Psych MSP Exam 2

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Mean square within or MS(wn) is known as the "_________."

"error term"

Between-subjects factor

- A factor that is studied using independent samples in all conditions - Involves using the formulas for a between-subjects ANOVA

Within-subjects factor

- A factor that is studied using related (dependent) samples in all levels - Involves a set of formulas called a within-subjects ANOVA

Threats to internal validity

- Confounds that must be controlled so that a cause-effect relationship can be demonstrated - History, maturation, testing, instrumentation, statistical regression, selection, selection interactions, mortality/attrition

What issues are most important when recruiting participants for an experiment (including ethical issues that should be addressed)?

- Informed consent: "study might involve listening to a three-minute song" - Prescreening: screen out those at increased risk; legally able (e.g. over 18) - Recruiting participants: power, diversity of sample, prescreening, nonprobability sampling - Random assignment: not necessary to randomly select the sample but random assignment essential (want similar groups to ensure individual differences are equally represented in each group)

Restriction of range

- Problem that arises when range between the lowest and highest scores on one or both variables is limited (produces a coefficient smaller than it would be if range were not restricted); floor and ceiling effects - Decreases the power of our study or our ability to see whether a relationship exists

Coefficient of determination (r^2)

- Proportion of variability accounted for by knowing the relationship (correlation) between two variables - Reflects the usefulness or importance of a relationship (think effect size)

Why do we compute confidence intervals?

- So that we have an interval estimation - Because we are trying to best describe the population

Two-sample experiment

- Subjects are measured under two conditions of the independent variable - Condition 1 produces sample mean X̄(1) that represents µ(1) and condition 2 produces sample mean X̄(2) that represents µ(2)

Which threats (to internal validity) apply to a group design?

- Threats due to experiences or environment: history, maturation, testing, instrumentation - Threats due to participant characteristics: attrition/mortality, selection, selection interactions

Post hoc comparison

- We compare all possible pairs of means from a factor, one pair at a time, to determine which means differ significantly - Only performed when F-obtained is significant

Why are 95% confidence intervals so common?

- α is usually .05 - 1-α = probability of avoiding a Type I error - .95 probability that the interval contains the sample mean

What are the 4 steps for computing the independent-samples t-test?

1. Calculate the estimated population variance for each condition 2. Compute the pooled variance 3. Compute the standard error of the difference between the means 4. Compute t-obtained for the two independent samples

What are the steps for computing F-obtained?

1. Compute the total sum of squares (SS(tot)) 2. Compute the sum of squares between groups (SS(bn)) 3. Compute the sum of squares within groups (SS(wn)) 4. Compute the degrees of freedom (k-1 between, N-k within, N-1 total) 5. Compute the mean squares 6. Compute F-obtained

Critical values for the independent-samples t-test (t(crit)) are determined based on what 3 things?

1. Degrees of freedom: df = (n(1)-1) + (n(2)-1) 2. The selected α 3. Whether a one-tailed or two-tailed test is used

What are the 4 different types of IV manipulation?

1. Environmental 2. Scenario 3. Instructional 4. Physiological

What are the two versions of a two-sample t-test?

1. Independent-samples t-test 2. Related-samples t-test (or dependent-samples)

What are the 3 ways to maximize the power of a t-test?

1. Larger differences produced by changing the independent variable increase power 2. Smaller variability in the raw scores increases power 3. A larger N increases power

What are the 4 more important things to do when designing a simple experiment?

1. Maximize power 2. Ensure IV manipulation is reliable and valid 3. Ensure DV manipulation is reliable and valid 4. Maximize internal validity

To maximize power in the independent-samples t-test, you should do what 3 things?

1. Maximize the size of the difference between the means 2. Minimize the variability of the scores within each condition 3. Maximize the size of N, that is, n(1) + n(2)

What are the three steps for setting up a one-sample t-test?

1. Set up the statistical hypotheses (H0 and HA); these are done in precisely the same fashion as in the z-test 2. Select alpha; α = .05 typically is used 3. Check the assumptions for a t-test

What are the 4 ways to maximize power in a simple experiment?

1. Strong manipulation of the IV 2. Extreme levels of the IV 3. Homogeneity of participants 4. Increase N

The critical F value (F(crit)) depends on what 3 things?

1. The degrees of freedom (both the df(bn) = k-1 and the df(wn) = N-k) 2. The α selected 3. The F-test is always a one-tailed test

What are the 4 assumptions of the independent-samples t-test?

1. The dependent scores measure an interval or ratio variable 2. The populations of raw scores form normal distributions 3. The populations have homogeneous variances (homogeneity of variance = the variances of the populations being represented are equal) 4. While Ns may be different, they should not be massively unequal

What are the 3 assumptions of the one-way between-subjects ANOVA?

