Statistics And Research Design

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Alpha (Level of Significance)

Back 1

-in psych research, alpha commonly set at either .01 or .05
-it's the rejection region
-for instance if alpha is set at .05 the statistical test indicates that the sample value is in the rejection region, results are significant

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Rejection Region

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-region of unlikely values
-both in one and two tail sampling (tail end)

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Retention Region

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-region of likely values
-central portion not tail

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Independent Variable

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it affects or alter status on another variable (dependent)
-often referred as "treatment" or "intervention", symbolized as "X"
-must have two levels (e.g. CBT and psychodynamic therapies effect on depression OR Treatment and No Treatment)

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Dependent Variable

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-status depends on independent variable
-outcome of the treatment
-symbolized by letter "Y"

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Organismic Variable

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-subject characteristics that can't be controlled by the researcher, often occurs in studies that are not looking for a causal relationship

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Interval Recording

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-observing a behavior for a period of time that has been divided into equal intervals and record whether or not occurs
-best for complex interactions and behaviors that have no clear beginnings or end like laughing, talking or playing

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Event sampling (recording)

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observing a behavior each time it occurs
-good for stdying behaviors that occur infrequently, that have a long duration, or that leave a permanent record

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Situational Sampling

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used when the goal of the study is to observe a behavior in a number of settings
-HELPS INCREASE the GENERALIZABILITY of a study's findings

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Sequential analysis

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coding behavioral sequences rather than isolated behavioral events
-used to study complex social behaviors

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True Experimental Research

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-only TER provides the amount of control necessary to conclude that observed variability in a dependent variable is actually caused by variability in an independent variable
-not only able to control experimental conditions but MOST IMPORTANT!!!!!!!!! is ABLE to randomly assign subjects to different treatment groups

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Random Assignment "Randomization"

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random assignment of subjects to groups

helps ensure that any observed differences btwn groups on the dependent variable are actually due to the effects of the independent variable

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Quasi-Experimental Research

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with this kind, u investigate the effects of an independent variable on a DV but does not provide the same degree of experimental control
-uses intact (pre-existing) groups or a single treatment group

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Random Assignment

vs

Random Selection

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RA
-distinguishes true experimental from quasi-experimental research
-allows more certainty that effect on DV was caused by IV

RS
-enables the investigato to generalize finding from the sample to population

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SIMPLE random sampling

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-reduces the probability that a sample will be biased in some way, every member of the population has an equal chance of being included

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STRATIFIED random sampling

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-dividing population into the appropriate strata and randomly selecting subjects from each stratum

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Cluster Sampling

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Cluster sampling is useful when it's not possible to identify or obtain access to the entire population of interest
-select clusters of individuals
-generally provides less precision, more about cost savings

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Choosing a research design:
(Maximizing Variability)

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make the levels of IV as different as possible
(like teaching participants in control group a certain procedure but control group)

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Choosing a research design:
Controlling Variability Due to Extraneous Variables

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radio frequency metaphor, u want to filter noise in order to get clear signal

randomization:

Matching subjects: Find subjects in pair who have matched characteristics in extraneous variables and assign them into different groups.

Blocking: If all subjects are treated as a big group, the within-group variability may be very huge. By dividing the experimental conditions into several "blocks", the researcher can localize error variance i.e. in each block the within-group variability is smaller (for instance in experiment on meds effects on depression, have groups mild, moderate, severe, and randomly assign)

-select subjects who are homogenous (subjects only with moderate sx's)

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Minimizing Random Error

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-don't fatigue ur subjects
-make sure the setting is free from distractions and fluctuations in environmental conditions
-make sure all measuring devices are reliable

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Threats to Internal Validity

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-maturation: examples are fatigue, boredom, hunger, physical and intellectual growth; include more than one group and randomly assign subjects to groups

-history: when an external event systematically affects status of subjects on the DV (i.e. change in hospital staff or policy)

-testing: minimize practice effects or administer measure only once

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Threats to External Validity

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-Demand characteristics: cues in the experimental setting that inform subjects of the purpose of the study or suggest what behaviors are expected of them

-multiple treatment interference: exposure to two or more levels of the IV

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Between-groups Designs

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different levels of the IV are administered to different groups of participants

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Factorial Design

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-used when a study has two or more IV, can analyze main effects of each IV as well as interaction btwn IV

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Main Effect

vs

Interaction

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ME: the effect of ONE IV on the DV

Interaction: the effects of TWO or MORE IV, usually the effects of an IV differ at different levels of another IV

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Within-subjects design (repeated measures)

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each participant receives at different times each level of the IV (time intervals, before and after)
-internal validity threatened by history
-susceptable to carryover effects
(multiple tx interferance)
-autocorrelation?

