Chapter 12 Flashcards
What are the 4 different scales of measurement?
nominal, ordinal, interval, and ratio scales.
What does the most appropriate statistical analysis and graph depend on?
depends on each variable’s scale of measurement.
What are the levels of a nominal scale? Example?
different categories or groups that have no intrinsic numerical properties.
Ex: two kinds of therapies for depression.
What is an ordinal scale? Example?
variables using an ordinal scale rank order the levels from lowest to highest (or least to most), but the intervals between each rank order are not equal.
a list of the top ten restaurants in halifax would use an ordinal scale.
What is an interval scale? Examples?
the distance between each level are equivalent in size.
Scores on an intelligence test.
Is there a meanigful zero point on interval scales?
no there are no meanigful zero points that indicate a total absence of the construct.
how do ratio scales contrast with interval scales? examples?
ratio scales have equal intervals in addition to a true zero point.
response time and age.
Is it easy to know precisely whether an ordinal or an interval scale is being used? Why or why not?
no.
Ex: we assume that asking people to rate their state of health on a 4-point likert scale uses an interval scale, when the points are labelled very good, good, fair, and poor. But it is difficult to claim that the difference between very good and good is the same as the difference beteeen fair and poor.
However, it is common practice to treat variables measured like this as an interval scale, because whe ordinal sclaes are averaged across many instances, they take properties similar to an interval scale.
Are the statistical procedures used to analyze data with interval and ratio variables identical?
yes. Importantly, data measured on interval and ratio scales can be summarized using an arithmetic average, or what is known as the mean. It is possible to provide a number that reflects the mean amount for these variables
what is the mean actually called?
an arithmetic average
What are variables measured on interval and ratio scales often referred to as? Why?
continuous variables because they represent an underlying continuum
What do we call variables using intrval and ratio sclaes? why?
continuous variables
they can be treated the same way statistically.
What is the first step a researcher should take in analyzing data? why?
exploring each variable separately. Doing so allows us to get a sense for what the data for each of our variables look like and also identify any possible errors that might have occurred during data collection.
What is a frequency distribution?
A representation of how often each score was observed, arranged from lowest to highest score.
What does a frequency distribution indicate?
the number of participants who recieve or select each possible score on the variable
What variables can you create a frequency distribution for?
variables using any scale of measurement.
What is an example of a frequency distribution I would be familiar with?
when professors present a graph showing ho many students got each score on an exam.
What do graphical representations of frequency distributions allow us to see?
what our data looks like at a glance. You can quickly see what scores are most common, which are infrequent, and the shape of the distribution. You can also tell us whether there are outliers.
What are outliers?
Scores that are very different from the rest of the scores in a dataset (i.e., much smaller or much larger); also known as extreme scores.
What might an outlier reflect?
may reflect a data entry error that can be corrected.
What are the types of graphs used to depict frequency distributions?
the bar graph, the pie chart, histogram.
What is a bar graph?
A graph using bars to depict frequencies of responses, percentages, or means in two or more groups.
What does a bar graph use? What are they commonly used for?
a separate and distinct bar for eahc piece of information.
used for comparing group means but can also be used for comparing percentages
What information goes on the X-axis for bar graphs? y-axis?
X = any categories
y = any values.
What is a pie chart?
A circular graph in which frequencies or percentages are represented as different “slices” of a pie.
What does a pie chart represent? When are they particularly useful?
relative percentages.
Thy are particularly useful when representing data on a nominal scale.
Are pie charts often used in journal articles? When are they often used.
no but they are often used in applied research reports, inforgraphics, newspapers, and magazines
What is a histogram?
A type of bar graph used when the variable on the x-axis is continuous, with each bar touching the adjacent bars (unlike in typical bar graphs).
What does a histogram display?
it uses bars to display a frequency distribution for a continuous variable.
Why do bars on the histogram touch each other?
to reflect the fact that the variable on the x-axis is a continuous variable.
How does a histogram contrast with a bar graph?
bar graphs have clear gaps between each bar helping to communicate the fact that values on the x-axis are nominal cetegories but histogram bars are touching to communicate the fact that the values on the x-axis are continuous.
What is a normal distribution?
A prevalent distribution of scores for continuous variables, in which the majority of scores cluster around the mean (or average), with fewer and fewer scores observed the further they fall from the mean.
What does the shape of distribution often look like on a histogram? what is this known as?
a bell-shaped curve.
A normal distrubtion.
What happens to scores in a normal distribution? What type of variables is this distribution possible for? When is this distribution frequently observed?
the majority of the scores cluster around the mean, with fewer and fewer scores observed the further you get from the mean. Only possible for continuous variables (i.e interval or ratio scales)
This distribution is frequently observed for many naturally ocuring variables (e.g height of dogs, wieght of cats, length of ferrets).
What is the mean?
A measure of central tendency, obtained by summing scores and then dividing this sum by the number of scores.
Why does the normal distribution make intuitive sense?
for many things, most observations are around the average, and it is uncommon to observe examples far from the average.
Why is normal distribution important? example?
because if our sample is drawn from a population of scores that are normally distributed, then we know a lot about this distribution. Ex: we know how many scores fall wihtin 1, 2, or 3 standard deviations from the mean.
