barnes test 2
e three categories of descriptive statistics that you can use to describe
: 1. How often a score appears in the sample. 2. The central tendency, which is a single score that summarizes the center of the distribution. 3. The variability of scores in your sample, which is the degree to which scores differ from each other.
Uniform distribution
: A non-normal distribution in which all scores or ratings have the same frequency.
Standard error of the estimate (sy′ )
: Average difference between the predicted Y values for each X from the actual Y values.
Outliers
: Responses or observations that deviate greatly from the rest of the data.
Inferential statistics
: Statistical analysis of data gathered from a sample to draw conclusions about a population from which the sample is drawn.
Statistical significance
: When the results of a study fall in the extreme 5% (or 1% if you use a more stringent criterion) of the sampling distribution, suggesting that the obtained findings are not due to chance alone and do not belong to the sampling distribution defined by the H0.
You can use the following descriptive statistics for nominal variables:
Frequencies and/or percentages to describe how often a nominal category appears inthe sample 2. The mode as a measure of central tendency
You can use the following descriptive statistics for ordinal variables:
Frequencies and/or percentages to describe the places or rankings in the sample 2. The median as a measure of central tendency 3. The observed minimum and maximum score or the range as a measure of variability
Practical significance:
The usefulness or everyday impact of results
Critical value:
The value of a statistic that defines the extreme 5% of a distribution for a one-tailed hypothesis or the extreme 2.5% of the distribution for a two-tailed test.
Ceiling effect:
all the scores are squeezed together at the high end
All experimental hypotheses are also
alternative hypotheses, but many alternative hypotheses are not experimental.
Floor effect
an experimental design problem in which independent variable groups score almost the same on a dependent variable, such that all scores fall at the low end of their possible distribution
Inferential statistics refer to statistics used to ______
analyze data from a sample to draw conclusions about a population from which the sample was drawn
Mean (M):
arithmetic average of a group of scores; sum of the scores divided by the number of scores
Correlational studies are used ______.
as a pilot study to examine trends before an experiment is conducted to assess reliability and validity of measures to supplement other studies
The standard error of the estimate represents the ______.
average difference between the predicted Y values (Y′) and their actual values
Malingering
characterized by the intentional creation of false or grossly exaggerated physical or psychological symptoms. respondents might attempt to exaggerate their psychological problems. Particularly in some applied testing contexts, respondents might be strongly motivated to appear more cognitively impaired, emotionally distressed, physically challenged, or psychologically disturbed than they truly are.Criminals might receive relatively mild sentences if they are diagnosed with a mental disorder, workers might receive monetary settlements if they are judged to have suffered an impairment at work
t z scores are standard scores that allow us to
compare scores from different distributions. z scores designate the number of standard deviations a score is from the mean of its distribution
Once you have named null and alternative hypotheses and your criterion level, you compute a statistical test and
compare the finding to the sampling distribution defined by your null hypothesis. If the finding falls in the region of acceptance, you retain the null hypothesis and assume that you do not have support for the alternative hypothesis. If the finding falls in the region of rejection, however, you reject the null hypothesis and accept or support the alternative hypothesis.
range restriction has an effect on
correlation designs
The distribution that is most likely to be normal is a ______ one.
mesokurtic
The ______ is the most appropriate measure of central tendency for a nominal variable.
mode
The mode is the
most frequent score in the sample.
acquiesce bias
s occurs when an individual consistently agrees with statements without regard for the meaning of those statements.
Social desirability bias can be affected by at least three sources
s. First, it can be affected by a test's content. Some psychological constructs have greater implications for social appeal than do others, Second, social desirability bias might be affected by the testing context. Socially desirable responding might be more likely to occur in contexts in which respondents can be identified, A third potential source of socially desirable responding is the personality of the respondent
Variables that affect the strength of the relationship can include
sample size, range restriction,, the sensitivity or validity of our measures, the environment in which data are collected,
pearson showed on what type of graph
scatterplot
The frequency of scores is a and its notation
simple count of how many times that score occurred in the sample, . The statistical notation for frequency is a lowercase and italicized f (
When scores cluster at one end of the distribution, it is said to be ______.
skewed
The effect size is a measure of the ______.
strength or magnitude of a relationship or difference
how to reduce type 1 error
stricter criterion and make it two tailed, because the regions of rejection are split between the two tails of the distribution, and therefore the critical value must be more extreme in order for the results to be considered statistically significant.
ways to minimize bias
testing context-response biases might be minimized by managing the way in which the test is presented to respondents and by managing the demands placed on the respondent within the testing situation.(anonymity, less test fatigue, test content-By choosing specific kinds of items or specific kinds of response formats, neutral questions. s. Test developers have used "forced-choice" items to minimize the existence of social desirability bias. Test developers can also design test formats to minimize the existence of the extremity problem. For example, they can provide only two choices for each item
An important concern about social desirability bias is t
that research results can be compromised. The most significant concern seems to be the possibility that individual differences in social desirability bias can create spurious or artificially strong correlations between measures that are "contaminated" by the bias.
