Quant Methods in Psych Exam Conceptual Final
When all of the points in a scatterplot lie on the regression line, the correlation between the two variables must be
+/- 1.0
When all the points on a scatter plot lie directly on the regression line, then the value of the correlation must be
+/-1
With respect to z-scores, for any sample the mean is always ___ and the SD is always
0, 1
If the regression lime has a slope of 0.5, then each single unit increase in X will be accompanied by how much of an increase in Y?
0.5
If the Pearson's r between variables X and Y is -.50, how much of variance in Y can be predicted by X?
25%; coefficient of determination = r squared
A frequency distribution would be mesokurtic if its standard deviation was 8 and its range was
48
If we use an alpha of .05 when testing the null hypothesis, what is the probability of incorrectly rejecting the null hypothesis?
5%
Using an alpha of .05 means the probability of making a Type I error is
5%
If we use an alpha of .01 when testing the null hypothesis, what is the probability of making a Type II error?
99%
Why is the term 2r(SEM1)(SEM2) not included in the independent samples t-test?
Because the r is assumed to be 0 in the independent samples t-test
If we do not have the population standard deviation, why can we not use the z-table to determine whether a sample mean is representative of a population?
Because we must estimate the SEM and the hypothetical distribution is more platykurtic except at N = ∞
Why do we conduct a post-hoc test if we find a significant F in a one-way ANOVA?
Because you don't know which means differ from which other ones when there are more than two of them.
When an ANOVA results in the rejection of the null hypothesis, then the ____ variability must be larger than the ______ variability.
Between-group and within-group
In the F statistic, the sum of squares between is influenced by
Differences between each group mean and the grand mean
In linear regression, if the slope is -.25, which of the following is true?
Every unit increase in X will result in a 1/4 unit decrease in Y
For equal numbers of scores, the paired t has more degrees of freedom than does the independent t
False, although it's N - 1 for paired samples and N - 2 for independent samples, N is # pairs of scores in paired samples t while it's # scores in independent samples t
Assuming that the mean differences and standard deviations are constant, you are less likely to reject the null hypothesis when using a paired-samples t-test than an independent samples t-test.
False, you are more likely to
In a 1-way ANOVA, if the sum of squares between remains constant and the number of means being compared increases, you are more likely to find a significant difference among the means.
False; ^#means -> ^dfb -> smaller MSb -> smaller F so less likely to beat the critical value
For an independent samples t-test and a paired samples t-test with same number of subjects, the degrees of freedom would be the same.
False; it's N - 1 for paired samples and N - 2 for independent samples
In an independent samples t-test, the value of t tells you what?
How many estimated standard errors of the difference you are above or below 0
The term -2r(SEM1)(SEM2) in the paired samples t-test causes the t-ratio to be ________ than it would if the term were excluded.
Larger; it makes the denominator smaller
If the within-group variability is small, then the separate sample groups are most likely to have (platykurtic or leptokurtic) distributions
Leptokurtic (all the scores are close to the cell mean)
Which of the following, if any, is true with respect to Pearson's r?
NOT that the variables must be ordinal, The ranges of values for X and Y can be no greater than + or minus 1 SD of their means., or the form of the relationship between X and Y can be non-linear; none of the above
When the data are in interval form and the distributions are normal, which correlation coefficient should be used?
Pearson's r
When the array of data points in a scatter plot slopes from lower left to upper right, is the correlation indicating a positive sign, or is it indicating a negative sign?
Positive
The total sum of squares is made up of two components, the _____, and the _____.
SSbetween and SSwithin
in the question about the drug and age relationship with hyperactivity, which F values would be most likely to be significant?
The F for the interaction
Within-group variability results from the accumulated differences between each individual score and ______.
The cell mean in which the score is located
Which of the following is used in determining the degrees of freedom between in the F-test?
