PSY 211QR Final Exam 2.0

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the individual conditions or values that make up a factor

Levels

SS∨btw÷df∨btw

MS∨between

MS∨btw+MS∨w/in

MS∨total

SS∨w/in÷df∨w/in

MS∨within

Sample mean

M₁, M₂

the total number of participants in all groups

N

(df∨total) total number of participants − 1

N-1

(df∨between) total number of participants − number of groups

N-k

1.00

On average, what value is expected for the F-ratio if the null hypothesis is true?

variable that is NOT manipulated by the researcher (Examples: sex & marital status)

Quasi-independent variable (Quasi-IV)

F distribution becomes more spread out with...

SMALLER sample sizes

r=

SP∨xy/√(SS∨x)×(SS∨y)

SS (Sum of squares)

SS₁, SS₂

In an analysis of variance, what determines the size of the sample mean differences?

SS∨btw

SS∨between+SS∨within

SS∨total=

In an analysis of variance, what determines the size of the sample variances?

SS∨w/in

df∨between and df∨within

The F critical value that is associated with the alpha level (or rejection region) is determined by

between-treatments variability and within-treatments variability

The basic "analysis" in ANOVA involves partitioning the total variability into 2 components:

the sample mean difference is more than chance

The larger the F-test value is, indicates that

the boundaries of common outcomes and rare outcomes

The level of significance (α level) will determine

to test for mean differences

The purpose of the t-test and F-test is the same which is

values farther from 0 indicate outcomes that are less likely to occur if the H₀ were true

The rejection region or alpha level is placed in the upper tail of an F-distribution because

means how scores in distribution differ; it associates with total individual differences

Total variability

score differences

Variance means

the size and difference among the sample means

We use variance to define and measure

an analysis of variance will evaluate all of the separate mean differences in a single test

When a study involves more than 2 treatment conditions

Using several t-tests increases the risk of a Type I error

When comparing more than 2 treatment means, why should you use an analysis of variance instead of several t-tests?

Order effects

When participation in one treatment influences the scores in another treatment

difference in scores within each group (treatment or condition)

Within-group variability

What kind of frequency distribution graph shows the frequencies as bars that are separated by spaces?

a bar graph

r²=0.25

a large effect or a large correlation

Effect size

a magnitude of the phenomenon of interest; measures the absolute magnitude of a treatment effect, independent of sample size

r²=0.09

a medium effect or medium correlation

For a research study, comparing attitude scores for males and females, participant gender is an example of what kind of variable?

a quasi-independent variable

The r between musical ability and IQ would probably be greatest from which of the following groups?

a random sample of adults

Statistically significant or significant

a result if it is very unlikely to occur when the null hypothesis is true; the result is sufficient to reject the null hypothesis, therefore a treatment has a significant effect if the decision from the hypothesis test is to reject H₀

A researcher administers a treatment to a sample of participants selected from a population with µ=80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis?

a sample mean much different than 80 with α=0.05

r²=0.01

a small effect or a small correlation

What position in the distribution corresponds to a z-score of z=+2.00?

above the mean by 2 points

In general, what is the effect of an increase in the variance for the sample of difference scores?

an increase in the standard error and a decrease in the value of t

Which of the following accurately describes a hypothesis test?

an inferential technique that uses the data from a sample to draw inferences about a population

ANOVA definition

analysis of variance -hypothesis testing procedure used to evaluate mean differences between two or more treatments/populations

Which of the following is true for most distributions?

around % of the scores will be located within one standard deviation of the mean

For which of the following situations would a repeated-measures research design be appropriate?

comparing mathematical skills for girls versus boys at age 10

What is the consequence of a Type I error?

concluding that a treatment has an effect when it really has no effect

What is the consequence of a Type II error?

concluding that a treatment has no effect when in really does

µ=Md±tsmd=Md±t(s/√n)

confidence interval for related sample t-test

A Pearson correlation is computed for a sample of n=18 pairs of X and Y values. What correlations are statistically significant with α=0.05, two tails?

correlations greater than or equal to 0.468 and correlation less than or equal to -0.468

As range decreases, r tends to

decrease

If an analysis of variance is used for the following data. what would be the effect of changing the value of M to 20? M₁=15 M₂=25 SS₁=90 SS₂=70

decrease SS∨btw and decrease the size of the F-ratio

If an analysis of variance is used for the following data. what would be the effect of changing the value of SS₁ to 50? M₁=15 M₂=25 SS₁=90 SS₂=70

decrease SS∨w/in and increase the size of the F-ratio

shape of the f distribution depends on...

