Stats, Research Design, Test Construction Flashcards
(37 cards)
Most effective form of counterbalancing?
Latin Square
idiographic and nomothetic
idiographic = single subject research designs
nomothetic = multiple subjects
Group Designs/Single Subject Designs/Behavioural Measurement
Group Designs
-between groups
-within subjects
-mixed designs
Single Subject Designs
-AB
-ABAB
-Multiple Baseline Design: across subjects, situations, and behaviours
-Simultaneous (alternating) treatment design
-changing criterion design
Behavioural Measurement
-time sampling: momentary time sampling, whole-interval sampling, event recording
Conditions of Experimentation
-analogue research
-clinical trials
Time Frame
-cross-sectional
-longitudinal
-cross-sequential
Sampling Procedures
-simple random sampling
-stratified random sampling
-proportional sampling
-systematic sampling
-cluster sampling
Threats to Internal Validity (8)
-factors other than the IV that may have caused change in the DV
-history - best control = control group
-maturation - best control = control group
-testing or test practice - best control = Solomon Four-Group Design
-instrumentation - best control = control group
-statistical regression - best control = control group
-selection bias - best avoided by random assignment
-attrition or experimental mortality - to assess - those who drop out should be compared on relevant variables via t-tests
-diffusion - best control = tight control of experimental situation
Threats to Construct Validity (4)
-factors other than the desired specifics of our intervention that result in differences (intervention-related)
-attention and contact with clients
-experimenter expectancies aka Rosenthal effect - keep experimenter blind
-demand characteristics - keep subj blind to tx condition
-John Henry effect - aka compensatory rivalry - groups not know about each other or given any sense of competition
Threats to External Validity (3)
-factors that interfere with generalizability
-sample characteristics
-stimulus characteristics
-contextual characteristics - reactivity –> Hawthorne effect
Threats to Statistical Conclusion Validity (4)
-low power
-unreliability of measures
-variability in procedures
-subject heterogeneity
Descriptive Stats
- Group Data
A. Measures of Central Tendency
-mean, median, mode
B. Measures of Variability
-SD, variance, range
C. Graphs - Individual Scores
A. Raw Scores
-percentage correct is a criterion-referenced or domain-referenced score
B. Percentile Ranks
-norm-referenced score
C. Standard Scores
-Z score formula = score - mean / SD
-raw score formula = mean +/- Z-Score (SD)
Descriptive Stats
- Group Data
A. Measures of Central Tendency
-mean, median, mode
B. Measures of Variability
-SD, variance, range
C. Graphs - Individual Scores
A. Raw Scores
-percentage correct is a criterion-referenced or domain-referenced score
B. Percentile Ranks
-norm-referenced score
C. Standard Scores
-Z score formula = score - mean / SD
-raw score formula = mean +/- Z-Score (SD)
Inferential Stats
Parameters = population values- mu is pop mean and sigma is pop SD
Standard Error of the Mean
-average amount of deviation in means across many samples
-standard error = SDpop / square root of N (pop size)
Hypothesis Testing
A. Key Concepts
-null hypothesis
-alternative hypothesis
-rejection region aka rejection of unlikely values (tail end of curve) - size of rejection region = alpha
-acceptance or retention region
Correct and Incorrect Decisions
-type 1 error - size of alpha corresponds to this (incorrectly reject null)
-type 2 error - probability of making type 2 error corresponds to beta (incorrectly accepting the null)
-power - ability to correctly reject the null - increased when sample size is large, magnitude of intervention is large, random error is small, stat test is parametric, test is one-tailed; power = 1 - beta; as alpha increases so does beta
Selecting Stastistical Tests
Three questions commonly asked:
-questions of difference –> analyzed with Chi-square, Mann-Whitney, t-test, ANOVA etc
-questions of relationship and prediction –> analyzed with Pearson r, Biserial, multiple regression, etc.