1. The experiment has only one independent variable and all conditions contain independent samples 2. The dependent variable measures normally distributed interval or ratio scores 3. The variances of the populations are homogeneous

What are the 3 assumptions for a t-test?

1. You have one random sample of interval or ratio scores 2. The raw score population forms a normal distribution 3. The SD of the raw score population is estimated by computing s(x), the estimated population SD

What are the degrees of freedom for an independent-samples t-test that uses two samples with n=12 in each sample?

22

If our α is .01, what would our confidence interval be?

99%

Fisher's Least Significant Difference (LSD) test

A commonly used post hoc test that computes the smallest amount that group means can differ in order to be significant

Experiment

A design that includes manipulation of an IV, measurement of a DV, random assignment, and control of confounds

Quasi-experiment

A group design in which a researcher compares pre-existing or naturally occurring groups that are exposed to different levels of a variable of interest

Squared point-biserial correlation

A measure of effect size for the independent-samples t test, providing the percentage of variance in the outcome (or DV) accounted for by the predictor (or IV)

Linear relationship

A relationship between two variables, defined by their moving in a single direction together

Correlation

A relationship between variables

Multiple regression (R)

A statistical technique that compares both the individual and combined contribution of two or more variables to the prediction of another variable; used when we have more than two variables and we want to know the predictive validity that results from knowing the relationship among all the variables

Levene's Test for Equality of Variances

A statistical test that examines whether the variability within different samples is similar

Eta squared (η^2)

A statistical test which tells us the percentage of variability in the variable we measured accounted for by the group

Multiple independent-groups design

A study examining the effect of a manipulated IV or the relationship of a variable which had three or more levels on a DV; the participants in each level of the IV are unrelated

Simple experiment

A study investigating the effect of a manipulated IV with two conditions on a DV; the IV is nominal scale and the DV is interval or ratio

Ecological validity

A type of external validity that assesses the degree to which a study's findings generalize to real-world settings

Correlational design

A types of study that tests the hypothesis that variables are related

Confound

A variable that varies systematically with the variables of interest in a study and is a potential alternative explanation for causality

What is the chance (probability) we have made a Type I error (rejecting the null when the null is really true)?

Alpha (α)

ANOVA is the abbreviation of what?

Analysis of variance

Which threat is not directly controlled for in an experiment?

Attrition/mortality

Standard error of the estimate

Average difference between the predicted Y values for each X from the actual Y values

What is the purpose of an experiment? A. Describe B. Predict C. Explain

C. Explain

Demand characteristics

Characteristics of the study that lead participants to guess at the study's hypothesis and change their behavior accordingly (threat to internal validity)

For nominal data, what is the appropriate test for comparing a sample to a population or an expected value?

Chi-square goodness of fit test

How does an experiment control for threats to internal validity?

Control for as many confounds as possible by: keeping extraneous variables controlled across IV conditions and using random assignment so participants are assigned to an IV randomly

Confidence interval

Defines the highest mean difference and the lowest mean difference (and the values in between) we would expect for a particular population mean we found in our study

Descriptive designs __________, correlational designs ___________, and quasi-experiments/experiments ___________.

Describe; predict; explain

Point estimation

Describes a point on the variable at which the µ is expected to fall

Point-biserial correlation coefficient (r(pb))

Describes the relationship between a dichotomous variable and an interval/ratio variable; interpreted similarly to a Pearson correlation coefficient

Effect size

Describes the strength of the effect of an IV (or the strength of the relationship between a predictor and outcome in a correlational study)

Mean square between groups

Describes the variability between the means of our levels

Mean square within groups

Describes the variability of scores within the conditions of an experiment

__________ and __________ designs have better external validity, while _________ and __________ designs have better internal validity.

Descriptive; correlational; quasi-experiments; experiments

Group design

Design in which a researcher compares two or more groups of participants who are exposed to different levels of a variable of interest

Treatment effect

Differences produced by the independent variable

In a one-sample t-test, what do you do after you compute the estimated population SD, or s(x)?

Divide that difference by the standard deviation of the sampling distribution of means; because σ(x) is usually not available, we use the estimated standard error of the means (SD(x) or S(x))

Regression equation

Equation that describes the relationship between two variables and allows us to predict Y from X

Mean square within or MS(wn) estimates what?

Estimates the error variance in the population

Mean square between groups or MS(bn) estimates what?

Estimates the variability of scores between the levels in a factor

What are the two measures of effect size for a one-sample t-test?

