T-Test
T-Tests Continued
Experiments
Experiments Continued
Experiments Super Continued
100
What is the difference between a within-groups and between-groups research design?
Between-groups: participants only experience one level of the IV
Within-groups: participants experience all levels of the IV
100
What are degrees of freedom (df)? What does it represent?
Number of independent pieces of information used to calculate a statistic. How many values in a data set are "free" to vary when calculating a statistic.
For t-tests, degrees of freedom are linked to the number of observations, or sample size (n-1)!
100
Define: Independent Variable (IV), Dependent Variable (DV), and Control Variables
IV: manipulated or controlled by the researcher to observe its effect on another variable
DV: variable being measured in the experiment as a result of variations in the IV
Control Variables: potential confounding factors that are kept constant to ensure a fair test
100
What is the difference between a posttest-only and pretest/posttest design?
Main difference lies in when the dependent variable is measured.
Posttest-only: DV measured only after the intervention
Pretest/posttest: DV measured before and after the intervention
100
How do quasi-experiments differ from true experiments?
True experiments: participants are randomly assigned to different groups
Quasi-experiments: not assigned randomly in a quasi-experiment, participants assigned to groups based on pre-existing characteristics (e.g., age, gender, race)
200
Null Hypothesis vs. Alternative Hypothesis
Null Hypothesis (H0): default or baseline assumption that there is no effect, no difference, or no relationship between variables
Alternative Hypothesis (Ha): claim that there is an effect, difference, or relationship between variables
200
State null and alternative hypothesis:
A researcher wants to know whether violent video games influence aggression. She recruited 10 people, 5 played Grand Theft Auto for 20 minutes (Group 1), and the other 5 played Pac Man (Group 2). She then measured aggressive tendencies (higher scores represent more aggression).
H0 = Violent video games do not influence aggression
H0: μ1 – μ2 = 0 or μ1 = μ2
H1 = Violent video games influence aggression (non-directional)
H1: μ1 – μ2 ≠ 0 or μ1 ≠ μ2
How would you write a directional alternative hypothesis?
200
In an experiment, what is effect size? How about statistical significance?
Effect Size: magnitude or strength of the relationship between two variable
Statistical Significance: refers to the likelihood that the results observed in a study are not due to random chance
200
What is random assignment? How does it help establish internal validity?
Ensures that there are no systematic differences between the participants in each group
200
How do large within-groups variances obscure between-groups differences?
When within-groups variance (noise) is large, it is harder to detect the signal (between-groups difference). That is, variability within each group can drown out the effect you are trying to detect.
Signal: The difference between group means (the actual effect of the treatment or intervention).
Noise: The variability within each group, which is unrelated to the intervention but occurs due to individual differences, measurement error, or other factors.
300
Under what circumstances do you select: one-sample t-test, independent samples t-test, paired samples t-test
One-sample t-test: comparing mean of a single sample to a known or hypothesized population mean
Independent samples t-test: comparing means of two independent group among one IV
Paired samples t-test: comparing the means of two conditions or time points on the same participant/subject
300
What is the assumption of homogeneity of variance? Why do we need to test for it in independent samples t-tests?
Homogeneity of variance assumes the level of variance for a particular variable is constant across the sample.
Independent samples t-tests: Levene's Test
If p-value for the Levene's test is greater than .05, variances are not significantly different from each other (homogeneity assumption of variance is met)
300
What are the four validities? Explain the questions you would have to ask to interrogate each of the four validities.
Internal: Does the study design rule out alternative explanations for the results?
External: How well do the results of a study generalize beyond the sample or setting of the study?
Construct: How well does a test or instrument measures the concept it is intended to measure?
Statistical: Are the conclusions accurately drawn from the statistical analyses?
(low statistical power, violation of statistical assumptions, or incorrect data analysis techniques)
300
What are some reasons studies may result in null effects?
Not enough variance between groups (true null effect)
Extremely high variability between groups obscures the effect of the IV (due to pre-existing differences)
Insufficient/inappropriate manipulation of the DV/IV
Poorly designed DV/IV
300
What is matching? Explain its role in establishing internal validity.
Experimental design technique in which participants who are similar on some measured variable are grouped into sets; the members of each matched set are then randomly assigned to different experimental conditions
Example: In educational research, school districts or classrooms may already be set up, and it may not be feasible to randomly assign students or teachers. Instead, researchers can match schools or students based on key characteristics (e.g., socioeconomic status, academic performance) to create comparable groups
400
Why do Z and T distributions differ? How does this impact hypothesis testing?