-questions of structure or fit –> analyzed with principal components or factor analysis, cluster analysis
Tests of Difference
Type of Data of the DV
-if Nominal or Ordinal: non-parametric like chi-square, mann-whitney, wilcoxon
-if Interval or Ratio: parametric like t-test and ANOVA
-if more than one DV: MANOVA
-# and levels of the IV
-sample independence or correlation
-assumptions for parametric: interval or or ratio data; homoescedasticity; normal distribution of data
-assumption for chi-square: independence of observations
Nominal Data = chi square or multiple sample chi square (more than 1 IV); McNemar if groups correlated
Interval/Ratio and Ordinal
-more than one DV ALWAYS equals MANOVA
-one group = single-sample t-test (I/R) or Kolmogoroc (Ordinal)
-one IV, two groups = independent t-test either independent or matched samples
-more than two groups = ANOVA
-one way ANOVA = one IV; two-way = 2 IV etc - independent data
-2-way ANOVA AKA factorial ANOVA
-mixed or split plot ANOVA = one independent groups IV and one correlated groups IV
-2 IVS both correlated = rm factorial ANOVA
-2 IVS one is blocked = blocked ANOVA
-covariate - a variable that you weren’t interested in that is affecting the outcome - ANCOVA helps to take out that variable
Tests of Difference: Degrees of Freedom
Single Sample Chi-Square
-nominal data collected for one IV
-df = #groups - 1
Multiple Sample Chi Square
-nominal data collected for two IVs
-df = (#rows - 1) x (#columns - 1)
T-Test for Single Sample
-df = N-1
T-Test for Matched or Correlated Samples
-df = #pairs - 1
T-Test for Independent Samples
-df = N-2
One-Way ANOVAs
-three possible DF: DFtotal; DFbetween; DFwithin
-DF total = N - 1
-DF between = #groups - 1
-DF within = DFtotal - DFbetween
Tests of Difference: Calculating Expected Frequencies in a Chi Square
-in chi-square, eg democrat repub, male female - score for each category = obtained frequencies
-are there sig differences between men and women in voting preference for democrats and republicans? chi-square
-calculate expected frequency - 2 scenarios when need to do this: 1) survey 200 people as to voting preference and gender. Expected frequency = 50 per cell. Total number of people / number of cells
2) where data is given in the cells - sum the row and column separately, multiply by one another, divide by sample size
Tests of Difference: Interpreting ANOVAs
One-Way ANOVAS
-one IV three groups or more
-ANOVA over multiple individual t-tests because the latter increases likelihood of type 1 error with every test run
-F-Ratio = ratio of MSbg/MSwg
-MS = variability
-BG = between groups
-WG = within groups
-variability WITHIN groups = error
-variabilitiy BETWEEN groups = good
wants BG high and WG lowe
-when F ratio is about 1, this is bad news, not significant - differences between group same as within all we have is error. As F ratio climbs to 2 or greater, then you have significance
-Post Hoc: pair-wise comparisons. Post-Hoc most conservative are Scheffe and Tukey - protect you from Type 1 errors (but increase chance Type 2 errors). Fischer’s LSD least protection from Type 1
Two-Way ANOVAs
-allow for main effects and interaction effects
-3 F ratios: one for each IV, one for the interaction
-if multiple things significant, must first interpret reaction effects then interpret main effects in light of interaction effects
-calculating main effects and interaction see p.35
MANOVAs
-more than one DV
-advantage = protects from type 1 error
Trend Analysis
-extension of an ANOVA
-when ANOVA significant may want to run trend analysis if IV has some kind of quantity e.g., dose of drug - tells you the patterns - e.g., curvilinear?
Tests of Relationship and Prediction
Bivariate Tests
-look at relationship between two variables only- X and Y
-correlation coefficient - X predictor Y criterion - ranges from -1 to +1
-coefficient of determination - always associated with the correlation; the square of the correlation; represents the amount of variability in Y that is accounted for or explained by X
Simple Linear Regression Equation
-when there is a correlation, there is the implication of a prediction - regression equation is the line of best fit aka the line that fits best through your scatter plot. it is done by the least squares criterion
-regression: y = a + b(x) - a = intercept b = slope
Assumption of Bivariate Correlations
1) linear relationship between X and Y
2) homoscedasticity
3) unrestricted range of scores between X and Y - if you restrict range you reduce your variability
Bivariate Correlation Coefficients
I/R + I/R = Pearson R
Ordinal + Ordinal = Spearman’s Rho or Kendall’s Tau
I/R + nominal dichotomous = biserial (artificial dichotomy) or point-biserial (true dichotomy naturally occurring men women)
true dichotomy + true dichotomy = phi
artificial dichotomy + artificial dichotomy = tetrachoric
Curvilenar relationship = Eta
Bivariate: Types of Correlations and Variables
Zero-Order Correlation
-most basic correlation
-X and Y - believed that there are no extraneous variables
Partial Correlation (First Order Correlation)
-effect of a third variable (Z) is removed
-third variable is removed because it is thought to be influencing or confounding both the predictor and the criterion
Part (Semipartial) Correlation
-remove effect of Z from only X or only Y but not both
Moderator Variable
