Statistics

Front 1

What is the difference between parametric and nonparametric tests?

Back 1

Parametric tests require interval level measurement, normality, and equal variance

Front 2

Chi-Square - Research question

Back 2

Do observed frequencies systematically differ from expected frequencies? If yes, significant.

Front 3

Chi-Square uses what level of measurement?

Back 3

Non-interval.

IV's involve discrete categories
DV is in the form of frequencies, proportions, probabilities, or percentages

Front 4

One-way Chi-Square: null

Back 4

observed distribution of frequencies = expected distribution of frequencies

Front 5

One-way Chi-Square: assumptions

Back 5

each observation falls into only one cell
observations independent
expect frequency for each category is not less than 5 (df >2) or 10 (df = 1)

Front 6

Two-way Chi Square: purpose

Back 6

Used when we have two IVs, determine whether the IVs are independent of one another

Front 7

Two-way Chi Square: null

Back 7

variables are independent in populations

Front 8

Two-way Chi Square: assumptions

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o Each observation falls into one cell
o Observations independent
o Expected frequency for each cell is not less than 5 (df > 2) or less than 10 (df = 1)

Front 9

Fisher’s Exact Test

Back 9

Given the marginal values (holding constant) how unusual are values in table? Can compute probability (what % of the time) of producing variables in matrix.

Front 10

McNemar's Test

Back 10

nominal data, repeated measures. 2x2 contingency table. Determines whether the proportion of “success” changes over time. Ignores diagonal, looks across cells that indicate change, one-way chi-square. Are row and column frequencies equal?

Front 11

Kappa

Back 11

measure of agreement among judges. What proportion of time do judges agree? Takes into account frequency due to chance. Assumes mutually exclusive, categorical data (judges put people into categories) Diagonal = judges see applicants exactly the same way.

Front 12

Correlation: basic definition

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Class of statistics, measure relationship between variables. All range from -1.0 to +1.0. Df = n-2

Front 13

Correlation: purpose

Back 13

explain variance, predict score.

Front 14

Correlation vs. covariance

Back 14

Covariance is the index of the tendency for two variables to covary together measured in original units. Difficult to interpret.

Correlation is measured in standardized units so variables are on the same scale.

Front 15

Correlation: null hypothesis

Back 15

ρ(xy) = 0 (correlation in population = 0)

Front 16

Non Nil Null

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ρxy ≠ 0

When ρ assumed to be zero, have normal distribution. Correlation can’t go beyond one. Shift ρ, sampling distribution becomes skewed, non-normal.

Front 17

Fisher's Z

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Covert r to z scores. Distributed as z, compare to critical z value.
Use when:
testing non nil null
Comparing two observed correlations
Averaging correlations

Front 18

When will correlation be maximum?

Back 18

Correlation will be maximum when both x and y are normally distributed and range is not restricted.

Front 19

Correlation types: Pearson's r/Pearson's product moment correlation

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2 continuous interval level variables, assume independent, normally distributed

Front 20

Correlation types: Point Biserial r

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(true) dichotomous variable x interval variable

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Correlation types: Biserial r

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artificial dichotomous variable x interval variable

Front 22

Correlation types: Phi coefficient

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two truly dichotomous variables

Front 23

Correlation types: Spearman's rank order correlation/rho

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two ordinal variables, compare ranks on each variable for each case, to the degree that the ranks are different, move away from 1.0.

Front 24

Correlation types: Tetrachoric correlations

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two dichotomous variables, at least one artificial

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Correlation types: polychoric correlation

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more than 2 levels, polytomous variables (i.e. likert scale), treat as ordinal level, but assume underlying distribution normal (measuring a latent interval variable)

Front 26

Correlation types: gamma

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ordinal data, based on concept of concordant and discordant pairs

Front 27

Correlation types: Kendall's tau-b and tau-c

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similar to gamma, but gives discordant pairs more weight

Front 28

Correlation types: Cramer's V

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nominal variables with more than two levels

Front 29

Linear Regression: purpose

Back 29

use relationship to predict one variable from the other
minimize mistakes by finding "line of best fit"

Front 30

Linear Regression: equation of a line

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y = a + bx
a is constant (y-intercept B0)
b is slope (regression weight, B1)

Regress y onto x

Front 31

Linear Regression

Beta Weight

Back 31

β1, regression weight in standardized units

Front 32

Linear Regression

Evaluating Output: R

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correlation between x and y
always positive

Front 33

Linear Regression

Output: R^2

Back 33

percent variance in y that can be explained given x

Front 34

Linear Regression

Output: ANOVA

Back 34

statistical test of model fit, is R different from zero?

