Statistics: Inferential Stats Concepts and Terms Flashcards
Inferential Statistics: overview
Descriptive stats = summarize data
Inferential Stats = make inferences about a population based on sample drawn from a population
Central Limit Theorem
Distribution approaches a normal curve as sample size increases
The mean of the sampling distribution = pop mean
SD of distribution = Standard Error of the Mean
Type I Error (α)
Rejection of a true null hypothesis
Research erroneously shows significant effects
Type II Error (β)
Retain a false null hypothesis
Research misses actual significant effects
Power (1-β)
Likelihood of rejecting false null hypothesis
Parametric v Nonparametric Tests:
Measurement Scales
Parametric Tests: Interval or Ratio Scales
Non-Parametric Tests: Nominal or Ordinal Scales
Parametric v Nonparametric Tests:
Commonalities and Differences
Both assume random selection and independent observations
Parametric tests (e.g. t-test, ANOVA) evaluate hypotheses about population means, variances, or other parameters.
Parametric Tests:
Assumptions
Normal Distribution
Homoscedasticity
Homoscedasticity
Assumption that variances of populations that groups represent are relatively equal
[For studies with more than one group]
One-way ANOVA vs Factorial ANOVA vs MANOVA
One-way ANOVA: ONE IV, ONE DV
Factorial ANOVA, two-way = 2 IV’s, three-way = 3 IVs
MANOVA: used whenever there is more than one dv
(MULTIvariate analysis)
Effect Size:
What is it?
Name two types
Measure of the practical or clinical significance of statistically significant results
Cohen’s d
Eta squared (η²)
Cohen’s d
Effect size in terms of SD (d = 1.0 = 1SD change)
Small effect size = 0.2
medium effect size = 0.5
large effect size = 0.8
Eta squared (η²)
Effect size in terms of variance accounted for by treatment
*Variance = σ², so think squared greek letter = variance
Bivariate correlation assumptions
Linearity
Unrestricted range of scores on both variables
Homoscedasticity
Bivariate correlation “language” (X, Y)
X = predictor variable
Y = criterion variable
Simple Regression Analysis
Allows predictions to be made with:
One predictor (X) One criterion (Y)
F ratio calculation
MSB/MSW
Mean square between divided by mean square within
F ratio range
F is always greater than +1
Larger F ratio = increased likelihood of stat significance
Statistical Power definition
Degree to which a statistical test is likely to reject a false null hypothesis (1-β)
Reject false null = show statistical significance
Ways to Increase Statistical Power
Increase alpha from .01 to .05
Increase sample size
Increase the effects of the IV
Minimize error
Use one-tailed test when appropriate
Use parametric test
Effects of increasing alpha from .01 to .05
Greater likelihood of rejecting null hypothesis
*Greater likelihood Type I error
Effects of decreasing alpha from .05 to .01
Decreased statistical power
However, increased confidence that statistically significant results are correct
Nonparametric tests and data distribution
Nonparametric only evaluates hypotheses about Shape of distribution
NOT distribution’s mean, variance, or other parameter
Two factors that determine critical value for statistical significance
alpha (e.g. .05)
degrees of freedom
Regression analysis: assumptions
Linear relationship between X and Y
regression line = “line of best fit”
Regression Analysis: coefficient range
-1.0 to +1.0
It’s a correlational technique
Multiple regression
two or more continuous or discrete predictors (X)
one criterion (Y)
Multicollinearity
High correlation between two or more predictors
Makes it difficult to interpret regression coefficients
if correlated, how to know which X accounts for change in Y?
Forward Stepwise Regression
One predictor is added in each subsequent analysis
Backward Stepwise Regression
Analysis begins with all predictors
One predictor is eliminated in each subsequent analysis
When to use Multiple Regression instead of ANOVA
when groups are unequal in size
when IV’s are measured on a continuous scale
Multiple Regression: factors that cause most Shrinkage
small original sample
large number of predictors
*result of cross-validation
Structural Equation Modeling (SEM)
Multivariate techniques
Evaluates the causal (predicted) influences of multiple latent factors
aka “causal modeling”
Structural Equation Modeling: 2 techniques
Path Analysis
LISREL
SEM: Path Analysis
Causal relationships among variables represented in path diagram
Coefficients indicate direction and strength of relationship between pairs of variables
Only recursive (one way)
SEM: LISREL
Linear Structural Relations Analysis
LISREL includes:
recursive (one way) paths
nonrecursive (two way) paths
latent traits
measurement error
Multivariate Techniques for Data Reduction
Factor Analysis
Cluster Analysis
Multivariate Data reduction: Factor analysis
Reduces larger number of variables to a small number of factors
Factors explain inter-correlations between variables
*e.g. to develop subscales for tests
Multivariate Data reduction: Cluster Analysis
Used to identify, define, confirm the nature and number of subgroups (clusters)
ANCOVA: main use
Removes variability due to extraneous variable
Interval recording/Event sampling
Measuring presence or absence of behavior during discrete intervals of a set period of time, or during an event
Trend Analysis
Analysis of Variance
Quantitative IV
Assesses linear and nonlinear (e.g. quadratic) trends
How to compensate for violation of homogeneity of variances
Decreasing alpha
Having equal-sized groups
Best way to increase External Validity
Randomly select participants from target population
Survival analysis
Used to evaluate the length of time to critical event
e.g. relapse, promotion
Multiple Regression Analysis:
Weighting of predictors
Predictor is weighted in:
direct proportion to criterion
inverse proportion to other predictors
Standard Error of the Mean calculation
σ/√N
