Term
| why use multivariate stats? |
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Definition
1 - evaluate complex causal models with more than 1 independent variable
2 - control for internal validity |
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Term
| Three criteria for causal inference using statistical control |
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Definition
Temporal Order
Covariation (established in bivariate analysis)
Internal validity (using multivariate) |
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Term
| Two major methods of control in statistical analysis |
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Definition
Physical - examine relationship in subgroups using multiple contingency tables
Statistical - use procedures that estimate results we would get using physical control |
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Term
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Definition
Zero-order partial gamma - gamma for entire sample
conditional gamma - gamma for a subtable
First order partial gamma - average of all conditional gammas (single value showing the relationship between X and Y across all values of the control variable. |
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Term
| Physical control (strengths and weaknesses) |
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Definition
Strengths
High sensitive to discovering conditional relationships
Only type of control we can use on nominal data
Weaknesses
cannot simultaneously control for many variables because we run out of cases
does not show if it is the spurious model or intervening model that is causes no relationship to appear. |
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Term
| Stat control - using multiple regression and partial correlation |
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Definition
multiple correlation coefficient (r)
multiple coefficient of determination (r^2)
Partial correlation coefficient
Partial CoD
Partial Slopes |
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Term
| Assessing multivariate models |
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Definition
Multiple CC (r)- 0-1, measures goodness of fit
Multiple CoD (r^2) - proportion of variation in Y explained by all independent variables |
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Term
| using partials to control for extraneous variables |
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Definition
Partial slopes or partial CC's
Zero order - controls for 0
First order - controls for 1
Second order - controls for 2 |
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Term
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Definition
Y = a + b1X1 + b2X2 + e
tells us whether a relationship exists controlling for the other variables in the equation.
If there is a relationship, it also tells us the direction. |
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Term
| Two types of partial slopes |
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Definition
Raw or unstandardized
Standardized or beta weights |
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Term
| Raw or unstandardized partial slope |
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Definition
change in Y produced by a one unit change in X controlling for the other independent variables in equation.
If 0, no relationship
If non-zero, use test of significance
cannot be used to determine which variable has the greatest effect on Y because it is sensitive to the amount of variation |
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Term
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Definition
Partial correlation coefficients
Gives a single measure to the degree of relationship between the two variables controlling for one or more other variables.
-1 to 1
1 is perfect, 0 is no relationship
Partial coefficient of determination
0 - 1
the proportion of the variation in the dependent variable that cannot be explained by the control variables but can be explained by the adjusted scores of the independent variable |
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Term
| Average Zero Order Correlation |
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Definition
| Partial correlation is the average of the zero order correlations produced when the sample is divided into homogeneous subsets based on the control variable (X2) and the zero order partial correlation is then calculated for each subset |
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Term
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Definition
| Partial correlation between X1 and Y is the zero order correlation between the residuals from the regression of Y on X2 and the residuals from the regression of X1 on X2 |
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Term
| Strength and weaknesses of statistical control |
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Definition
STRENGTHS
can control for numerous variables simultaneously
get a single summary measure indicating strength of relationship across all categories of the control variables
WEAKNESSES
no empirical solution to the choice between spurious and intervening models
insensitive to conditional relationships
multi-colinearity |
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Term
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Definition
Descriptive measures in sample = statistics (xbar, s, r, etc.) univariate, bivariate, multivariate
Descriptive measures in population are parameters (mue, rho) |
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Term
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Definition
generalizing from the statistics to the parameters
you can infer that your sample stats do or do not apply to the population.
you might be wrong, but we measure the risk you have of being wrong. |
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Term
| General Statistical Test Steps |
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Definition
formulate hypothesis
carry out project and calculate appropriate measure of association
calculate probability of obtaining a measure of association at least this large between our variables when there is no such relationship in the population
decide whether or not observed relationship applies to population or not. |
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Term
| Formal Steps in modern statistical test |
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Definition
1. formulate research hypothesis - always use specific parameters (H1)
2. formulate Null hypothesis - that the research hypothesis is wrong. includes ALL logical outcomes besides H1 (this is H0)- we directly test the null, and the infer that we accept or reject the H1.
3. calc probability of getting observed sample stat assuming H0 is true.
4. decide -
if prob is below .05 we reject h0 (accept h1)
if prob is above .05 we accept h0 (reject h1) |
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Term
| Formal steps in classical statistical test |
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Definition
1. formulate research hyp.
2. formulate null hyp.
3. calculate sampling distribution or samp dist of a test stat (actually never do this, just know what it would look like)
4. select significance level or rejection region(s)
5. compute sample stat or test stat and decide on null and infer on research hyp. |
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Term
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Definition
rejecting a true null hypothesis
probability of a type 1 error happening is our level of significance
if it is .05, than 5 times out of 100 we are wrong |
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Term
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Definition
accepting a false null hypothesis
inversely related to probability of type 1 error.
bigger the sample = weaker the measure of association, therefore weaker the relationships |
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Term
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Definition
Some sample statistics (r) do not have a known sampling dist. thus we use a stat (called an inferential stat) that has a known distribution (t, or f)
mechanics for changing different stats to inferential stats differ, but logic of test is the same. |
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Term
| Use of tests of significance on population? |
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Definition
Critics say - your measure of association for the population occurred by chance (you can give them probability it did...)
- or they say - your population is really just a sample when you take time into account |
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Term
| statistical significance vs substantive significance |
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Definition
stat sig = relatioship is there
sub sig = how important is this relationship? |
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