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98 Cards in this Set
- Front
- Back
what does probability convey about an event's occurrence?
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it's our expectation or confidence in the event
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what is the probability of a random event based on?
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the relative frequency of the event in the population
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what is random sampling?
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selecting a sample so that every individual or score in the population has an equal chance of being selected
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what is sampling with replacement
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replacing the individuals or events from a sample break into the population before another sample is selected
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what is sampling without replacement?
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is not replacing the individuals or events from a sample before another is selected
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how does sampling without replacement affect the probability of events, compared to sampling with replacement?
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over successive samples, sampling without replacement increases the probability of an event, because there are fewer events that can occur; with replacement, each probability remains constant
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what are events independent?
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when the occurrence of one does not influence the probability of the other
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what are events dependent?
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when the occurrence of one influences the probability of the other
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what does the term "sampling error" indicate?
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it indicates that by chance, we've selected too many high or low scores so that our sample is unrepresentative. then the mean does not equal (mu) that it represents.
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when testing the representativeness of a sample mean, what is the criterion probability?
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it is the probability that defines means as too unlikely to accept as representing the (mu) of the underlying raw score population
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when testing the representativeness of a sample mean, what is the region of rejection?
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it is the area in the tail(s) of a sampling distribution containing the least likely and least representative sample means
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when testing the representativeness of a sample mean, what is the critical value?
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it is the minimum z-score needed for a sample to lie in the region of rejection
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what does comparing a sample's z-score to the critical value indicate?
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it indicates whether or not the sample's z-score ( and the samples (mean)) lies in the region of rejection
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what is the difference between using both tails verses one tail of the sampling distribution in terms of the size of the region of rejection?
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when using both tails, one-half of the region of rejection is in each tail of the sampling distribution
when using one tail, the entire region of rejection is in one tail of the distribution |
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what is the difference between using both tails verses one tail of the sampling distribution in terms of the critical value?
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using both tails involves one critical value (usually ± 1.96);
using one tail involves a different critical value (usually ±1.645). |
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why does random sampling produce representative samples?
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because by chance the sample has the same characteristics as the population
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why does random sampling produce unrepresentative samples?
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because by chance the sample does not have the same characteristics as the population
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why, if a sample mean is in the region of rejection,do we reject that the sample represents the underlying raw score population?
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because it is a mean that would virtually never occur if we had been representing that population
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why, if a sample mean is not in the region of rejection do we retain that sample represents the underlying raw score population?
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because we have a mean that occurs frequently and is likely when representing this population
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when we compute the z-score of a sample mean, what must you compute first?
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the standard error of the mean
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when we compute the z-score of a sample mean it describes the mean's location among other means on what distribution?
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the sampling distribution of means
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when we compute the z-score of sample means, what does the distribution show?
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it shows all possible means from a raw score population and their frequency
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Why does the possibility of sampling error present a problem to researchers when inferring a relationship in the population?
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sample may:
1) poorly represent one population because of sampling error or 2) represent some other population |
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what are inferential statistics used for?
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they are used for deciding whether or not sample data are likely to represent a particular relationship in the population
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what does αlpha stand for and what two things does it determine?
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stands for the criterion probability
it determines the size of the region of rejection and the theoretical probability of a Type 1 error |
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what are two major categories for inferential procedures?
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parametric and non parametric procedures
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what characteristics of your data determine which inferential procedure you must use?
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use parametric procedures with a normally distributed, interval, or ratio dependent variable; otherwise use, nonparametric procedure
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what happens if you seriously violate the assumptions of a procedure?
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the true probability of a Type 1 will be larger than our alpha
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what is a statistical reason to design a study so you can use parametric procedures?
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they are more powerful
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what are experimental hypotheses?
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they describe the predicted relationship that may or may not be demonstrated in an experiment
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what does H0 communicate?
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the null hypothesis indicates that the sample represents a population such that the predicted relationship does not exist
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what does Ha communicate?
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the alternative hypothesis indicates that the sample represents a population such that the predicted relationship does exist
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why do you use one-tailed test?
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when predicting the direction the scores will change
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when do you use a two-tailed test?
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when predicting a relationship but not the direction that scores will change
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what does "significant" convey about the results of an experiment?
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the sample relationship was so unlikely to occur if there was not a relationship in nature that we conclude there is a relationship in nature
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why is obtaining significant results a goal of behavioral research?
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because we want to study relationships and we believe that we've found only one when it is significant
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why is declaring the results significant not the final step of the study?
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because the goal is to understand the relationship and behaviors, so the final step is to understand and interpret the relationship.
