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7 Cards in this Set
- Front
- Back
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WHat are the sources of variance that go into the numerator and the denominator of the f-stat?
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F = treatment effects + individual differences + experimental error------
individual differences + experimental error the only difference between the numerator and the denominator is the presence of treatment effects in the numerator |
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F stat equation
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• So, the only difference between the numerator and the denominator is the presence of treatment effects in the numerator
• If the treatment effect is large, F will be large. • If there is no treatment effect (treatment effect = 0) the F-ratio will be close to 1.0 • The denominator of the F-ratio only has unsystematic sources of variation, and is therefore often referred to as the error term • If the null hypothesis is true, then both the numerator and denominator measure the same thing – unsystematic error due to sampling error |
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What does the f-distribution look like? What should the value of F be if the null hypothesis is true?
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• Because the F-ratio is the ratio of two variance (and variance is always positive), the F-ratio will always be positive.
• Under the null hypothesis, the F-ratio should be close to 1. • The F-distribution is always greater than 0, and has a mode at 1. • The exact shape of F depends on the df. df for the numerator of the F-ratio = dfB dffor the denominator of the F-ratio = dfW • The critical value for F can be found in the F table (to be discussed in class) |
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Regression Equation and what it tells you:
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• Linear Relationships
• Can be expressed by Y = bX +a • “a” is the intercept – the point at which the lines hits the Y-axis on a graph. o When X=0, Y=a or when x=0, y = the intercept. • “b” is the slope – the steepness of the line. Tells you how much Y will change when X increases by 1 unit • The equation for a line, however, does not address the data scattered around the line. Regression, allows us to draw the best fitting line through the data keeping that “error” in mind. |
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•Four types of scales
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•Nominal -- includes labels or categories; no size or magnitude information
•Ordinal -- includes ranking information; ordered by magnitude •Interval -- equal intervals between numbers reflect equal differences in magnitude; no absolute zero •Ratio -- like interval scales, but there IS an absolute zero. |
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•Discrete vs. Continuous Variables
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•Discrete -- implies that the numbers are separate, individual, indivisible categories.
•Continuous -- continuous scales are not limited to a fixed set of categories. **Real Limits for continuous variables: for a continuous variable, each score really corresponds to an interval on a scale. The boundaries that separate the intervals are called the real limits. The real limits are located exactly half-way between the scores. The upper real limit is half way above the score, and the lower real limit is half way below the score. |
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oSkewness
oKurtosis |
oSkewness – the degree to which the distribution departs from being symmetrical
Positively skewed – tail extends in the positive direction Negatively skewed—tail extends in the negative direction Kurtosis – the degree to which a distribution is pointy or flat and spread out. Leptokurtic-- pointy Platykurtic – flat and spread out |