A confidence interval tells you ______.
the margin of error of your results
Suppose, however, that you want to be more confident that your findings do not belong on the sampling distribution defined by your null hypothesis. Then, you might select
the more stringent .01 criterion level, where the region of rejection is composed of only 1% of the sampling distribution
One of the easiest types of effect size to understand is
the percentage of variability in one variable (the dependent variable), which is accounted for by the independent variable (in the case of experiments) or which is accounted for by the relationship with another variable (in the case of correlations)
A percentage is what and how is it calculated
the proportion of a score within a sample. , divide the frequency by the total sample size and multiply the result by 100:
After the first test, your professor found a correlation of r = -.23 between students' self-reported anxiety and test scores. This means that ______.
there is a weak negative relationship between anxiety and test scores
Coding:
The process of categorizing information.
Hypothesis testing:
The process of determining the probability of obtaining a particular result or set of results.
Median (Mdn):
The score that cuts a distribution in half.
Alternative hypothesis (Ha ):
A prediction of what the researcher expects to find in a study.
The potentially important benefits of using balanced scales more than outweigh their meager cost
(incurred by generating negatively keyed items and reverse scoring those items).
Multiple regression (R):
- used to predict a dependent variable based on 2 or more independet (predictor)variables - the statistic used in multiple regression is the multiple correlation coeffcieint, symbolized as R -Dependent variable is continuous (interval or ratio- level data) -Predictor variables are continous (interval or ratio) or dichotomous (branched into two directions) - the correlation index for a dependent varialbe and more than two independen (repdictor) varaibles: R -does not have negative values, shows strength of relationship, not direction - R^2 is an estimate of the proportion of variability in the dependent variable accounted for by all predictors
why should researchers worry about extremity bias
. Studies have shown that differences in the tendency to use extreme response options are fairly stable across measures and across time
represents the unaccounted-for differences in the sample
. The diversity of your sample can be a source of error. This is called within-groups variance (or error variance) and
Key factors that impact the power of a study are:
1. Sample size (larger sample size = more power) 2. Amount of error in the research design (less error = more power) 3. Strength of the effect (stronger effect = more power)
When you have normally distributed interval or ratio data, you should report the following descriptive statistics:
1. The mean as a measure of central tendency 2. The standard deviation as a measure of the variability among scores
Do not report the mean and standard deviation of a skewed distribution. Instead, report:
1. The median as a measure of central tendency 2. The observed minimum and maximum or the range as a measure of the variability among scores It can also be useful to include: 1. A cumulative percentage for the majority of the distribution 2. The possible minimum and maximum for interval scales
If you reject the null hypothesis at p < .02, the probability of a Type I error is ______ and the probability of a Type II error is ______.
2%; zero
Negative correlation:
A relationship where scores on two variables move in opposite directions (one increases while the other decreases).
Positive correlation:
A relationship where scores on two variables move in the same direction (both either increase or decrease).
Standard deviation (SD): SD or SX .
A single number that summarizes the degree to which scores differ from the mean.
Central tendency:
A single score that summarizes the center of the distribution.
Sampling distribution:
A distribution of some statistic obtained from multiple samples of the same size drawn from the same population (e.g., a distribution of means from many samples of 30 students).
Scatter Plot Graph
A graph of plotted points that show the relationship between two sets of data that do not depend on each other where the line is not connected. (Ex. height versus weight)
Two-tailed hypothesis:
A hypothesis stating that results from a sample will differ from the population or another group but without stating how the results will differ.
One-tailed hypothesis:
A hypothesis stating the direction (higher or lower) in which a sample statistic will differ from the population or another group.
Bimodal distribution:
A non-normal distribution that has two peaks.
Skewed distribution:
A non-normal distribution that is asymmetrical, with scores clustering on one side of the distribution and a long tail on the other side.
Platykurtic curve:
A normal distribution that is relatively spread out and flat.
Mesokurtic curve:
A normal distribution with a moderate or middle peak. Leptokurtic curve: A normal distribution with most of the scores in the middle and a sharp peak. Platykurtic curve: A normal distribution that is relatively spread out and flat.