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Mixed Designs

Back 27

-combines between groups and within-subjects designs

-measuring the DV OVER TIME or ACROSS TRIALS
-in this type of study, time or trials is an additional IV and is considered a within-subjects variable because comparisons of on the DV will be made within subject across time or across trials

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Type I error

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-rejecting a TRUE null hypothesis
-as the value of alpha INCREASES (.01 to .05), the probability of rejecting a true null hypothesis also increases

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Alpha

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-level of significance
-if alpha is set at .05, it means 5% of the sampling distribution represents rejection region (.025 for 2-tailed test)

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Type II error

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-retaining a false null hypothesis
-more likely when alpha is low, sample size is small, and when IV is not administered sufficiently

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Ordinarily, want to reject null hypothesis when it is false

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-at this point, study said to have statistical power
-power increases as alpha increases and vice versa
-more power when:
**increase alpha
**increase sample size
**IV effects maximized (control for extraneous variables)
**reliable DV measure
**using 1 tailed test
**power parametric statistical test

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Parametric Tests

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-used for interval (e.g. scores on tests) or ratio (e.g. number of aggressive acts) data

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Nonparametric Tests

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-used for variables that have been measured on a nominal (e.g. gender, attitude) or ordinal (e.g. Likert scale, ranks, 1st 2nd) scale

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Chi-Square Test

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-Nominal data, like comparing the number of people who prefer one of four political candidates
-

Front 35

Single sample chi-square test
(nonparametric)

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"single variable"
-"goodness of fit"
-descriptive study
-one variable (Schizophrenic DO in parent: one, both, neither)
-degrees of freedom is C-1 where C= the number of "columns" ( so above would be 3-1)

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Multiple Sample Chi-Square Test
(nonparametric)

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"multiple variable"
-descriptive or experimental
-2 or more variables
-schizophrenic do in parent (one, both, neither) and subtype (catanonic, paranoid, disorganized, undifferentiated, residual)
-degrees of freedom (C-1) * (R-1). so above would be (3-1)*(5-1)=2*4=8

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Mann-Whitney U Test

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-alternative to t-test for independent samples
-One IV: two independent groups
-One DV: rank-ordered data

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Wilcoxon Matched-Pairs Signed-Ranks Test

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-alternative to t-test for correlated samples
One IV: two correlated groups
-One DV: rank-ordered data

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Kruskal-Wallis Test

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-alternative to one-way ANOVA
One IV: two or more independent groups
-One DV: rank-ordered data

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Student's T-test for a single sample

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-one iv: single group
-one DV: interval or ratio data

ONLY ONE GROUP sample mean compared to known population mean

-using 20 6th grade student with ADHD, give them a procedure, and compare achievement scores with other 6th graders with ADHD

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Student's T-test for independent (unrelated) sample

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-alternative nonparametric is Mann-Whitney
-take 20 ADHD students, 10 get procedure and 10 don't, compare means btwn groups

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t-test for correlated (related) samples

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-within subjects, compare b4 and after IV has been applied
-alternative parametric is Wilcoxon
-take 20 ADHD students, get initial achievement scores, train them, get scores again, and compare performances

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ANOVA

Back 43

-analysis of variance
-use to compare 2 or MORE means
-makes this comparison while keeping Type 1 error at level of significance

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Decision Outcomes for Hypothesis Testing

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-what you want is power, u want a false null hypothesis and to reject it

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One-Way Anova

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-Kruskal-Wallis is nonparametric alternative
-F-ratio: (mean square btwn: MSB)/(mean square within: MSW)
-when NULL HYPOTHESIS (IV no efffect on DV)is true
**MSW and MSB are the same
**F-ratio is equal to 1

-when null hypothesis is FALSE,
**MSB is larger than MSW
**F-ratio is greater than 1

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Factorial Anova

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-used when a study employs 2 or more independent variables
-variability BTWN independent groups

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Randomized Block Factorial Anova

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-when "blocking" has been used to control extraneous variable (building the EV into the study, subjects are grouped or "blocked"

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ANCOVA

Back 48

-key terms: covariate,regression analysis, statistically removing variability in the DV that is due to EV

Front 49

Repeated Measures ANOVA

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-within subjects
-different levels of an IV or combinations of the levels of two or more IVs are sequentially administered to each subject