Front 35

Linear Regression

Output: t-tests

Back 35

tests if regression weight significantly different from zero

Front 36

Linear Regression

Output: standard error of estimate

Back 36

magnitude of residuals/errors. Large = poor fit. If x and y unrelated, best guess of y is mean of y. On average, will be 1 SD off. As soon as relationship between x and y is not zero, SEy will decrease (estimate becomes more accurate). By using regression equation, how big are the mistakes you are now making? Compared to SDy, how much have you improved?
• Function of correlation and number of cases
• Larger r2 and larger N, smaller standard error

Front 37

Linear Regression

Output: regression outliers

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Misfit, compare observed and predicted y for each case, how close is estimate? Can remove extreme cases from model and identify problematic cases.

Front 38

Linear Regression

Output: Adjusted R^2

Back 38

sample not perfect representation of population, R always inflated, adjusted R^2 takes into account sampling error and amount of predictors, estimates R^2 in population. Always lower than R^2.

Front 39

Linear Regression

Output: Sums of Squares

Back 39

SS total is total variance in system to be explained
SS regression is the variance explained by the regression model
SS residual is whatever variance is left unexplained

Front 40

Linear Regression: assumptions

Back 40

• Homoscedasticity
• Linearity
• Independence
• Normality

Front 41

Homoscedasticity

Back 41

when we run regression, assume standard error constant term up and down regression line, errors don’t vary up and down range of predictions (same accuracy in prediction)
o Violation: at low levels of x, no variability in y, at higher levels, more variability in y

Front 42

Part-whole correlations (item-total correlations)

Back 42

in measurement, frequently correlate item response with total test score. Raw correlation would be problematic. Total score is made up of the item in which you are correlating so you are correlating the item to itself. Overestimating the correlation because correlation with self is 1.0.

Front 43

Regression to the mean

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if a variable is extreme on its first measurement, it will tend to be closer to the average on second measurement. More extreme scores on one variable connected to less extreme scores on another, seen as causal, it’s not. Characteristic associated with less than perfect data/correlation. Only time it would not happen is if correlation is perfect. It is a methodological artifact.

Front 44

Nonparametric Tests: Mann-Whitney U

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Similar to independent samples t-test, treats dependent variable as ordinal. Can’t talk about means.

Front 45

MW-U: null

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distribution of scores in the two populations from which samples were drawn are identical.

Front 46

MW-U: requirements

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1 IV with two levels and case appears in only one group

Front 47

MW-U Rank sums test

Back 47

Compare ranks of scores across 2 independent samples
o Order from lowest to highest, add ranks together
o If null true, rank sum of each group should be equal
Ex. Group 1 = , Group 2 = 35;
o U is defined as the number of Group 2 scores (because ranked higher) preceding each Group 1 score
o What is probability associated with this? Based on all possible orderings.
o Output: < 20 cases, report exact significance, >20 cases, asymp. Significance

Front 48

Wald-Wolfowitz test

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looks for runs in the data. More runs = less significant, less = more likely to be extreme groups

Front 49

Wilcoxon T

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paired (dependent) samples t-test (treats DV as ordinal)

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Wilcoxon T rank sums test

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compute a difference score and rank these differences, evaluate rank sum of positive differences in comparison to rank sum of negative differences. If positive or negative change is equally likely, sums will be close. T is defined as the smaller of the two numbers

Front 51

Wilcoxon T requirements

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one IV with two levels, case appears in both levels

Front 52

Wilcoxon T null

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sum of positive ranks will equal sum of negative ranks.

Front 53

Kruskal-Wallis one-way ANOVA (KWANOVA)

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Direct extension on Mann-Whitney U to cases with > 2 IV groups
Compare rank sums across multiple groups
Test statistic = H, distributed as chi-square

Front 54

KWANOVA null

Back 54

all group rank sums are equal

Front 55

KWANOVA requirements

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one IV with > 2 levels, cases in only one group, minimum number of cases in each group > 6

Front 56

Friedman's test

Back 56

> 2 repeated measures, similar to repeated ANOVA, distributed as chi-square (H)
Compare mean ranks, significant: mean rank across time periods is changing, NOT mean of data.

Front 57

Resampling

Back 57

Interested in comparing two means drawn from populations that are known to be non-normal (shouldn’t be computing a t-test or a correlation)
Test doesn’t exist or we don’t have confidence with necessary assumptions
Need to compute our own distribution

Front 58

Sampling with replacement

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probability of choosing always the same, two sample values independent (what we get one first sample doesn’t effect second sample), covariance = 0

Front 59

Sampling without replacement

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two sample values aren’t independent, covariance > 0

Front 60

Permutation/randomization test

Back 60

treat our data as the population, redistribute observed data without replacement to test hypothesis of no effect. Have two groups, compare after each redistribution, build distribution of a statistic

Null: no difference between groups, drawn from same population

Front 61

Bootstrapping

Back 61

sampling with replacement, what is variability within group, how stable is statistic? Helps establish confidence intervals.

Front 62

Monte Carlo

Back 62

repeated sampling from population, trying to understand how sensitive statistical tests are, i.e. to departures from normality