degrees of freedom between within treatments

df (degree of freedom)

df₁, df₂

Sampling distribution

distribution of statistics obtained by selecting all of the possible samples of a specific size from a population

Linear transformations of X or Y or both X and Y

do not have any effect on r

Extreme data points (outliers) can have a

dramatic effect on the correlation

Coefficient of determination=r²

effect size

Which of the following confidence intervals also indicates a significant difference between treatments with α=0.05?

estimate that μ1 - μ2 is in an interval between 2 and 10 with 95% confidence

√(s²/n)

estimated standard error

Critical region

extreme sample values that are very unlikely to be obtained if the H₀ is true

Hypothesis testing for r: if p> alpha-not significant

fail to reject H₀

Linear transformation

if either X or Y or both variables are transformed to a new variable(s) via addition, subtraction, multiplication and/or division

Under what circumstances will the distribution of sample means be normal?

if the population is normal, or if the sample size is greater than 30

If an analysis of variance is used for the following data. what would be the effect of changing the value of SS₂ to 100? M₁=15 M₂=25 SS₁=90 SS₂=70

increase SS∨w/in and decrease the size of the F-ratio

What correctly describes the effect of increasing the alpha level (for example, from 0.01 to 0.05)?

increase the likelihood of rejecting H₀ and increase the risk of a Type I error

For the independent-measures t statistic, if other factors are held constant, increasing the sample mean difference will...the chances of a significant t statistic and...measures of effect size.

increase, increase

For an independent-measures t-statistic, what is the effect of increasing the number of scores in the samples?

increasing the likelihood of rejecting the null hypothesis and have little or no effect on measures of effect size

within-treatment variance is computed for...

individual scores from each sample

What happens to the standard error of M as sample size increases?

it decreases

When n is small (less than 30), how does the shape of the t-distribution compare to the normal distribution?

it is flatter and more spread out than the normal distribution

What happens to the expected value of M as sample size increases?

it stays constant

Which of following accurately describes an independent-measures study?

it uses a different group of participants for each of the treatment conditions being compared

What describes what a confidence interval does?

it uses a sample mean to estimate the corresponding population mean

(df∨within) number of groups − 1

k-1

In a particular experiment, the value of r is 0.95 between X and Y

low scores on X are associated with low scores on Y

Correlation describes the

magnitude and direction between 2 variables

The r is a measure of the

magnitude and direction of the linear relationship between X and Y

d=Md/s of d=t/√n

magnitude of mean difference (Cohen's d)

t=Md/Smd

mean difference between 2 treatment conditions

Cohen's d

mean difference divided by the standard deviation

Expected value of M

mean of the distribution of sample means is equal to the mean of the population of scores (µ)

Standard error of M

measures the average distance between M (sample mean) and µ (population mean)

r² (coefficient of determination)

measures the proportion of variability in 1 variable that can be determined from the relationship with the other variable

η²

measures the proportion of variance in scores accounted for by the difference between treatments

the number of participants in each group

n

For the repeated-measures t-statistic, df=?

n-1

H₀: µD=0 (Related samples & two-tails)

no difference between the population means

H₀: µ₁−µ₂=0 (Independent samples & two-tails)

no difference between the population means

If a frequency distribution is shown in a bar graph, what scale was used to measure the scores?

nominal or ordinal

p>0.05

not significant, retain H₀

df=df₁+df₂

n₁+n₂−2

Sample size

n₁, n₂

p value

probability of obtaining sample data (obtained z-value) assuming H₀ is true

Type I error

probability of rejecting the null hypothesis when H₀ is true; probability of falsely concluding that there is an effect when there is no effect

Type II error

probability of retaining the null hypothesis when H₀ is false; probability of falsely concluding that there is no effect when there is an effect

multiple comparisons

problem where using several t tests can be very inefficient and time consuming

r is sensitive to the

range characterizing the measurements

Hypothesis testing for r: if p< alpha-significant

reject H₀

Repeated-measures research design

research strategy in which the 2 sets of data are obtained from the same groups of participants

Independent-measures research design

research strategy that uses a separate group of participants for each population (between-subjects design)

n

sample size per group

In analysis of variance, what is measured by MS values?

sample variance

SS/df

sample variance

Difference score

score obtained by subtracting 2 scores D=X₂-X₁

p<0.05

significant, reject H₀

σ/√n

standard error of M

√(σ²/n)

standard error of M

alternative hypothesis

states that at least one mean is different from the others

One-tailed test (directional hypothesis test)

statistical hypotheses specify either an increase or decrease in the population mean, they make a statement about the direction of the effect