Z-distribution: More precise estimates, larger samples, and population standard deviation is know
T-distribution: Less precise estimates, smaller samples, population standard deviation is unknown
400
Identify APA-formatting errors below (paired-sample t test):
Students scored significantly higher in psychology knowledge after completing their SMP (M = 7.5) than when they were in Intro (M = 6), t(3) = 5.2, p < .05, estimated d = 2.58 representing a large effect. The mean change in scores was 1.5 points lower in Intro, 95% CI [-2.42, -.58]. Ninety-five percent of the variability in psychology knowledge scores is explained by where they were in the major (intro or SMP level).
Errors:
-Missing SD
-Cohen's d not italicized
-"Ninety-five percent" should be "95%"
-Inconsistent decimal points
Correct statement:
Students scored significantly higher in psychology knowledge after completing their SMP (M = 7.5, SD = 1.73) than when they were in Intro (M = 6, SD = 1.41), t(3) = 5.2, p < .05, estimated d = 2.58 representing a large effect. The mean change in scores was 1.5 points lower in Intro, 95% CI [-2.42, -.58]. 90% of the variability in psychology knowledge scores is explained by where they were in the major (intro or SMP level).
400
What are the three criteria for establishing causation?
Covariance (correlation): demonstrated association between the IV and DV
Temporal Precedence: method was designed so that the causal variable clearly comes first in time, before the effect variable
Internal Validity: ability to eliminate alternative explanations for the association
400
What are comparison groups and double-blind studies? How do they help researchers avoid threats to internal validity?
Comparison Groups: group in an experiment that does not receive the treatment or intervention being studied. Used to determine whether the treatment caused a significant change
Double-blind Studies: participants nor the researchers conducting the study know who is in the experimental group and who is in the control group. Prevents bias.
400
Threats to internal validity (review)
History: occurs when an external, historical event happens for everyone in a study at the same time as the treatment
Maturation: occurs when in an experiment or quasi-experiment with a pretest and posttest, an observed change could have emerged more or less spontaneously over time (internal changes)
Regression: Occurs when in an experiment or quasi-experiment with a pretest and posttest, an observed change could have emerged more or less spontaneously over time (external changes)
Attrition: Occurs when people drop out of a study over time
Testing Threats: When researchers measure participants more than once, they need to be concerned about testing threats to internal validity (e.g., have they gotten used to/better at the same measure? Is it unreliable/not valid? etc)
Instrumentation: Threat to internal validity that occurs when a measuring instrument changes over time
Observer Bias: Bias that occurs when observer expectations influence the interpretation of participant behaviors or the outcome of the study
Demand characteristics: Cue that leads participants to guess a study’s hypothesis or goals; a threat to internal validity
500
T-Tests: what does the numerator represent? What does the denominator represent? What factors affect each?
Numerator: represents difference between the means of the two groups being compared, affected by magnitude of the difference between group means
Denominator: represents standard error (SE) of the difference in means, accounts for the variability in the data due to chance, affected by sample size
larger sample size → leads to smaller SE!
500
Calculate r-squared for the independent samples t-test below
r2 = t2 / (t2 + df)
R-squared calculation:
r2 = t2 / (t2 + df)
r2 = 2.762 / (2.762 + 47)
r2 = 2.762 / (2.762 + 47)
r2 = 7.6176 / (7.6176 + 47)
r2 = 7.6176 / 54.6176
r2 = 0.13947152566 = 0.14
About 14% of the variance in the dependent variable is explained by the independent variable
500
Define: design confounds, selection effects, order effects (threats to internal validity)
Understand how experimenters can avoid each
Design confounds: occurs when a second variable happens to vary systematically along with the intended independent variable
Selection effects: kinds of participants at one level of the IV are systematically different from those at the other level (independent-groups designs only)
Order effects: threat to internal validity in which exposure to one condition changes participant responses to a later condition (within-groups designs only)
500
Define: measurement error, individual differences, situation noise
(causes of within-groups variance)
Understand how experimenters can avoid each
Measurement error: A human or instrument factor that can randomly inflate or deflate a person’s true score on the dependent variable (unreliable/unprecise tools)
Individual differences: Psychological characteristics that distinguish one person from another (e.g., intelligence, personality traits, and values)
Situation noise: Unrelated events or distractions in the external environment that create unsystematic variability within groups in an experiment
500
Define:
Non-equivalent control groups design, interrupted time-series design, and nonequivalent groups interrupted time-series design
Non-equivalent control groups design: at least one treatment group, one comparison group, participants have not been randomly assigned to the two groups, at least one pretest and one posttest
Interrupted time-series design: quasi-experiment in which participants are measured repeatedly on a DV before, during, and after the “interruption” caused by some event
Nonequivalent groups interrupted time-series design: at least one treatment group, one comparison group, participants have not been randomly assigned to the two groups, participants are measured repeatedly on a DV before, during, and after the “interruption” caused by some event, and the presence or timing of the interrupting event differs among the groups