The number of groups being compared
Why does the array of points in a scatter plot usually form an oval shape
There are most points in the middle of most distributions and fewer points on either extreme
Chi square can be used only if the frequency expected value of all cell entries is at least 5
True
To do a factorial ANOVA, there must be a minimum of at least four different treatment conditions
True (2 x 2 is the smallest possible)
If the correlation between X and Y is high and the correlation between X and X is high, then the correlation between Y and Z must be high
True; all 3 are sharing a lot of the same variance
In a hypothetical study, a researcher wanted to see if there was any effect of 3 different drugs on whether or not people with asthma experienced improvement (i.e., she asked them whether they felt better or not after taking the drug). The appropriate test would be
a chi-square
With respect to experimental data, the denominator in the t-ratio represents the variation in the dependent variable due to
all sources of variation except the independent variable
A study found that, compared to a placebo, a drug intended to reduce hyperactivity in teenagers reduced hyperactivity in those under 15, but increased hyperactivity in those under 15. This result would be described as
an interaction between the drug and age; interactions occur only between IVs when the effect of one IV (the drug) depends on the level of a 2nd IV (the age), so it couldn't be an interaction between age and hyperactivity
In the χ2 test, the null hypothesis is that
any difference between the frequency observed and the frequency expected is due to sampling error
When doing a t-test, our obtained t-value must ________ the critical value in the table (for the designated degrees of freedom) in order to _________ the null hypothesis.
be equal to or greater than; reject
The greater the spread among the various sample means, the larger the (between or within) variability.
between
A negative z-score means that the value is
between the 0 and 50th percentile
The null hypothesis for the single-sample t-test is that any difference between the sample mean and the population mean is due to
chance, random variation, and sampling error
The effect size statistic for the paired-samples t-test is
cohen's d
As σ gets smaller, the standard error of the mean would
decrease
With respect to an independent samples t-test, as the sample SDs get larger, the probability of rejecting the null hypothesis
decreases
In a single-sample t-test, as the sample SD increases, the size of the obtained t-value ____, making it ______ likely to reject the null hypothesis.
decreases; less
The variance, or mean square, results from dividing the sum of squares by _____.
degrees of freedom
In matched-subjects design, the subjects should be equated on some variable(s) that is/are related to the (dependent or independent) variable.
dependant
A five-group research design with six subjects in each group has _____ between degrees of freedom and ______ within degrees of freedom
dfb=4; dfw=25; dfb=#levels-1 and dfw=N-#levels
Each single data point on a scatter plot represents
each individual score on X and Y
The computed value of t in an independent samples t test tells you how many ______ you are from ______
estimated standard errors of the difference; 0
In the paired samples t-test, the value of t tells you how many _______ you are from ______________.
estimated std. errors of the difference ; 0
The effect size statistic for the 1-way ANOVA is
eta-squared
In the t-statistic, the denominator represents variability in the DV due to ____________, while the numerator represents variability in the DV due to _______.
everything except the independent variable; the independent variable and sampling error.
A correlation of =.75 must be significant, regardless of the degrees of freedom
false
If X correlated significantly with Y, then X is probably the cause of Y
false
If a researcher asks subjects to identify their sexual orientation as either heterosexual, homosexual, or bisexual, sexual orientation is being measured on an ordinal level.
false
If the correlation between X and Y is zero, the best predictor of the value of Y is the mean of X.
false
In addition to an interval-ratio level predictor,a nominal predictor can also be used in linear regression analysis.
false
In experimental research, the dependent variable represents the cause, and the independent variable represents the effect.
false
In linear regression, the intercept is the value of X when the value of Y is 0
false
In linear regression, the mean value of all residuals will be greater for a correlation of -.70 than for a correlation of +.60.
false
On a factorial ANOVA, the interaction effect will always be significant if the main effects are themselves significant
false
The higher the correlation, the more a predicted Y value may deviate from the mean of the Y distribution
false
The paired t ratio may never be used for making population inferences
false
The t-test or the z-test can be used if the dependent variable is nominal.
false
Whenever a correlation is significant, the possibility of a cause-and-effect relationship is totally ruled out
false
With respect to a factorial ANOVA, if both main effects are significant, the interaction must also be significant.
