Statistics- Final Exam
Pearson correlation coefficient is only appropriate when:
The variables are linearly related
Convergent Validity
a measure correlates with variables with which it is expected to correlate
Discriminate Validity
a measure does not correlate with variables to which it should be unrelated
As sample size increases, the distribution of scores in the sample:
approaches the shape of the distribution of scores in the population.
Ratio Variable
are interval variables, but with the added condition that 0 (zero) of the measurement indicates that there is none of that variable.
descriptive statistics
brief descriptive coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of it. Descriptive statistics are broken down into measures of central tendency and measures of variability, or spread.
Interval Estimate
based on our sample statistic, a range of sample statistics we would expect if we repeatedly sampled from the same population (e.g., confidence interval)
Another name for a paired-samples t test is:
Dependent samples t-test
Other factors remaining constant, how does SM affect the width of a confidence interval?
If SM is larger then the confidence interval will be wider.
Inferential statistics
makes inferences about populations using data drawn from the population. Instead of using the entire population to gather the data, the statistician will collect a sample or samples from the millions of residents and make inferences about the entire population using the sample.
Meta-Analysis
considers many studies simultaneously to estimate an overall effect size.
One-Tailed Test
directional hypothesis, only one critical value/region (doubles the odds of finding an effect in a particular direction)
The main difference between an interval variable and a ratio variable is that an interval variable:
does not have a true zero point.
Within-Groups Designs
he same people experience all conditions/levels of the independent variable •Each person is their own control. •Comparisons are made within the person.
p-value
probability of obtaining a test statistic at least as extreme as the one observed if the null hypothesis (H0) is true
The p value is the:
probability of obtaining a test statistic at least as extreme as the one observed, given that the null hypothesis is true.
Operational Definition
the specific methods used to measure or represent the variables of interest
Outlier analysis
the study of factors that influence the dependent variable.
Parametric Tests
inferential statistical tests based on assumptions about populations
In a dependent-samples t test, the null hypothesis posits that the mean of the comparison distribution is:
0
When calculating variance, the mean of the deviations is always equal to:
0
Central Limit Theorem
A distribution of means will be approximately normal if N is large enough (30+).
In general how does the pooled variance estimate impact the results of an independent-samples t test?
A smaller pooled variance estimate makes it more likely that we will reject the null hypothesis.
zScores
Az score is a measure of the distance between a raw score (X) and a population mean (μ) for a given standard deviation (σ).
As sample size increases, the shape of the sampling distribution of the mean:
Becomes narrower
Discrete Variables
Can only take on specific values, such as whole numbers.
Roman wanted to assess the internal consistency of his measure of happiness so he measured reliability estimates by comparing items within his test. He reported a reliability estimate of 0.75. What measure of reliability is Roman using?
Coefficient alpha
As sample size increases, the standard error:
Decreases
Between-Groups Designs
Different people complete the tasks, and comparisons are made across groups.
Other things being equal, a larger sample size will _______ effect size.
Have no effect on
Variability
How far is a typical value from the center (mean or median) of a distribution?
How is the formula for Cohen's d different from the formula for the independent-samples t test?
How is the formula for Cohen's d different from the formula for the independent-samples t test?
Other factors remaining constant, how does Sdifference affect the width of a confidence interval?
If it is large then the confidence interval will be wider.
Test-Retest Reliability
If nothing has changed, two administrations of the same test should result in similar measurements (provide consistent information).
Robust
In many cases, parametric tests can provide useful answers even when assumptions are violated
Mehl (2007) published in the journal Science the results of an extensive study of 396 men and women, comparing the number of words uttered per day by each sex. What statistical test should Mehl use to analyze the data?
Independent samples t-test
non-parametric tests
Inferential statistical analyses that are NOT based on a set of assumptions about the population
What is the primary difference between descriptive and inferential statistics?
Inferential statistics allow researchers to draw conclusions about populations while descriptive statistics simply organize and summarize data.
Pearson correlation coefficient can be used with what kind of data?
Interval or ratio data.
A measure is said to be valid if:
It measures what it's supposed to measure
Linear Transformations
Linear transformations include adding, subtracting, multiplying by, and/or dividing by a constant (k).
Outliers have the greatest effect on the:
Mean
After grading all of her philosophy exams, Sylvia realizes that the distribution of scores is positively skewed. Which measure of central tendency would be most appropriate for Sylvia to use in this example?
Median
If our data is nominal we should use _________ as a measure of central tendency.
Mode
As sample size gets larger the t distributions get:
Narrower
Nominal Variable
Nominal variables have two or more categories without having any kind of natural order
A bar graph is usually used with __________ data, while a histogram is used with _________ data.
Nominal, scale
In a within-groups design where each participant is measured twice, the appropriate hypothesis test is a(n):
Paired sample t-test
Order Effects
Participants' behavior may change when the dependent variable is measured a second time (also called practice effects).
Gambler's Fallacy
People often mistakenly assume that probability changes depending on past events that are independent.