Leptokurtic curve:
A normal distribution with most of the scores in the middle and a sharp peak.
The difference between one-tailed and two-tailed hypotheses is ______.
A one-tailed hypothesis predicts the direction of the difference and a two-tailed hypothesis does not.
Null hypothesis (H0):
A prediction of no difference between groups or no relationship; the hypothesis the researcher expects to reject.
Experimental hypothesis (Ha ):
An alternative hypothesis for an experiment stated in terms of differences between groups.
Region of acceptance:
Area of sampling distribution generally defined by the mean +/−2 SD or 95% of the distribution; results falling in this region imply that our sample belongs to the sampling distribution defined by the H0 and result in the researcher retaining the H0.
Parameters:
Statistics from a population.
______ and ______ are effect sizes.
Cohen's d; proportion of variability accounted for
what is a correlation and correlation design
Correlation: A relationship between variables. Correlational design: A type of study that tests the hypothesis that variables are related.
Confidence interval:
Defines the interval that we are confident contains the population µ represented by our sample mean; typically, we compute the 95% confidence interval. A confidence interval describes the margin of error for a statistic. It tells us the range (or interval) within which we expect our statistic to fall with a certain confidence level.
Point-biserial correlation coefficient (rpb):
Describes the relationship between a dichotomous variable and an interval/ratio variable; interpreted similarly to a Pearson correlation coefficient.
Regression equation:
Equation that describes the relationship between two variables and allows us to predict Y from X. (Y′ = bX + a):
why do we use correlation design
Ethical Issues, Examining Stable Traits or Characteristics There are some variables that we are not able to manipulate or control,s pilot studies to see whether an experiment should be conducted. Supplementing Another Design, Increased External Validity, Assessment of Measurement Reliability and Validity
Histogram:
Graph used to display interval or ratio data in which the frequency of scores is depicted on the y-axis and the interval ratings or ratio scores are depicted on the x-axis. Adjacent bars represent the frequency of each rating or score.
Frequency polygon:
Graph used to display interval or ratio data in which the frequency of scores is depicted on the y-axis and the scores are depicted on the x-axis. Points represent the frequency of each score. The points are connected with straight lines that begin and end on the x-axis.
Types of Response Bias
Guessing, social desirability, acquiescence, random/careless, extremity, malingering
When we use inferential statistics, we ask the question:
Is our sample representative of our population? In other words, does our sample seem to belong to the population, or is it different enough that it likely represents a totally different population?
Which of the following is not a characteristic of a normal distribution?
It is shaped like an upside-down bell or U shape.
Numerical coding:
The process of categorizing and numbering information for quantitative analyses.
Negative skew:
One or a few negative scores skew the distribution in the negative direction, but most of the scores cluster on the positive end of the scale.
Positive skew:
One or a few positive scores skew the distribution in the positive direction, but most of the scores cluster on the negative end of the scale.
o two processes through which socially desirable responding occurs
One process is conscious impression management (IM), where test takers intentionally attempt to appear socially desirable.(statelike). . A second process is an unconscious self-deception (SD), where test takers hold unrealistically positive views of themselves, firmly believing their overestimation of their psychological characteristics.
The statistic used to assess relationships between two interval/ratio variables is a ______.
Pearson's correlation coefficient
interval/ratio scale what test
Pearson's r, is the statistical test used to determine whether a linear relationship exists between two variables. The test requires that each of the two variables (referred to as X and Y) is measured using an interval or ratio scale.
Mu (µ):
Population mean.
Sigma (σ):
Population standard deviation.
Linear regression:
Process of describing a correlation with the line that best fits the data points.
Type I error:
Rejecting null hypothesis when it is true
careless or random responding
Sometimes test takers provide responses that are truly random or somewhat random. Whether due to carelessness or to a lack of motivation to respond meaningfully, some respondents might choose answers in a completely random or semirandom fashion that is unrelated to item content.
Pearson's r (Pearson product-moment correlation coefficient):
Statistic used to describe a linear relationship between two interval/ratio measures; describes the direction (positive or negative) and strength (between ±1.0) of the relationship. Linear relationship: A relationship between two variables, defined by their moving in a single direction together.
Normal distribution:
Symmetrical distribution in which scores cluster around the middle and then taper off at the ends.
Predictor variable:
The X variable used to predict a Y value.
Sensitivity:
The ability of a measurement instrument to detect differences.
Power:
The ability to reject the null hypothesis when it is, in fact, false.
Variance (SD 2 ):
The average of the squared difference between the mean and scores in a distribution, or the standard deviation squared.
Kurtosis:
The degree of the peak of a normal distribution.