false
If the range of either set of sample scores is in any way restricted, the Pearson r will overestimate the degree of correlation
false, it will underestimate it
On a four-group design, the between degrees of freedom for a one-way ANOVA must equal 4
false, it's three dfb=#levels-1
The type 2 error occurs when the null hypothesis is rejected when it should not have been
false, that's a type 1 error
When the obtained value of F is larger than the table value of F for a given number of degrees of freedom, the null hypothesis cannot be rejected
false, the null hypothesis IS rejected
ANOVA demands that at least four sample groups must be compared
false, three is enough
Negative correlations, even when significant, never predict better than chance
false; Significant correlations always predict better than chance
The Pearson r assumes that the association between X and Y is always curvilinear
false; it assumes it's linear since nonlinear relationships would not yield significant results
The null hypothesis for the chi-square test is
fo=fe
As σ gets larger, the standard error of the mean would _____ making it _____ likely to reject the null hypothesis.
increase, less
As the value of an inferential statistic (e.g., t, z, χ2, etc.) decreases, the probability that the null hypothesis is true
increases
With respect to the paired-samples t-test, as the size of the r increases, the t-ratio _____ making it ________ to reject the null hypothesis.
increases, more likely; ^r -> smaller denominator -> larger t ratio
In a one-way ANOVA, as the sum of squares within increases, the probability of accepting the null hypothesis
increases; ^SSw -> ^MSw -> F-MSb/MSw
A researcher hypothesizes that a sample of men will score lower than a sample of women on the Compassion and Empathy Scale, an interval-ratio level measure. The statistical test to use would be the
independent samples t test
If a researcher wanted to determine if there was a difference between a sample of lawyers and a sample of doctors in their annual income (measured in dollars) the appropriate inferential statistic to use would be the
independent samples t test
If a researcher wanted to determine if there was a difference between a sample of Democrats and a sample of Republicans in their annual income (measured in dollars) the appropriate inferential statistic to use would be the
independent samples t-test
The paired t and the within-subjects F should be used only when the data are in the form of at least (interval, ordinal, or nominal) measures
interval
A z-test or t-test can be used when the dependent variable is
interval/ratio
Which of the following is TRUE with respect to the standard deviation?
it can be 0, its value depends on the sample size, it cannot be negative, it functions as a denominator when computing z-score, and it can never be more than ½ the range
Which of the following is FALSE with respect to the standard deviation?
it can never be zero
When calculating the paired t ratio, what effect does a substantial correlation have on the size of the resulting t ratio?
it increases t; by reducing the size of the est SEdiff
Which of the following is false with respect to the sampling distribution of the difference?
it is the basis for the single-sample t-test
In a sample of high school runners' times in the 1600 meters, the mode was 4:50, the mean was 4:35, and the median was 4:42. What can we say about the distribution?:
it's negatively skewed
In a sample of salaries in a company, the mean is $60K, the median is $62.5K, and the mode is $65K. What can we say about the distribution?
it's negatively skewed
Which of the following is false with respect to the sampling distribution of the mean?
its mean must always be zero
Which of the following, if any, are characteristics of the normal distribution?
its mean, median, and mode are all equal, its form is mesokurtic (SD=1/6 range), and the areas under the curve are fixed
When a calculated F ratio has a large value, it indicates that the variability between groups is (larger or smaller) than the variability within groups
larger; F = MSbetween/MSwithin
The single straight line that lies closest to all the points on a scatter plot
least squares regression line (LSRL)
Given a data set with a standard deviation of 7 and a range of 60, you should conclude that the distribution is
leptokurtic
The sampling distribution of the _________ is a frequency distribution of an infinite number of _______ taken from the same _____.
mean; sample means; population
When dealing with a skewed distribution, which measure of central tendency is most valid?
median
The regression line represents the line that
minimizes the residuals when using the value of X to predict the value of Y, intersects the Y axis at the point where the X variable equals 0, and slopes downward when the correlation between x and Y is negative
When all its assumptions are met, the paired t is (more or less able) than the independent t to reject null when only a small difference exists between the sample means
more; due to smaller est SEdiff
The correlation between a criterion variable and several predictor variables
multiple R
Normal distributions
must have a standard deviation equal to ⅙ of the range, have an equal mean, median, and mode, and the percentage of cases between the mean and a value 1 SD above the mean, must be identical to the percentage of cases between the mean and a value 1 SD below the mean
Most likely sign of the correlation between the number of visible police cruisers on the highway and the number of cars exceeding the speed limit
negative
When the regression line slopes from upper left to lower right, then the sign of the correlation must be
negative
With respect to the level of measurement, for a chi-square test, the dependent variable is _____ and the independent variable is ______.
nominal, nominal
A researcher hypothesizes that left-handed subjects will score higher on the Picture Arrangement Test (PAT) than right-handed subjects. The design is ____; the dependent variable is ____; the independent variable is _____.
non-experimental; scores on the PAT; whether the subject is right or left-handed
In linear regression analysis, if the slope is +.50, which of the following is true?
not that you can predict the variance in Y from the value of X.
