicting X from Y or converse (Y from X)
- Validating new measurement tools
- Check instrument reliability
- Hypothesis Testing
Ex: New SAT |
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Term
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Definition
| each individual is represented by a point so that the horizontal position corresponds to the independent variable and the vertical position is the dependent |
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Term
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Definition
| This is used when the values on the horizontal axis are measured on an interval or ratio scale. The points are connected by a straight lines. |
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Term
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Definition
| an individual with an X and/or Y values that are substantially different from the values obtained for the other individuals in the data set |
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Term
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Definition
| whenever a correlation is computed from scores that do not represent the full range of possible values, you should be cautious in interpreting the correlation. the correlation within the restricted range (ex. sample of fellow college students to test relationship between IQ and creativity - IQs are going to be unvaried) could be completely different from the correlation that would be obtained from a full range of scores. |
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Term
| What is the difference between p and r? |
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Definition
| p represents the population correlation and r represents the sample correlation. |
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Term
| Hypotheses for Pearson HT |
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Definition
H0: ρ = 0:
There is no correlation between variables X and Y in the population
H1: ρ ≠ 0:
There is a real correlation between
variables X and Y in the population |
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Term
| What are the hypotheses for a one-tailed correlation hypothesis test? |
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Definition
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Term
| What is represented in the numerator and in the denominator of the Pearson r formula? |
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Definition
numerator: the degree to which X and Y vary together (covariability of X and Y)
denominator: the degree to which X and Y vary separately (variability of X and Y separately) |
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Term
| Sum of the Products of Deviations |
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Definition
measures amount covariability of 2 variables
numerator in r |
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Term
| r^2 values (small, medium and large effect) |
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Definition
small = .01
medium = .09
large = .25 |
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Term
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Definition
| The variable in a study that is expected to change as a result of alteration of the independent variable. The dependent variable is NOT manipulated by the experimenter. It is the measured variable. For example, how does one react to questions (dependent variable) when hungry, distracted by music, with aircraft passing over (all independent variables). |
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Term
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Definition
| The variable that is manipulated by the experimenter. By attempting to isolate all other factors, one can determine the influence of the independent variable on the dependent variable. For example: What is the influence of brightness of light (independent variable) on whether people read billboard text (dependent variable)? In this example, the experimenter would vary the brightness of the light and measure recollection on text. |
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