-a third variable that influences the strength of the relationship between the predictor and the criterion
-sometimes a correlation is stronger at certain points in the scatter plot and weaker at others
Mediator Variable
-explains why there is a relationship between predictor and criterion
-when you take our mediator you often no longer have sig relationship
Multivariate Tests
-involve several Xs and one or more Ys
Multiple R
-big cousin of little Pearson r
-correlation between two more Xs and single Y
-Y is always I/R at least one X is I/R
-squaring multiple R gives the coefficient of multiple determination
Multiple Regression
-uses multiple R- allows the prediction of the criterion (Y) based on the values of the predictors (C)
-multiple regression equation: Y = a + b1x1 + b2x2 + b3x3 etc
-to optimize ability to predict- desirable to have low correlation between predictors and moderate-high correlation between each predictor and criterion
-multicollinearity: when predictors are highly correlated with each other and are thus essentially redundant
-compensatory technique
-stepwise regression: computer-generated re: ordering of variables based on how strongly they are related to criterion. Can be backward or forward. forward is adding one at a time starting with strongest. Backward is removing one at a time starting with weakest. allows researcher to come up with fewest possible predictors
-hierarchical regression: researcher controls the analysis, adding variables to the regression analysis in the order that is most consistent with proposed theory
Canonical R and Canonical Analyses
-2 more Xs AND 2 or more Ys
-allows you to evaluate the relationship between two sets of variables- a predictor set and a criterion set
-Canonical R = the relationship; Canonical Analyses = the prediction
Discriminant Function Analysis
-no correlation- just predicting
-special case of multiple regression equation
-Y is nominal data NOT interval/ratio
-allows a researcher to predict membership in a group based on knowledge of a set of predictor variables
Loglinear Analysis
-used to predict a categorical criterion (Y) but our Xs are also nominal
Path Analysis
-applies multiple regression techniques to testing a model that specifies CAUSAL links among variables (versus correlation can’t speak to causation)
-depends on a researcher having already developed a clearly articulated causal model that rests on a strong theoretical or empirical base
-straight arrows denote causal relationships and are called paths
-variables are described as exogenous or endogenous
-models can be recursive or non-recursive
-estimates of the causal relationships among variables are called path coefficients and are determined by multiple regression equations
-path coefficients are analyzed to see if the pattern predicted by the model has emerged
Structural Equation Modelling
-enables researchers to make inferences about causation
-can be used to test many different causal pathways that involve multiple predictors and criterion variables
-LISREL = linear structural relations - makes distinctions between independent and dependent variables in addition to latent and manifest variables. looks at direct and indirect effects and unidirectional and bi-directional paths
Tests of Structure
-used when the researcher is interested in discovering which variables in the set fit best together or form coherent subsets that are relatively independent of one another
-eg., factor analysis of WAIS subtests
Factor Analysis
-used to reduce a large number of variables into a smaller number of factors
-extracts as many significant factors from the data as possible
-a factor = a dimension that consists of any number of variables
-first factor is always the strongest
-Eigenvalues = tells you the strength of the factor. aka characteristic root. Eigenvalues less than one usually not interpreted or considered significant
-Correlation Matrix = table of intercorrelations among tests of items
-Factor Loadings = determine which variables constitute a common factor. correlations between a variable and the underlying factor. interpreted if they are equal to or exceed plus or minus .30
-Factor rotation - makes the factors distinct and easier to interpret
-Orthogonal Rotations and Communality - results in factors that have no correlation with one another. Communality = how much of a test’s variability is explained by the combo of all the factors
-Oblique Rotations - factors are correlated
-Principal Components Analysis - no empirical or theoretical guidance on the values of communalities. components = uncorrelated factors. Factors are empirically derived - no prior hypotheses
-Principal Factor Analysis - communality values ascertained before the analysis
Cluster Analysis
-involves gathering data on a variety of dependent variables and statistically looking for naturally occurring subgroups in the data
-no a priori hypotheses
-e.g., MMPI-2 for police officers into 3 profile groups
Test Construction: Reliability
Reliability = consistency in measurement
Classical Test Theory (The True Score Model)
-any obtained score is a combination of truth and error: X = T + E
-Total variability = true score variability + error variability
-Reliability is the proportion of true score variability
-Reliability coefficient is either rxx or rtt
-Minimum acceptable reliability = .80
-common sources of error: content sampling, time sampling, test heterogeneity