Hypothesis test

statistical method that uses sample data to evaluate a hypothesis about a population

z-statistic

statistical significance test used to test hypotheses about an unknown population mean when the original population mean (µ) and SD (σ) are known

t-statistic

statistical significance test used to test hypotheses about an unknown population mean when the original population mean (µ) is known, but population standard deviation (SD) σ is unknown

Two-tailed test

statistical test in which the critical area of a distribution is two sided and tests whether a sample is either greater than or less than a certain range of values

Standard deviation (for sample)

s₁, s₂

Variance (for sample)

s₁², s₂²

mean difference between groups/standard error

t

Repeated-measures design (pre-post design)

t-test for 2 related samples used to test a hypothesis about the population mean difference between 2 treatment conditions using sample data from a repeated from a repeated-measures study -data consists of 2 scores for each individual

the alpha level is impacted by multiple t tests

test-wise alpha and experiment-wise alpha

Counterbalance

testing different participants under the different conditions in different orders

In a hypothesis test, if an independent-measures t statistic has a value of zero, then

the 2 sample means must be equal

the bigger the between-treatment variance compared with the within-treatment variance....

the BIGGER the f ratio

test-wise alpha

the alpha level for a specific test

experiment-wise alpha

the alpha level for the whole study (with every comparison this increases, type 1 error increases)

Distribution of sample means

the collection of sample means for all of the possible random samples of a particular size (n) that can be obtained from a population

t-distribution

the complete set of t-values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df); approximates the shape of a normal distribution

levels

the conditions or groups that make up the factor

Sampling error

the discrepancy that exists between sample statistic and the corresponding population parameter

factor

the independent variable

Law of large numbers

the larger the n, the smaller the standard error is and the more accurately the sample represents its population

What is directly addressed by the null hypothesis?

the population after treatment

For a two-tailed hypothesis test evaluating a Pearson correlation, what is stated by the null hypothesis?

the population correlation is zero

Which of the following is the most appropriate response to the question "what is the correlation of abstract reasoning (X) for a group of high school seniors?"

the question is meaningless

Value of correlation is affected by

the range of scores in the data

ANOVA allows...

the researcher to control the experiment-wise alpha level

What is a serious concern with repeated-measures study?

the results will be influenced by order effects

A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment. If all of the participants show improved performance of 8 or 9 points after treatment, then the researcher should find___.

the sample mean difference is near zero.

between-treatment variance is computed for...

the sample means

Even a single outlier can have a dramatic effect on r when

the sample size is small

What term is used to identify the standard deviation of the distribution of sample means?

the standard error of M

What is a fundamental difference between the t-statistic and a z-score?

the t-statistic uses the sample variance in place of the population variance

In an independent-measures hypothesis test, what must be true if t=0?

the two sample means must be equal

null hypothesis in terms of variance

the variance between population means is zero

alternative hypothesis in terms of variance

the variance is bigger than zero

H₁: µD≠0 (Related samples & two-tails)

there is a difference between the population means

H₁: µ₁−µ₂≠0 (Independent samples & two-tails)

there is a difference between the population means

The null hypothesis for the independent-measures t-test states

there is no difference between the 2 population means

What is the purpose for post hoc tests?

to determine which treatments are significantly different

N

total sample size for all groups

A correlation of r=-0.90 means that the data points cluster closely around a line that slopes down from left to right

true

A researcher obtained a correlation of r=+0.62 between the amount of time spent watching television and level of blood cholesterol. This means that there is a general tendency for people who watch more television also to have higher blood cholesterol

true

Pearson correlation of r=-1.00 means that all the data points fit perfectly on a straight line

true

What would produce the largest value for an independent-measures t statistic?

two sample means that are close together & values that have a small variance

Estimated standard error

used as an estimate of the real standard error, when the value of σ is unknown, it is computed from the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean, M, and the population mean, µ.

Degrees of freedom

used to describe how well the t-statistic represents a z-score

mean squares (MS)

variance in ANOVA

Confidence interval

when an interval estimate is accompanied by a specific level of confidence (or probability)

Practice effects

when similar tasks (Task A & Task B) are presented twice, participants often get better at the Task B because of practice

When interpreting correlation coefficient several things have to be considered EXCEPT

whether X and Y variables are measured in the same scales

(M-µ)/σ

z-score

Which of the following z-score values represents the location closest to the mean?

z=+0.5

Population mean

µ₁, µ₂

Which of the following is the correct null hypothesis for an independent-measures t-test?