If class rank were the variable we were using, the level of measurement would be
ordinal
When both the independent and dependent variables are interval/ratio level, which statistical test should be used?
pearson's r
Inferential statistics (such as the independent samples t and chi-square) are referred to as 'inferential' because they are used to draw conclusions about ___ from ___.
populations, samples
Inferential statistics (such as the independent samples t and chi-square) are referred to as 'inferential' because they are used to draw conclusions about ___ from ___.
populations; samples
Most likely sign of the correlation between the amount of media news coverage of crime and the public's fear of crime
positive
Most likely sign of the correlation between the higher a person's score on the SOGS, a test of gambling addictions, the more moving-violation citations the person has had
positive
Most likely sign of the correlation between the more a person uses illegal drugs, the greater the likelihood of illness and premature death
positive
The coefficient of determination is equal to _______ and tells us ___________.
r squared; the % of variability in Y accounted for by X
The resulting correlation between two variables when the effects of a third variable have been statistically ruled out
r; correlation
Assuming that a sample is taken at random from a population, any difference between the sample mean and the population mean is referred to as
sampling error
When we fail to reject H0, we are concluding that the results (e.g., the difference between means) are due to
sampling error
When you know the population mean, but the population standard deviation is unknown, and you want to determine if a sample mean is "significantly different" from the population mean, you should use a(n)
single sample t-test
In linear regression, the change in value of Y that occurs with each unit change in X is referred to as the
slope
The amount of increase in Y that accompanies a given increase in X
slope
The average distance from the mean in a set of measurements in a sample is the conceptual definition of the
standard deviation
The sampling distribution of the mean has a standard deviation referred to as the
standard error of the mean
The standard error of the difference is
the SD of the sampling distribution of the difference
The standard error of the mean is
the SD of the sampling distribution of the mean
A political scientist wants to find out if voters are more likely to prefer a senate candidate who is in favor of strict enforcement of immigration laws. She describes two candidates, each the same except that one supports strict enforcement while the other does not. She then asks a sample of voters which candidate they would vote for. The correct statistical test to use would be
the chi-square test
With respect to the t-table, with an extremely large sample size (i.e., N = ∞ ) which of the following is true
the critical values of t become virtually identical to those in the Z table (e.g., 1.96 for α = .05, 2-tailed)
In an experiment, the numerator in the F statistic is a measure of
the effect of the independent variable on the dependent variable
The fact that the paired t has fewer degrees of freedom than does its independent counterpart, and that fact alone, has what effect on the probability of achieving significance
the fact alone decreases it
Between-group variability results from the accumulated differences between each sample mean and _____.
the grand mean
Total variability results from the accumulated differences between each individual score and _____.
the grand mean
With respect to experimental data, the numerator in the t-ratio represents the variation in the dependent variable due to
the independent variable and sampling error
Whether or not a mean difference between two samples is statistically significant depends on
the magnitude of the difference, the size of the sample, and the amount of random variation within each sample
In linear regression analysis, the intercept is determined by what factors?
the mean of X, the mean of Y, and the slope of the regression line
With respect to the "sampling distribution of the mean,"
the mean, median, and mode must all be equal to the population mean and the distribution of the means must be normal, even if the actual population distribution from which the samples are taken is not
The degrees of freedom for the chi-square statistic is influenced by which of the following?
the number of rows and columns in the contingency table
In estimating the standard error of the mean, we use the sample SD, but then divide it by the square root of N-1 instead of N. Why?
the sample SD is a biased estimate, consistently underestimating the population SD
The slope of the regression line is determined by
the standard deviation of both X and Y, the sign and absolute value of Pearson's R for X and Y
If the F statistic is significant in the 1-way ANOVA, the next step to take would be
to reject the null hypothesis and conduct a post-hoc test
ANOVA assumes that the data are at least interval
true
Chi square may be used only with nominal data
true
Effect size may only be applied to the paired t when the t ratio has been shown to be significant.
