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53 Cards in this Set
- Front
- Back
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Binomial Distribution rules |
1. N trials 2. Only 2 possible outcomes 3. mutually exclusive 4. independence between the outcomes of each trial 5. probability stays the same from trial to trial
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Binomial Expansion |
P2 + 2P1Q1+Q2 Exponent = number of times that term is used in the outcome Number in the front = number of possible outcomes with those combinations. |
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Binomial table |
pre-solved binomial expansion for many values of N |
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Normal approximation approach |
As N increases the binomial distribution becomes more normally shaped (eventually we can use z scores b/c it is normal enough) Rules: 1. mean =NP 2. Standard deviation = Square root of NPQ. |
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Alternative Hypothesis (H1) |
the one that claims the difference in results between conditions is due to the independent variable (directional or non-direcitonal) |
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Null Hypothesis (Ho) |
If the null is false, the alternative must be true. (mutually exclusive and exhaustive.) For non-directional the null says the IV has no effect. For directional (it either has no effect or different direction.) |
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Results are not significant when |
... we fail to reject the Ho.
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Type I error |
a rejection of the null when it is true |
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Type II error |
when we retain Ho and it is false. |
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Beta |
Probability of making a type II error |
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Alpha |
Have to choose it ourselves, but if its too low = increases chance of making a Type II error. If experiment is for exploratory stuff use higher alpha levels (.10 or .20) if experiement is to communicate new facts to the scientific community use conservative levels (.o5 or .01) |
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Tails |
If H1 is nondirec. we evaluate the obtained result or any even more extreme in both directions (2 tails) if H1 is directional we evaluate only the tail of the distribution that is in the direction specified by the Hypothesis. |
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Tailed probability evaluations |
Evaluations should always be two-tailed unless the experimenter will retain Ho when results are extreme in the direction opposite to the predicted direction. |
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Significant |
The results are probably not due to chance - statistically significant (reject the null). |
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Practically/theoretically important |
increases with the size of the effect. |
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Repeated Measure Design |
Measure the same thing twice for the same people (ie... once in 2000 and once in 2010). |
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Correlation |
concerned with finding out whether a relationship exists and its degree/magnitude (o-1) and direction (+or-) |
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Regression |
concerned with using the relationship for prediction |
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Why are correlational studies/techniques important? |
1. one factor may cause the other 2. allow us to measure "test-retest reliability" (how correlated are the scores from the two different administrations of the test. |
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Scatter plot |
a graph of paired X and Y values |
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Linear relationship |
can be most accurately represented by a straight line. |
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Positive v. negative relationships |
Positive: as x increases, y increases; direct relationship. Negative: as x decreases y increases (or vice versa); inverse relationship. |
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Perfect v. Imperfect Relationships |
Perfect: a positive or negative relationship exists and all of the points fall on the line. Imperfect: a relationship exists but the points do not all fall on the line. |
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Regression line |
Line that best fits the data and can be used for prediction. |
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Correlation coefficient |
expresses quantitatively the magnitude/direction of the correlational relationship (vary between -1 and 1) 0 = no correlation |
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Pearson r |
measure of the extent to which paired scores occupy the same or opposite positions within their own distributions. Allows you to compare scores that were measured in different units (ie: weight and cost) if the relationship is perfect their pearson r scores will be the same (same position in their distributions. |
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Pearson r (2nd interpretation) |
r = the squre root of the proportion of the variablitity of Y accounted for by X. |
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r2 |
Coefficient of determination: Proportion of the total variability of Y that is accounted for by x |
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Shape of the relationship |
linear/curvilinear (if linear use pearson R, if curvilinear use eta) |
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Measuring Scale |
Pearson r uses interval or ratio - but other coefficients are used for ordinal, etc scaling. |
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Spearman rank order correlation coefficient Rho |
used when one or both of the variables are only of ordinal scaling (correlation between ranks) |
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Effect of Range on Correlation |
restricting the rang of either of the variables will have the effect of lowering the correlation. |
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Effect of Extreme scores: |
An extreme score can drastically alter the magnitude of the correlation coefficient (smaller the sample = larger the effect. |
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Correlation does not imply causation |
4 options for correlation: 1. correlation between x and y is spurious (by chance) 2. x is the cause of y 3. y is the cause of x 4. a third variable is the cause of the correlation between x and y. |
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Least-squares regression line |
line that minimizes errors of prediction according to a least-squares criterion. (E(Y - Y')^2) |
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Y v. x variables |
Generally label the variable to which we are predicting as the Y variable and the variable we are predicting from as the X variable. |
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Standard Error of the estimate |
acts as a measure of the average deviation of the prediction errors about the regression line. (average for how likely the prediction is to be wrong.) (for each x value) |
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assumption of homoscedasticity |
to be meaningful we must assume that the variability of Y remains constant as we go from one x score to the next. |
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3 main assumptions when using linear regression for prediction |
1. relationship b/w x and y must be linear 2. basic computation group must be representative of the prediction group 3. the linear regression equation is properly used just for the range of variables on which it is based.
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Pearson r |
is the slope of the least-squares regression line when the scores are plotted as z scores. |
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Multiple regression |
an extension of simple regression to situations that involve two or more predictor variables. |
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Descriptive statistics |
focused on presenting and describing sets of scores in the most meaningful/efficient way |
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Inferential statistics |
use the sample scores to make a statement about a characteristic of the population |
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Hypothesis testing |
the experimenter is collecting data in an experiment on a sample set of subjects in an attempt to validate some hypothesis involving a population |
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Parameter estimation experiments |
experimenter is interested in determining the magnitude of a population characteristic |
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Random Sample |
a sample selected from the population by a process that ensures that: 1. each possible sample of a given size has an equal chance of being selected. 2. all the members of the population have an equal chance of being selected into sample. |
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Why is random sampling important? |
1. generalize from a sample to a population it is necessary to apply the laws of probablitiy to the sample. 2. to generalize from a sample to a population it is necessary that the sample be representative of the population |
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sampling with or without replacement |
whether or not people/things can be included more than once. |
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a priori |
classical viewpoint (deduce from reason alone). P(A) = Number of events classifiable as A/Total number of possible events |
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a posteriori |
After the fact, after actually testing it (actually rolling the die) empirical, comes from experience. Number of times it has occurred/ total numbers of occurrences. |
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Probability of 1 v. oo |
1 = the event will occur 0 = the event will not occur |
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addition rule |
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Multiplication rule |
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