µ₁−µ₂=0

effect size

η² eta squared

small effect

η²=0.01

medium effect

η²=0.06

large effect

η²=0.14

% of variance in DV (dependent variable) can be explained by IV (independent variable)

η²×100=

SP∨xy

∑(X-M∨x)(Y-M∨y)

SS∨x

∑(X-M∨x)²

SS∨y

∑(Y-M∨y)²

K

# of treatments or means

Alpha level

(level of significance) probability value that is used to define the very unlikely outcomes if the null hypothesis is true

Cohen's d

(mean difference)/(pooled variance)

r

(∑(X-M∨x)(Y-M∨y))/(√∑(X-M∨x)² × (Y-M∨y)²)

Which of the following are requirements of a random sample?

--every individual has an equal chance to be selected --the probabilities cannot change during a series of selections --there must be a sampling replacement

A scatter plot shows data points that are widely scattered around a line that slopes down to the right. Which of the following values would be closest to the correlation for theses data?

-0.40

Alternative hypothesis

-Research hypothesis (H₁) -Hypothesis that has an effect, a difference, change, and something happened

Null hypothesis

-Statistical hypothesis (H₀) -Hypothesis that has no effect, no difference, no change, nothing happened

What are examples of dependent samples?

-samples that are biologically related or related by some important variable (husband-wife, twin pair, siblings) -each subject in one sample is matched on some relevant variable with a subject in the other sample -a group may be measured twice, such as pretest -postest situation

two sources of variance

-the treatment is causing scores to be different from one another -individual differences or error unrelated to the treatment

If the null hypothesis is true, the t statistic (on average) should have a value of

0 (zero)

On average, what value is expected for the t-statistic when the null hypothesis is true?

0 (zero)

Suppose the correlation between height and weight for adults is +0.60. What proportion (or percent) of the variability in weight can be explained by the relationship with height?

40% 100-60=40

The 80% confidence interval for the difference between 2 population means extends from 6.00 to 12.00. Based on this information you can conclude that the difference between the 2 sample means was?

9 points (calculated by finding what mean difference was in M₁−M₂±tcv(sm₁-sm₂); the middle value of the values given is the answer)

the numerator of the F-ratio

A treatment effect refers to differences between scores that are caused by the different treatment conditions. The differences (or variability) produced by treatment effects will contribute to

F values always will be positive numbers

Because the F-test is computed from 2 variances,

difference in means across groups (treatments or conditions)

Between-group variability

(M-µ)/s

Cohen's d

d=(M₁−M₂)/sp

Cohen's d

Subsequent calculations are based on

D rather than raw scores (X)

variable that is observed for changes in order to assess the effect of the treat

Dependent variable (DV)

the denominator of the F-ratio it provides a measure of the amount of variance due to chance

Error term

the overall probability of a Type 1 error that accumulates over a series of separate hypothesis tests and is usually substantially greater than the stated alpha for any of the individual tests

Experimentalwise alpha level

variance (differences) between treatments/ variance (differences) expected with no treatment effect

F

positively skewed

F-sampling distribution is

Fatigue effects

If a task requires tremendous effort & time, participants may get tired at Task B & produce worse performance

a significant difference between treatments

If the numerator is sufficiently bigger than the denominator, then there is

a greater amount of between-group variables & a smaller amount of within-group variables

If we want a very large F-score, we need

Between-group variability because it is associated with treatment/experimental effect

If you are a researcher, which variability would you hope to be large, between or within?

sum of squares (SS) and variance that standard deviation

In ANOVA, variability is more often denoted with

the sum of df∨between and df∨within

In an analysis of variance, df∨total will always equal

0, because the values don't vary

In an independent-measures experiment with 3 treatment conditions, all 3 treatments have the same mean, M₁=M₂=M₃. For these data SS∨between equals?

variance

In analysis of variance MS provides a measure of

2 variances

In analysis of variance, the F-ratio is a ratio of

An independent (or quasi-independent) variable

In analysis of variance, what is a factor?

positively skewed with all values greater than or equal to zero

In general the distribution of F-ratios is

the null hypothesis is wrong

In general, a large value for an F-ratio indicates that

MS∨within

In the F-ratio, what value is the denominator?

MS∨between

In the F-ratio, what value is the numerator?

variable that is manipulated by the researcher; usually consists of the 2 (or more) treatment conditions to which subjects are exposed

Independent variable (IV)


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