Within-groups variance (or error variance):
The differences in your sample measure that are not accounted for in the study
A Pearson's r provides two pieces of information about the correlation:
The direction (positive or negative) of the relationship The strength or magnitude of the relationship
Region of rejection:
The extreme 5% (generally) of a sampling distribution; results falling in this area imply that our sample does not belong to the sampling distribution defined by the H0 and result in the researcher rejecting the H0 and accepting the Ha
coefficient of determination (r^2)
The fraction of the variation in the values of y that is accounted for by the least-squares regression line of y on x.
Possible minimum and maximum scores:
The lowest and highest scores possible for the measurement instrument.
Criterion level:
The percentage of a sampling distribution that the researcher selects for the region of rejection; typically, researchers use less than 5% (p < .05).
Percentile:
The percentage of the distribution that scored below a specific score.
Type II error:
a false negative, the incorrect acceptance of a null hypothesis
z score:
a measure of how many standard deviations you are away from the norm (average or mean)
Through the process of numerical coding, you have created
a nominal variable.
Which of the following is most appropriate for graphing nominal data?
bar graph
best ways to graph nominal data
bar graphs, Bar graph: Graph used to display nominal or ordinal data in which the frequency of scores is depicted on the y-axis and the categories for nominal data or ranks for ordinal data are depicted on the x-axis. Nonadjacent bars represent the frequency of each category or rank
you should always plan your statistical analysis
before you conduct your study
Criterion variable:
dependent variable, Predicted variable.
Random sampling is less important in a correlational study than in a
descriptive one
. Before deciding the best way to describe a variable that is either interval or ratio, we must first
determine the type of distribution
The range is the
distance between the minimum score and the maximum score.
limits of correlational design
does not equal causality and dont know direction or if third variable
guessing and when used
f tests used in these kinds of consequential situations, respondents might be motivated to guess. Particularly for tests that have a limited set of response options (e.g., multiple-choice questions), respondents may guess at an answer in an attempt to raise their scores. guessing can compromise the quality and meaningfulness of test scores
After the first quiz to assess student knowledge of the reading material, a professor reports that student scores ranged from 0 to 2 on the 10-point quiz. If the students really read the material, what could explain the scores?
floor effect
social desirability response bias is the tendency
for a person to respond in a way that seems socially appealing, regardless of his or her true characteristics.
The regression equation is the formula ______.
for the line of best fit
One way to determine if your distribution meets the criteria for a normal distribution is to
graph the data and evaluate the shape of the distribution.
implications of acquiesce bias
hard to differentiate who is actually pleased with their job, , if some people engage in acquiescent responding while others do not, then test users might not be able to use test scores effectively to identify which people have a high level of the construct being assessed. e human resources director, for example, might end up hiring several applicants who are simply acquiescent responders rather than truly conscientious workers.serious implications for behavioral research, potentially compromising researchers' ability to answer their research question accurately. reverse coding can help this, find correlation bw variables, bias can affect research by creating correlations that are artificially more positive than they should be.
Interval and ratio data can be plotted on a
histogram or frequency polygon
If we have the mean and standard deviation of a normal distribution of interval or ratio scores, we can determine
how many standard deviations a score falls above or below the mean
Variability describes
how much scores differ in a sample
how to reduce type 2 error
increase sample size, by choosing a less stringent criterion
way to reduce within-groups variance
increase the homogeneity of the sample by limiting the population from which your sample is drawn to only senior psychology majors, or to only women, or to only those who have owned a cell phone for at least five years, and so on. Another way to reduce this type of error is to systematically evaluate potential differences in your sample. For example, you might determine if there is a relationship between year in school and texting, or gender and texting, or if texting is related to how long someone has owned a cell phone.o systematically evaluate potential differences in your sample, select appropriate statistical tests, , select reliable and valid measures, choose measures that are sensitive.
A sample's skewness statistic (G1 )
indicates the degree of skew in that sample's distribution
factors that might make random/careless responding particularly likely to happen
l, respondents might provide responses that are not well considered, that are careless, or that are random when they are not motivated to be thoughtful and careful (Krosnick, 1999). When might respondents experience such lack of motivation? Two conditions that might reduce respondents' motivation to be careful and thoughtful are coercion and anonymity
The lowest score obtained for a variable in your sample is cal
led the observed minimum score,
The strength of the effect refers to the
magnitude or intensity of a pattern or relationship, and increases the likelihood that the pattern or relationship will be detected.
e effect size tells you the
magnitude or strength of the effect of a variable.