Front 50

Mixed (Split-Plot) ANOVA

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-One IV is between groups
and One IV is within-subjects variable

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Trend Analysis

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-is there a statistically significant linear or nonlinear TREND btwn IV and DV
-one or more IV

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MANOVA

Back 52

-one or more IV
-2 or more DV
-simultaneously assess the effects of the IV(s) on all DVs

Front 53

Effect Size

Back 53

-if a study shows statistical significance, calculating for effect size to find out if it is also practically or clinically significant

Front 54

Cohen's d

Back 54

-mean of one group subtracted by mean of other group divided by pooled standard deviation for two groups (often experimental and control groups)

**0.2=small
**0.5=medium
**0.8=large

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r square and eta square

Back 55

-percent of variance in outcome variable that is accounted for by variance in the tx

-in a study about effects of antidepressant on BDI scores, an eta square of .30 indicates that 30% of variability in BDI scores is accounted for by variability in drug dose

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Scattergram

Back 56

-X and Y
-X (predictor) variable is on horizontal axis

-Y (criterion) is vertical

Front 57

Pearson r

Back 57

-most common correlation coefficient
-range is -1.0 to +1.0
-the closer coefficient is to -1.0 OR +1.0, the stronger the relationship
-positive (direct) correlation, value of Y increases as values of X increase
-conversely when there is a negative (inverse) relationship

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3 assumptions when using Pearson r and most other coefficients

Back 58

Linearity
-can be see as a straight line
-if relationship is nonlinear, Pearson r will UNDERESTIMATE the degree of association

Unrestricted Range:
-unrestricted range of scores on both variables
-data collected from people who are heterogenous with regards to characteristics measure by X and Y.
-if ppl are homogenous, Pearson r will be an underestimate

Homoscedasticity
-range of Y scores is ABOUT the same for all values of X
-

Front 59

Interpretation of a Correlation Coefficient:
Degree of Association

Back 59

-a large coefficient alone does not mean that variability in one variable causes variability in the other variable
-it's the research method that permits causal inferences (e.g. if it is a true experimental method, a researcher can infer a cause-effect relationship when correlation coefficient is sufficiently large)
-closer coefficient is to -1.0 or +1.0, the stronger the association btwn variables
-closer it is to 0, weaker the association

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Interpretation of a Correlation Coefficient:
Coefficient of Determination

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-square the correlation coefficient
-obtain shared variability

Front 61

Interpretation of a Correlation Coefficient:
Hypothesis Testing

Back 61

-the smaller the sample, the larger the correlation coefficient must be to be statistically significant

Front 62

Regression Analysis

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-allows predictions to be made
-unless the coefficient is equal to +1.0 or -1.0, there will be some error in prediction

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Multivariate Techniques: Overview

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-used to assess the degree of association among three or more variables
-and to make predictions that involve, at minimum, 2 predictors and one criterion

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Multivariate Techniques: Multiple Regression

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2+ predictors ---> 1 continuous criterion
-SAT Verbal, SAT Math, and high school GPA used to predict college GPA

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Multiple Regression

vs

ANOVA

Back 65

-MR used more
-MR permits adding or subtracting IV (predictors) to the analysis to determine which subset of variable best explains variability in the DV (criterion)

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Multivariate Techniques: Types of Multiple Regression

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-simple or simultaneous regression
**all predictors (IV) on the criterion (DV) at once

-stepwise regression (explain the greatest amount of variability in the criteorion using/identifying fewest numbers of predictors)
**step-up (forward): one predictor is added in each subsequent analysis
**step-down (backward): all predictors and one predictor eliminated in each subsequent analysis
-

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Multivariate Techniques: Canonical Correlation

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-2+ predictors--->2+ continuous criteria

-measure of job knowledge, assertiveness, and years experience used to predict superviosr performance ratings and yearly sales

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Multivariate Techniques: Discriminant Function Analysis

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-2+ predictors--->1 discrete (nominal) criterion
-Battery of tests used to help college freshman choose a college major

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Multivariate Techniques: Causal (Structural Equation) Modeling

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-cannot predict causality but provides some evidence their causal model or theory is correct or incorrect

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Multivariate Techniques: Causal (Structural Equation) Modeling:
PATH ANALYSIS

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-one-way causal flow, relationships between observed (measured) variables ONLY
-ur evaluating the viability of a causal model for a set of variables

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Multivariate Techniques: Causal (Structural Equation) Modeling:
LISREL

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-Unidirectional and bidirectional causal relationships btwn observed (measured) AND latent variables as well as impact of measurement error