Eta squared and Cohen's d

Dependent-groups experiment

Experiment in which the groups are related, in that participants were matched prior to exposure to the IV or in that the participants experience all levels of the IV

Between experiments and quasi-experiments, ___________ have better internal validity and ___________ have better external validity.

Experiments; quasi-experiments

The statistic for the ANOVA is _______.

F

True or false: There is more focus on external validity in an experiment as compared to a quasi-experiment.

False (Quasi-experiment; they often use real-world interventions rather than artificial lab settings)

If ________ is false, then MS(bn) contains estimates of both error variance (which measures difference within each population) and treatment variance (which measures difference between the populations).

H(0) or null

If __________ is true, each condition is a sample from the same population.

H(0) or null

When ________ is true, MS(bn) estimates the variability among the individual scores in the population just like MS(wn) does, and so MS(bn) should be equal to MS(wn).

H(0) or null

The null hypothesis in numerical terms is H(0): M = µ. Another way to consider the null is as an equation, which is?

H(0): µ - M = 0 (zero)

We know that in an independent-samples t-test we could state our null as H(0): µ(1) = µ(2). However, we usually state it as __________ instead.

H(0): µ(1) - µ(2) = 0

What are the threats (to internal validity) of a one group pre-post test design?

History, maturation, instrumentation (all have to do with experiences or environment) and statistical regression (biased recruitment)

Mean square between groups or MS(bn) is used to determine what?

How each level mean deviates from the overall mean of the experiment (indicates how different the level means are from each other)

What threats (to internal validity) are inherent to a quasi-experiment?

Instrumentation, selection, attrition/mortality

We assume there is one value for the error variance in the population and each _________ estimates that value.

MS(wn) or mean square within groups

___________ is an estimate of the error variance, the inherent variability within a population represented by the samples.

MS(wn) or mean square within groups

The greater the _________, the more accurately the t-distribution represents the population means (S(x) will be closer to σ(x)).

N (sample size)

Degrees of freedom = __________ because we are making an estimate about the population and we are dealing with a sample.

N - 1

One-group pre-posttest design

Nonexperimental design in which all participants are tested prior to exposure to a variable of interest and again after exposure

For interval or ratio data, what is the appropriate test for comparing a sample to a population or an expected value?

One-sample t-test

Experimenter expectancy effect (or Rosenthal effect)

Phenomenon in which a researcher unintentionally treats the groups differently so that results support the hypothesis (threat to internal validity)

Hawthorne effect

Phenomenon in which participants change their behavior simply because they are in a study and have the attention of researchers (threat to internal validity)

What are the two ways to estimate the population mean (µ)?

Point estimation and interval estimation

Matched random assignment

Process in which participants are put into matched sets and then each member of the set is assigned to one IV level so that all in the set have an equal chance of experiencing any of the levels

Linear regression

Process of describing a correlation with the line that best fits the data points (Y' = bX + a)

Prescreening

Process of identifying those who have characteristics that the researcher wants to include or exclude in the study

Between-subjects experiment (or independent-groups experiment)

Random selection, each subject serves in only one condition

Floor effect

Restricting the lower limit of a measure so that lower scores are not assessed accurately (lowest score of a measure is set too high)

Ceiling effect

Restricting the upper limit of a measure so that higher levels of a measure are not assessed accurately (highest score of a measure is set too low)

What terms make up a summary ANOVA table?

Source (treatment, error, total), sum of squares (SS(B), SS(W), SS(tot)), degrees of freedom, MS/mean square, and F-obtained

Interval estimation

Specifies a range of values within which we expect to µ to fall

What would you do if you wanted to get the estimated population variance from the estimated population SD?

Square everything (eliminate the square root sign from the estimated population SD formula)

How does the standard error of the difference differ from the standard deviation?

Standard error of the difference is the average variability in a sampling distribution of differences BETWEEN means, while SD is the average variance of each score FROM the mean

Pearson's r (Pearson's product-moment correlation coefficient)

Statistic used to describe a linear relationship between two interval/ratio measures; describes the direction (positive or negative) and strength of the relationship

Predictor variable

The X variable used to predict a Y value; term used instead of DV in a correlational design

Standard error of the difference between the means (SD(x-x))

The average variability in a sampling distribution of differences between means

t-distribution

The distribution of all possible values of t computed for random sample means selected from the raw score population described by H(0); each has a calculated mean, SD, and t-obtained

Internal validity

The extent to which we can say that one variable caused a change in another variable

Experiment-wise error rate

The overall probability of making a Type I error anywhere among the comparisons in an experiment

One-sample t-test

The parametric inferential procedure for a one-sample experiment when the standard deviation of the raw score population must be estimated; compare a sample to a population, to a known or expected score

Analysis of variance (ANOVA)

The parametric procedure for determining whether significant differences occur in an experiment containing two or more sample means

Independent-sample t-test

The parametric procedure used for testing two sample means from independent samples

Two-sample t-test

The parametric statistical procedure for determining whether the results of a two-sample experiment are significant

Criterion variable

The predicted variable

Power

The probability of rejecting the null when the null is in fact false

Manipulation check

The process of verifying that the participants noticed/attended to the manipulation; usually appears after the DV measure

In relation to an ANOVA, what does eta squared (η^2) indicate?

