Statistics & Test Construction

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Cumulative frequency

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Total number observations that fall at or below each score

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Kurtosis

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the relative peakedness of a distribution: more peaked = leptokurtic, more flat = platykurtic

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Skewed distribution

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More than half of the observations fall on one side of distribution: positive = low score, negative = high score

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Measures of central tendency

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mode (Mo), median (Md)
mean (M or X)

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Relationship bet measures of central tendency in skewed distributions

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positively skewed d: mean, greater than median, greater then
mode, negatively skewed d: mode, greater than median, greater than mean

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Measures of variance

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range, variance, standard deviation

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Def: variance

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a measure of variability calculated by dividing the sum of squares: SS / n (population) SS / n-1 (sample)

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Def: standard deviation

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square root of the variance, a measure of variability of scores around the mean: SS / n - then take square root

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Re: Inferential statistics, What is a sample statistic used for?

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To estimate a population parameter

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Sampling error

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Random error responsible for diff bet sample values and population

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Sampling distribution of the mean

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distribution of means obtained if large number of equal-size random samples are drawn from same population

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3 predictions of Central Limit Theorem

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1. as sample size increases, sample distribution of mean approaches normal distribution; 2. mean of sampling distribution of the mean = population mean; 3. SD of sample distribution of the mean = population SD divided by square root of sample size

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Def: Standard error of the mean. What does it measure?

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SD of sampling distribution of the mean; variability due to effects of random error

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What happens to standard error when 1. SD larger & sample size smaller; 2. SD samller & sample size larger

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1. SE larger; 2. SE smaller

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2-tailed vs 1-tailed hypothesis

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2-tailed = nondirectional;1-tailed = directional

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Rejection / critical region

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region of unlikely values; lies in one or both tails of sampling distribution; values occur as a result of sampling error

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retention region

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region of likely values

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What happens to hypotheses if sample statistic is in rejection region

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null hypothesis is rejected; alternate hypothesis is retained

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What happens to hypotheses if sample statistic is in retention region

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null hypothesis is retained; alternate hypothesis is rejected

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Size of rejection region defined by...

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alpha; level of significance; note: alpha = 0.05; means 5% in rejection region

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Type I error

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reject a true null hypothesis

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Type II error

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retain a false null hypothesis

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Statistical "confidence"

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certainty about the decision re: null hypothesis

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Statistical "power"

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ability to reject a false null hypothesis

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Parametric tests

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evaluate hypotheses about population means, variances etc.; e.g. t-test, ANOVA; interval or ratio scale

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non-parametric tests

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evaluate hypotheses about shape of distribution; e.g. Mann-Witney U test, Wilcoxon; ordinal or nominal scale

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degrees of freedom

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N-1 (t-test)
C-1 (chi-square)

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What information do you use to select an inferential statistic?

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scale of measurement; dependent variable; study design

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What statistical test would you use for nominal data?

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single-sample Chi-square; multiple-sample Chi-square

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What statistical test would you use for ordinal data?

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Mann-Witney U-test; Wilcoxon matched pairs test; Kruskal-Wallis test

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What are the non-parametric alternatives to:
1. independent t-test
2. correlated t-test
3. one-way ANOVA

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1. Mann-Witney
2. Wilcoxon
3. Kruskal-Wallis

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What statistical tests would you use for interval and ratio data?

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t-test, ANOVA

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Name types of t-tests

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simple sample; independent samples; (between); correlated samples (within)

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Name types of ANOVA

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one-way;
factorial (2-way, 3-way);randomized block factorial; ANCOVA; repeated measures; mixed (split-plot); MANOVA

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When use one-way ANOVA vs. factorial ANOVA?

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one-way = 1 IV; factorial = 2+ IVs

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What are the Post Hoc tests for ANOVA?

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Scheffe's S test; Tukey's HSD test;Fisher's LSD test

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Which Post Hoc test is least vulnerable to Type I Error, but more vulnerable to Type II error?

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Scheffe's; Tukey's

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Which Post Hoc test is least vulnerable to Type II Error, but more vulnerable to Type I error?

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Fisher's

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The numerator of the f-ratio is a measure of variablity due to...?

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treatment effects & error

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In ANOVA, the "mean square within" provides info about:

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sampling fluctuations

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Why use one-way ANOVA instead of seperate t-tests?

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To reduce Type I error rate

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How do you calculate f-ratio?

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MSB/MSW

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The f ratio is expected to be near

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1

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How do you calculate MSB?

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SSB/df

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How do you calculate MSW?

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SSW/df

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When & why to use MANOVA

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1+ IV;2+ DV (interval/ratio); *helps increase statistical power by assessing effects of IV on all DVs

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Ex: planned "a priori" analysis (4)

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Dunn-Bonferroni; t linear contrasts; orthogonal comparisons; trend analysis

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Axis on scattergram

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X = IV = predictor; Y = DV = criterion

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Which correlation coefficient is most commonly used with...1. interval and ratio data; 2. rank data; 3. nominal data

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1. Pearson r (also Eta); 2. Spearman rank; 3. Contingency (C)

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How do you translate correlation coefficient score into something meaninful?

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calculate coefficient of determination to provide a measure of shared (explained) variability.
- square the coefficient: e.g. if coefficient is .60, .60 x .60 = .36, .36 x 100 = 36%; therefore, 36% of scores on DV explained by IV... remaining 64% is unexplained variance.

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When & why use: regression analysis

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to predict a score on a criterion (DV) based on person's obtained score on predictor (IV)

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How do you locate a regression line?

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least squares criterion

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When and wy use: multiple regression

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2+ continuous or discrete predictors; 1 criterion

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Ex: multiple regression

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1. simultaneous (simple); 2. stepwise; 3. hierarchical

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When use multiple regression instead of ANOVA?

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If groups are unequal in size; if IVs on a continuous scale

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When & why use: canonical correlation

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[an extension of mult reg]; 2+ continuous predictors; 2+ continuous criterions

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Ex: multivariate techniques (4)

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multiple regression,
canonical correlation, discriminant function analysis, logistic regression

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Ex: bivariate correlational techniques (2)

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scattergram, correlation coefficient

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Ex: bivariate prediction (1)

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regression analysis

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Ex: multivariate techniques (2)

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path analysis; LISREL

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Ex: correlation & prediction tehcniques (4 main)

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bivariate correlational techniques; bivariate prediction; multivariate techniques: correlation & prediction; multivariate techniques: causal modeling

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When and why use: discriminant function analysis

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2+ continuous predictors; 1 discrete criterion