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what is power?
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the probability of not making a Type II error
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why do researchers want to maximize power?
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so we can detect relationships when they exist and thus learn something about nature.
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what results makes us worry whether we have sufficient power?
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when results are not significant, we worry if we missed a real relationship
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why is a one-tailed test more powerful than a two-tailed?
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in a one-tailed test the critical value is smaller than in a two-tailed test; so the obtained value is more likely to be significant
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What are the advantage and disadvantage of two-tailed test?
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the advantage is that we need not predict the direction in which the IV will change the dependent score
the disadvantage is they are less powerful |
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what are the advantage and disadvantage of one-tailed tests?
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the advantage is they are more powerful
the disadvantage is that we must accurately predict the direction in which the indepndent variable will change the dependent scores |
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when the assumptions of a procedure require normally distributed interval/ratio scores, are we referring to scores on the independent or dependent variable?
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dependent variable
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what distinguishes an interval and ratio variable from nominal or ordinal variables?
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interval and ratio scores measure actual amounts, but an interval variable allows negative scores
nominal variables are categorical variables ordinal scores are the equivalent of 1st, 2nd, etc. |
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what distinguishes a skewed versus a normal distribution?
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a normal distribution is bell shaped and symmetrical with two tails
a skewed distribution is asymmetrical with only one pronounce tail |
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what does a sampling distribution of means show?
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all means that occur by chance when sampling a particular raw score population
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a mean having a z beyond +/- 1.96 is where?
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in the region of rejection
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how often do means in the region of rejection occur when dealing with a particular raw score population?
what does this tell you about your mean? |
if (alpha) = 0.05, then less than 5% of the time
that it is less than a 5% chance of representing the raw score population |
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what is the difference between a real relationship and one produce by sampling error?
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a real relationship occurs in nature (in the"population"). one produced by sampling error occurs by chance, and only in the sample data
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what does a relationship produced by sampling error tell us about nature?
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nothing
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why can no statistical result prove that changing the independent variable causes the dependent score to change?
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because statistics don't "prove" anything
it is always possible that some hidden variable is the cause |
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what one thing does a significant result prove?
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that our sampling mean was unlikely to occur if we were representing a particular raw score population
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why are there different values of t(crit) when samples have different Ns?
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different Ns produce differently shaped t-distributions, so a different t(crit) is needed to demarcate a region of rejection equal to (alpha)
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what must you determine in order to find t(crit)?
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the degrees of freedom?
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what is the symbol for Pearson correlation coefficient in the population?
summarize the steps involved in analyzing a Pearson correlational study |
p
determine if the coefficient is significant by comparing it to the appropriate critical value; if the coefficient is significant, compute the regression equation and graph it, compute the proportion of variance accounted for, and interpret the relationship |
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summarize the steps involved in analyzing the results of a one-sample experiment
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create a hypothesis and design a study to obtain (mean) of dependent scores under one condition to compare to known (mu) under another condition ; determine if (mean) differs significantly from (mu) ; if it does, compute confidence interval for (mu) being represented, and interpret relationship psychologically
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what is the final step when results are significant in any study?
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to describe the relationship and interpret it psychologically, sociologically. etc.
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what is power?
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the probability of rejecting Ho when it is false (not making a Type II error)
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what outcome should cause you to worry about having sufficient power?
why? |
when a result is not significant
because then we may have made a Type II error |
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at what stage do you build in power?
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when designing a study
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what are the three aspects of maximizing the power of a t-test?
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maximizing the difference between (mean) and (mu)
minimizing the variability in independent scores maximizing N |
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what are the three aspects of maximizing the power of a correlation coefficient?
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avoid a restricted range of X or Y
minimize the variability in the Y scores at each X scores maximize N |
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while conducting a one-sample experiment:
what two parametric procedures are available? what is the defining factor for selecting between them? what are other assumptions of the t-test? |
the t-test and z-test
compute z if the standard deviation of the raw score population is known; compute t if raw score population is estimated by Sx that we have 1 random sample of interval or ratio dependent scores, and the scores are approximately normally distributed |
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inferential statistics
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procedures for deciding whether sample data represents a particular relationship in the population
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parametric
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inferential procedures require assumptions about the raw score populations being represented
they are performed when we compute the mean |
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nonparametric
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inferential procedures do not require stringent assumptions about the population being represented. they are performed when we compute the median or mode
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why must a relationship be significant to be important?
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we must first believe that it is a real relationship, which is what significant indicates
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why can a relationship be significant and still be unimportant?