The proportion of variance in the dependent variable that is accounted for by changing the levels of a factor

What are we stating if we reject the null in an independent-samples t-test?

The sample mean difference represents a difference between two population µs that is significantly different from zero

F-distribution

The sampling distribution showing the various values of F that occur when H(0) is true and all conditions represent one population

Standard error of the means (σ(x) or SEM)

The standard deviation of the sampling distribution of means

Cohen's d (d)

The standardized size of the difference between the two means

Line of best fit

The straight line that best fits a correlation and consists of each X value in the relationship and its predicted Y value

Sum of squares (SS)

The sum of deviation scores that are obtained by subtracting the mean from each score

Sum of squares total or SS(total)

The sum of squared deviations around the mean of the entire sample

Diffusion of treatment

The treatment administered to one group is shared with another group through cross-group interactions (threat to internal validity)

What is σ(x)?

The true standard deviation of the raw score population

Y predicted (Y')

The value that results from entering a particular X value in a regression equation

What does it mean if Levene's test is significant?

Variances are not homogeneous (homogeneity of variances assumption is violated) and p < .05

When is a one-way ANOVA performed?

When only one independent variable is tested in the experiment

When is the Tukey HSD multiple comparisons test used?

When the Ns in all levels of the factor are equal

When are two samples independent?

When we randomly select participants for a sample, without regard to who else has been selected for either sample

What is tested in a chi-square goodness of fit test?

Whether the observed frequencies of the categories reflect the expected population frequencies

What are reasons for conducting a factorial study?

You have reason to expect that the relationship between your variables will depend on a third, moderating variable or you want to systematically control confounds or extraneous variables

Because we can have different regions of rejection (critical values), the probability of __________ can change.

a Type I error

You'll have an independent-groups factorial design if __________.

all the IVs or predictors (factors) are independent groups

You'll have a dependent-groups factorial design if __________.

all the IVs or predictors are dependent groups

We perform interval estimation by creating a ______________.

confidence interval

When the t-test for independent samples is significant, a __________ for the difference between the two µs should be computed.

confidence interval

When F-obtained is significant, it indicates that two or more means ___________. It does not indicate which specific means __________.

differ significantly (x2)

Using the ANOVA allows us to compare the means from all levels of the factor and keep the _________ equal to α.

experiment-wise error rate

When there are more than two means in an experiment, using multiple t-tests results in a _________ much larger than the one we have selected.

experiment-wise error rate

In ANOVAs, an independent variable is called a ____________.

factor

At a card players' club, the poker players had a contest with the blackjack players to see who could win the most money. The appropriate design for testing the significance of the difference between the means is __________.

independent-samples t-test

The symbol for the number of levels in a factor is _________.

k

The ANOVA uses different terminology for variance. What we previously called the estimated population variance is now a ____________.

mean square (mean of squared deviations)

With the one-sample t-test, we find the difference between the ____________ and our ____________.

population mean; sample mean

When the F-test is significant, we perform __________ comparisons.

post hoc

Differently shaped t-distributions will have differently shaped ______________.

regions of rejection

If the differences between our two groups' means is greater than what we would expect by chance, we __________.

reject the null and retain the alternative

If the difference between our two groups' means is about what we would expect because of individual differences, we __________.

retain the null

The computations for the ANOVA require the use of several ___________.

sums of squared deviations / sum of squares (SS)

In an experiment involving only two conditions of the independent variable, you may use either a _________ or _________.

t-test; ANOVA

Post hoc comparisons are like __________.

t-tests

Always use a ___________ confidence interval even if your test is one-tailed.

two-tailed

You'll have a mixed factorial design if _________.

you have at least one independent-groups factor and one dependent-groups factor

Calculating a one-sample t-test is a very similar process to calculating a __________.

z-score

Use the ______ test when σ(x) is known and use the ______ test when σ(x) must be estimated by calculating sample SD or s(x)

z-test; t-test

The confidence interval for a single _________ describes a range of values of __________.

µ

When we use a t-test, we only have one comparison between the two means in an experiment, so the experiment-wise error rate equals _________.

α (alpha)

We obtain the appropriate value of t(crit) from the t-tables using both the appropriate ________ and ________.

α and df


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