PSY 211QR Final Exam 2.0
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)