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significant means only that we believe that the relationship exists in the population; a significant relationship is unimportant if it accounts for little of the variance
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whats the difference between the purpose of descriptive and inferential statistics?
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descriptive procedures are for summarizing important characteristics of data;
inferential procedures are for deciding whether the sampling relationship is likely to be found in the population (in nature) |
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when should you use a parametric versus a nonparametric inferential procedure?
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use parametric procedures when the data are normally distributed, interval or ratio scores
use nonparametric with any other type of score |
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what is the design of the study when we compute the z-test and t-test versus when we compute a correlation coefficient?
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the z- and t-test are used to compare the mu of a population when exposed to one condition of the independent variable to the scores in a sample that is exposed to a different condition. a correlation coefficient is used when we have measure the X and Y scores of a sample
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what does a correlation coefficient tell you?
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it indicates the strength of the linear relationship between a set of X and Y scores
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when do you compute r?
rho? |
pearson coefficient with normally distributed, interval or ratio X and Y scoresfor sample rho = population |
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when is linear regression used?
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with a significant Pearson r to predict Y (criterion) scores based on participants' X (predictor) scores
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what do we mean by the restriction of range?
why is it a problem for the size of correlation coefficient? |
when the range of X or Y is limited and artificially small
it produces an artificially small r |
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why is it a problem for the power of a correlation coefficient to have restriction of range?
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a smaller r reduces power, increasing the likelihood that we will miss a relationship that exists in nature
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a scientist has conducted a two sample experiment:
a) what two parametric procedures are available? b) what is the deciding factor for selecting between them? |
the independent-samples t-test and the related samples t-test
whether the scientist created independent samples or related samples |
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how do you create independent samples?
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created when selecting and assigning participants to a sample without considering those selected for the other sample
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what are the two ways to create related samples?
what other assumptions must be met before using either two-sample t-tests? |
each score in one sample is paired with a score in the other sample by matching pairs of participants or by repeatedly measuring the same participants in all conditions
the scores are interval or ratio scores; the population are normal and have homogenous variance |
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what is homogeneity of variance?
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occurs when the variances of the populations represented in our study are equal
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what is the difference between n and N?
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n is the number of scores in each condition
N is the number of scores in the experiment |
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all other things being equal, should you create a related-samples or an independent-samples design? why?
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a reason to prefer a related design, if appropriate, is because the related samples t-test is more powerful
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what does the confidence interval for mu(d) indicate?
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it indicates a range of values of mu(d), any one of which (D) is likely to represent
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what does a confidence interval for the difference between two (mu)s indicate?
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it indicates a range of differences between two (mu)s, one of which is likely to be represented by the difference between our sample means
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what does effect size indicate?
what does d indicate? |
it indicates the size of the influence that the independent variable had one dependent scores
it measures effect size using the magnitude of the difference between the means of the conditions |
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why is effect size useful during the final task after completing the analysis of significant results?
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because it indicates the size of the impact the independent variable has on the dependent variable and the behavior it reflects
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after obtaining a statistically significant two sample t(obt) what are three things you should do to complete your analysis?
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graph the results, compute the appropriate confidence interval, and compute the effect size
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what is the difference between an experiment vs a correlation study in terms of the design?
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we actively change one (independent) variable and measure the other to produce a relationship vs simply measuring two variables to observe a relationship that might be present
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what is the difference between an experiment vs a correlation study in terms of how we examine the relationship?
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we compute the mean in each condition to see if dependent scores change as the conditions change vs computing the correlation coefficient to summarize the entire relationship at once
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what is the difference between an experiment vs a correlation study in terms of how sampling error might play a role?
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sampling error might produce misleading (means) by chance vs producing the misleading correlation coefficient by chance
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what does it mean to "account for variance"?
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to predict Y scores by knowing someone's X score
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how do we predict score in an experiment?
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we predict the mean of a condition for participants in the condition
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which variable is an experiment is potentially the good predictor and important?
when does that occur? |
independent variable
when the predicted mean score is close to most participants' actual score |
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in an experiment. what are three ways to try to maximize power?
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produce large differences between the means of the conditions; have small variability in scores within each condition; take a large n in each condition
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what does maximizing power do in terms of our errors?
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it minimizes the chances of making a Type II error
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for what outcome is it most important for us to have maximum power and why?
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if the results are not significant, so we can be confident that we did not miss a relationship that exists in nature
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you have performed a one-tailed t-test. when computing a confidence interval, should you use the one tailed or two tailed t(crit)?
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a confidence interval always uses the two-tailed t(crit)
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