The type of sampling that leads to a representative sample is _______ sampling.
Random
When calculating a confidence interval for a paired-samples t test, what value should be at the center?
Sample mean difference
A newspaper article reported that the typical American family spent an average of $81 for Halloween candy and costumes last year. A sample of 16 families this year reported spending a mean of $85, with a sample standard deviation of $20. What statistical test would we use to determine whether these data suggest a significant change in holiday spending?
Single sample t-test
What type of statistical test would we use to compare a sample to a population for which we know the mean but not the standard deviation?
Single samples t-test
The ___________ is the most common measure of variability because it uses every score in a distribution and is easy to interpret.
Standard Deviation
psychometrics
The branch of social science that specializes in the development of tests and measures
When calculating a confidence interval for an independent-samples t test, what value should be at the center of the interval?
The difference between sample means
How is the formula for Cohen's d for a paired-samples t test different from the d formula for the single-sample t test?
The mean and standard deviation are for difference scores rather than individual scores.
standardization
The process of converting individual raw scores in a distribution to a set of scores for which we know the percentiles
standard error
The standard deviation of the sampling distribution of means
How does the sampling distribution of means for a sample with N = 5 differ from that of a sample with N = 100?
There is more variance in the sample distribution with N =5 than with N = 100.
If you calculate the standard deviation of a distribution of scores and obtain a value of 0, which of the following statements is necessarily true?
There is no variability in the distribution—that is, all of the scores are the same.
Correlational Studies
Variables are measured, not manipulated.
Counterbalancing
Vary the order of presentation of different levels of the independent variable from one participant to the next to minimize order effects.
Ordinal Variable
a categorical variable for which the possible values are ordered. Ordinal variables can be considered "in between" categorical and quantitative variables.
Directional Hypotheses
a change or difference is expected in a particular direction (effect in the opposite direction would be uninteresting and unimportant)
Non-Directional Hypotheses
a change or difference is expected, but either direction would be interesting or potentially important
Coefficient Alpha
a measure of internal consistency reliability based on the strength of the correlations among items on a measure •Average of all possible split-half correlations •Distinct from alpha level •Often called Cronbach's alpha because it was made famous by psychologist Lee Cronbach. •Generally want 0.80 or higher, but it depends how scores will be used
Interval Variable
a measurement where the difference between two values is meaningful. The difference between a temperature of 100 degrees and 90 degrees is the same difference as between 90 degrees and 80 degrees.
What falls within the 95% confidence interval?
a set of values that will include the population mean 95% of the time when repeatedly sampling from a population
Point Estimate
a single number used to estimate a population parameter - the sample mean (M) is often used to estimate a population mean (μ)
Interpolation
assume that a value between two data points follows the same pattern
Continuous Variables
can take on a whole range of values. How tall are you?
Performing inferential statistics often involves:
comparing the observed mean to a distribution of means.
One of the first steps in calculating the paired-samples t statistic is:
creating a difference score for each pair in the sample.
Type 2 Error
fail to reject the null hypothesis when it is false (false negative)
The difference between the denominator of the z test and that of the single-sample t test is that:
in the z test we divide by the actual population standard error (This answer is set as correct), but in a t test we divide by the sample standard error (This answer is set as correct).
Pooled variance
is a weighted average of the two estimates of variance that are calculated when conducting an independent-samples t test.
Internal Validity
maximize confidence about what causes an effect by ruling out as many alternative explanations as possible in the research design
With very few degrees of freedom, the test statistic:
needs to be more extreme to reject the null hypothesis.
Two-Tailed Test
non-directional hypothesis, two critical values/regions (more conservative)
A point estimate is:
one number used to estimate the population parameter.
In hypothesis testing, the population parameter for the correlation coefficient is represented by:
p (rho)
Expected relative-frequency
probability refers to the likelihood of an event occurring based on the actual outcome of many trials.
Type 1 Error
reject the null hypothesis when it is true
Partial correlation investigates the correlation between two variables after statistically ________ the effect of a third variable.
removing
Sneaky Sample
sample is not from the population that inferences are about - can happen when participants are preselected to promote a certain outcome or self-selected to provide data
Biased Scale
scaling to skew the results
What will impact the width of the confidence interval for an independent-samples t test?
standard error
A calculated effect size of -0.75 for a paired-samples t test would tell us:
that the sample means were 0.75 standard deviation units apart.
Alpha
the "acceptable" probability of a Type I error, used to determine critical value(s)
Expected Relative Frequency Probability
the mathematical expectation of what will happen over the course of many, many observations
A z statistic indicates:
the number of standard errors a sample mean is from the population mean.
Inter-Rater Reliability
two trained individuals evaluating the same thing should provide similar measures.
Ceiling Effect
variable cannot take on values above a certain point
Floor Effect
variable cannot take on values below a certain point
In a two-tailed hypothesis test, a z statistic that is less extreme than the critical values indicates that:
we don't have enough evidence to reject the null hypothesis.
The advantage of standardization is that:
we know the percentiles to which standard scores correspond.