is malingering a serious concern
malingering is a legitimate concern in psychological assessment, and experts conclude that the failure to consider its influence "potentially carries high costs for insurers, disability systems, and ultimately society at large"
The mean tends to be pulled down by extreme negative scores in a negatively skewed distribution. Consequently, the mean underestimates the central tendency and should not be reported. The median is higher than the mean in a negatively skewed distribution and as such is a better estimate of the central tendency. The mean tends to be pulled up by extreme positive scores in a positively skewed distribution, overestimating the central tendency. The median is lower than the mean in a positively skewed distribution and as such is a better estimate of the central tendency.
mean underestimates the central tendency and should not be reported. The median is higher than the mean in a negatively skewed distribution and as such is a better estimate of the central tendency. The mean tends to be pulled up by extreme positive scores in a positively skewed distribution, overestimating the central tendency. The median is lower than the mean in a positively skewed distribution and as such is a better estimate of the central tendency.
There are three types of central tendency
mean, median, mode
The point in a distribution at which 50% of the scores are below and 50% of the scores are above is known as the ______.
median
When an interval or ratio variable is skewed, what is the appropriate measure of central tendency to report?
median
how to use strong correlation design
reliable/valid measures, variability, external validity,
acquiescence bias may be most likely to occur when
n respondents do not easily understand test items—because the items are complex or ambiguous, because the testing situation presents distractions, or because the respondent naturally tends to have difficulty understanding the material
The Effects of Random/Careless Responding
n those responses tell us nothing about the individual's standing on the psychological construct(s) that we are attempting to measure. merits attention and concern.
When we find statistical significance it suggests that our results were ______.
not due to chance alone and do not belong to the sampling distribution defined by the null hypothesis
The sampling distribution is defined by the ______.
null hypothesis
Central tendency is a
number that represents the central score, around which other scores cluster
Descriptive statistics are the
numbers used to summarize the characteristics of a sample. They are used when you have data from quantitative measures such as age, heart rate, or responses on a rating scale. Additionally, descriptive statistics can be used to analyze qualitative (nonnumerical) measures if you code the data as number
and the highest score obtained is the
observed maximum score.
If you reported that participants in your study were aged between 18 and 64, you would be reporting the ______.
observed minimum and maximum
The mean tends to be pulled up by extreme positive scores in a positively skewed distribution,
overestimating the central tendency. The median is lower than the mean in a positively skewed distribution and as such is a better estimate of the central tendency.
If you wanted to know what proportion of your sample consisted of left-handed people, you would be wondering about the ______.
percentage
You are studying the relationship between pet ownership (yes-no) and life satisfaction. You should compute a ______.
point-biserial correlation coefficient
When two variables move in the same direction together (both increase or both decrease), they will be ______.
positively correlated
By substituting an X value in the regression equation, we compute the ______.
predicted Y (Y′) value that falls on the line of best fit
Inferential statistics are based on
probability theory, which examines random events
, diviThe cumulative percentage is the
proportion of the sample that falls within a specified interval. You might, for example, want to report the percentage of participants in the sample who were between the ages of 18 and 23.
. Ratio scales measure
quantity and have both equal intervals and a true zero.
ways to measure variability
range, variance, standard deviation, minimum and maximum scores
Interval scales are
ratings in which we assume there are equal intervals between scores. Interval scales do not have a true zero, meaning that there is no fixed starting point and a score of zero does not indicate complete absence of a quality
Most of the time we use a two-tailed or nondirectional hypothesis in hypothesis testing so that we can
reject findings that are rare for our distribution,
e best example of managing test content to reduce the effect of bias might be the
use of balanced scales to cope with acquiescence bias. A balanced scale is a test or questionnaire that includes some items that are positively keyed and some that are negatively keyed.test user must
the problem of extreme and moderate response biases (or "extreme response style") refers to the tendency to
use or avoid extreme response options. extremity bias can create ambiguity in respondents' scores, which can lead decision makers to make inappropriate decisions on the basis of those scores. produce results that lead to inaccurate conclusions
Cohen's d is another commonly
used measure of magnitude of an effect. The larger the value of Cohen's d, the stronger the effect size.
do not say that we "proved" the alternative hypothesis because
we are working with probability in inferential statistics
Inferential statistics allow us to determine
whether the outcome of our study is typical or unusual in comparison to our sampling distribution.
probs wit social des bias
y. If responses are caused by a motivation to appear socially desirable, then they fail to reflect the respondents' true levels of the constructs being assessed. This can diminish the reliability and validity of the measurement process.
Do not assume an outlier is a mistake unless
you have reason to do so. An outlier often represents an actual extreme response that would be important to acknowledge and analyze.