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Standard Error of the Mean

Back 72

-also known as the standard deviation of the sampling distribution (which is part of the Central Limit Theorem)

-it is a measure of variability that is due to the effects of random error

-the larger the population standard deviation and the smaller the sample size, the larger the standard error and vice-versa (THE SmaLLER THE SAMPLE SIZE, the LARGEr The SEM)

-SEM increases as population standard deviation increases

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Proband

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An individual who presents with a genetic disorder, and whose family is then investigated

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Autocorrelation

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-can result in an inflated value of an inferential statistic
-often a result of repeated (within-subject) designs
-possibility exists that subjects performance on posttest may be similar to pretests

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Discriminant Function Analysis

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-an appropriate technique when 2 OR MORE continuous PREDICTORS will be used to estimate a person's status on a SINGLE, DISCRETE (NOMINAL) CRITERION

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Solomon Four-Group Design

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Use this design when it is suspected that, in taking a test more than once, earlier tests have an effect on later tests, for example by learning or priming effects.

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time-sampling technique

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-also known as interval recording
observation made at prespecified intervals and whether or not the behavior was occuring at that time is recorded

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F-ratio

Back 78

******Larger F---> more statistically significant

= MSB/MSW

=(mean square btwn divided by mean square within)

=MSB --> variability btwn tx groups, estimate of variability due to both error and the effects of the independent variable

=MSW-->variability within each of the tx groups, a measure of variability for subjects who have been treated alike and PROVIDES AN ESTIMATE OF VARIABILITY THAT IS DUE TO ERROR ONLY

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Event Sampling

Back 79

-or event recording

-observing a behavior each time it occurs

-good for behaviors that occur infrequently

Front 80

Situational Sampling

Back 80

observing the behavior in a number of settings
-helps increase generalizability

Front 81

Sequential Analysis

Back 81

coding behavioral sequences rather than isolated behavioral events
-used to study complex social behaviors

Front 82

In a positively skewed distribution

Back 82

mean is GREATER THAN the median which is greater than mode

(reverse in negatively skewed)

-i'm in a mean median mode today

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Effects of Mathematical Operations on Measures of Central Tendency and Variability

Back 83

-u may have to add, subtract, divide or multiply using a constant with each score

-when ADDING or SUBTRACTING, will increase mean but not standard deviation

-when multiplying or dividing, changes mean and standard deviation

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Moderator variable

Back 84

a moderator is a qualitative (e.g., sex, race, class) or quantitative (e.g., level of depression) variable that affects the direction and/or strength of the relation between an independent or predictor variable and a dependent or criterion variable

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Mediator Variable

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one that explains the relationship between the two other variables

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Single subject designs

Back 86

-often used with one subject or a small number of subjects, but can also be used with groups of subjects

-different from group designs
**includes at least one baseline (no tx) and one tx phase (each subject then is his own no-tx control)

**DV is measured repeatedly at regular intervals throughout the baseline and tx phases (repeated measure of DV helps control any maturational effects)

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Single subject designs: AB Design

Back 87

-single baseline (A) and single tx (B) phase

***NOTE: single AB phases can extend over time

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Single subject designs: Reversal (Withdrawal) Designs (ABA, ABAB)

Back 88

one or more baseline and/or tx phase
-provides additional control over potential threats to a study's internal validity

-sometimes withdrawal of tx can be unethical

-doesn't provide evidence if effects of IV persist

Front 89

Single subject designs: Multiple Baseline Design

Back 89

-doesn't require withdrawal of tx during study (in fact once tx is applied, not withdrawn) but instead sequentially applying the tx
**either to different behaviors of the subject
**to the same subject in different settings
**to the same behavior of different subjects

Front 90

Relationship btwn power and confidence

Back 90

-inverse
-power: ability to reject false null hypothesis, think of it as number
-confidence: certainty we have about a decision already made about null hypothesis

**• If you decrease power (from .05 to .01) then you increase your confidence and have less chance of making an error
• If you increase power (from .01 to .05), the you decrease confidence but have a greater chance to reject null, but there could be more errors

Front 91

Degrees of freedom Single Sample Chi-Square Test

Back 91

(C-1)
**C= number of "columns"

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Degrees of freedom Multi Sample Chi-Square Test

Back 92

(C-1)(R-1)
**R=number of rows

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Degrees of freedom t-Test for a single sample,

Back 93

N-1

Front 94

Degrees of freedom, t-Test for Correlated Sample

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N-1 (n=number of pairs of scores)

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Degrees of freedom, t-Test for independent samples

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N-2