true
For the Pearson's r, degrees of freedom are assigned on the bases of the number of paires of scores minus the constant 2
true
If X correlates 0.9 with Y, then Y must also correlate 0.9 with X
true
In a factorial ANOVA, when neither main effect is significant, the interaction may still be significant.
true
In a linear regression analysis, the higher the Pearson's r, the lower the values of the residuals
true
No correlation is ever greater than +1 or less than -1
true
Only if the researcher manipulates an independent variable can a study be considered an experiment.
true
Significant correlations always predict better than chance
true
The F ratio is a non-directional, two-tail test of differences among sample groups used whenever data are in interval form
true
The more a correlation deviates from 0, the better its predictive accuracy
true
The paired t has as its ultimate goal the detection of differences between two sets of interval measures when the data sets are correlated
true
The paired t may test only the hypothesis of association, whereas the independent t may test the hypothesis of difference as well
true
The reason there is only one number shown for degrees of freedom in any t-test is that the degrees of freedom between must always be 1.
true
The use of the factorial ANOVA is required whenever there is more than one independent variable and the data are in interval form
true
To test for "goodness of fit" a 1 X K chi square may be performed
true
To use the Pearson r, both sets of paired scores must be composed of at least interval data
true
chi square is a nonparametric statistical test
true
An F ratio of 5.00 indicates that the variance between groups is 5 times greater than the variance within groups
true; F = MSb/MSw
When an ANOVA results in the rejection of the null hypothesis, the between-group variability must be greater than the within-group variability.
true; F=MSb/MSw and you can't beat the critical value with an F smaller than 1
The higher the correlation between X and Y, the more information about Y is contained in X
true; correlation is % of variability in Y accounted for by X
For both t and F, whether from correlated or independent designs, the more subjects being tested, the greater is the number of degrees of freedom
true; df is determined by # of subjects
In an ANOVA, both the number of levels of the independent variable and the size of the sample influence the degrees of freedom within.
true; dfw= N-#levels
The more degrees of freedom a given t ratio has, the higher the likelihood of rejecting the null hypothesis
true; higher df = smaller SEdiff = larger t value
When comparing correlations from two separate and unmatched samples (other things being equal), the larger the sample sizes, the higher the likelihood of finding a significant difference
true; higher sample size -> smaller denominator -> larger obtained value
A Pearson r of 0.90 means that the percentage of information about Y contained in X is roughly 81%
true; the coefficient of determination is r squared
The higher the Pearson r, the higher the coefficient of determination.
true; the coefficient of determination is r squared
Compared to an alpha level of .01, if we use an alpha level of .05,
we are more likely to make a Type I error
When we reject the null hypothesis
we determine that it is unlikely to be true
The MAIN reason we never prove anything in social science research is that
we draw conclusions about populations from sample data.
A Type I error occurs when
we reject H0 when in fact H0 is true
A researcher predicts that athletes taking nutritional supplements will gain more strength than those not doing so. He randomly assigns them to the supplement/no supplement conditions, then has them all engage in the same training routine after which he determines the amount of strength gained. The independent variable is _____, the dependent variable is _________ and the design is _____
whether or not they get the supplement; gain in strength; experimental
When estimating a population mean using confidence intervals, what determines whether you use a value from the t-table or the z-table?
whether you have the population standard deviation (σ)
With respect to estimating a population mean, compared to a 95% confidence interval, a 99% confidence interval will be
wider
In the regression equation, what term denotes the point where the regression line crosses the ordinate
y-intercept
The value of Y when X equals 0
y-intercept
When you know the population mean (μ) and the population standard deviation (σ), and you want to determine if a sample mean is "significantly different" from the population mean, you should use the
z-test
If, in reality, there really is a difference between the unknown population mean (that a sample represents) and the population mean to which you are comparing it, the probability of making a Type I error is
zero
______ is a parameter, while _____ is a statistic
µ ; SD
Using statistical notation, the null hypothesis for the 2-tailed z-test would be
μ sample = μ population