What is a standard deviation? What is it a common measure of?
The average deviation of scores from the mean (the square root of the variance).
Standard deviation is a common measure of variabiliy, or how the scores are spread out with repsect to the mean (i.e how far each score is from the mean)
What is the ideal normal distribution?
one with percentage of data falling within 1 and 2 SD of the mean.
LOOK AT FIGURE 12.3
In a normal distribution, what percentage of the scores fall within 1 standard deviation above and below the mean? what percentage of the data fall within 2 standard deviations above and below the mean?
about 68% fall within 1 SD
about 96% fall within 2 SD
AKA very few scores appear greater than 2 SD from the mean.
When we use descriptive stats like a histogram to visualize our sample data, what do we often want to figure out?
we often want to figure out if our sample data is drawn from a population that is normally distributed bcause this will determine what stats we should use.
What statistics should only be used if our sample data are drawn from normally distributed populations?
parametric statistics like t-test and f-tests.
If we do not have data that is normally distributed, what statistics do we have to use?
non -parametric statistics
What is visualizing frequency distribution good for? What else can we do? What is this called?
taking an initial look at our data in order to gain a sense of it, but we can also calculate statistics to describe or summarize our data. These statistics are known as descriptive statistics.
What are descriptive statistics?
Statistics that describe and summarize the data collected; these include measures of central tendency (e.g., mean), variability (e.g., standard deviation), and covariation (e.g., Pearson correlation).
What are the 2 main types of descriptive statistics?
(1) measures of central tendency
(2) measures of variability.
What do measures of central tendency try to capture?
how participants scored overall, across an entire sample, in various ways.
What do measures of variability attempt to summarize?
how differently the scores are from each other, or how widely the scores are spread out or distributed.
How do you calculate describtive statistics in studies that make a comparison between groups?
separately for each group.
What is central tendency?
A single number or value that attempts to summarize all of the data, describing the typical score or where most of the scores fall.
What does the central tendency tell us?
tells us what scores are like as a whole, or how people scored on average.
What are the 3 measures of central tendency?
(1) the mean
(2) the median
(3) the mode.
how is the mean calculated? How is it represented in calculations? in scientific reports?
a set of scores obtained by adding all the scores together and then dividing this number by the number of scores.
In calculations the means is represented by X (with a bar over the top) it is pronounced as X bar.
In scientific reports it is abbreviated as M.
When is the mean appropriate?
the mean is only appropriate when analyzing scores that use an interval or ratio scale. (ie a continuous variable) because the actual values are used and so the values must be numerically meaningful
What does the mean provide us with?
a single value that summarizes age for each group.
What is the median?
A measure of central tendency defined as the middle score in a distribution that divides the distribution in half (or an average of the two middle scores).
for an odd number of scores, is it easy to identify which score falls right in the middle with the median? How do we find the median for an even number of scores.
yes.
for an even number of score,s the middle will fall between 2 different numbers, so we take the mean of these 2 values.
How is median abbreviated in scientific reports?
Mdn
What kinds of variables can the median be calculated for?
continuous variables just like the mean. It is also approrpriate when scores are on an ordinal scale, because it takes into account only the rank order of these scores.
What is the mode?
A measure of central tendency; the most frequent score in a distribution of scores.
What can the mode be calculated for? What is mode the only measure of central tendency appropriate for?
can be calculated for variables that employ interval, ratio, or ordinal scale.
it is the only measure of central tendnecy appropriate for scores on a nominal scale.
Can there be more than one mode? When?
yes. When there are values that tie for most frequent.
What relationship do we see between the mean, the median, and the mode if the data are perfectly distributed?
they will all be equal (ie have the same value)
When will the mode, median, and mean be different?
when the data deviate from a normal distribution
How do you know when to use the median, mode, or mean?
the measure you will ofcus on will depend on what you are interestedi n knowing
If you are most interestedi n which choice was most popular in your sample, use the mode
If you want to incorporate all of your data and understand what the average response was, use the mean
As a general rule what measures of central tendency should you calculate?
all that are appropriate for the variable based on its scale of measurement.
What is an important note about the mean?
it is very susceptable to outliers. If there are scores that are very different from most other scores, either very high or very low, then the mean caqn be misleading. In this case, the median would be most appropriate.
What would be the best measure of central tendency for family income of a country? Why?
the median because a relatively small number of people have extremely high incomes, using the mean would it appear that the average person makes more money than is actually the ase.
Do we have to consider the distribution of the data when deciding on which measure of central tendency to use?
yes. if the data are normally distributed, not symmetrical with most data near the mean, but instead the distribution is skewed to one side or another, then the mean will als obe skewed. This makes the median a better representation of central tendency.
DO ACTIVITY 12.1
what is variability? What does variability characterize?
The amount of dispersion for scores around some central value.
Variability characterizes the amount of spread in a distribution of scores, for continuous varables (i.e interval or ratio scales)
What is a common measure of variability? What does it indicate? How is it abbreviated in scientific reports? in formulas?
the standard deviation which indicates hoe far away the scores tend to be from the mean, on average.
in secitific reports it is SD
In formulas it is abbreviated as s.
When is the SD small? when does it become larger?
when most people have scores close to the mean,it beomes larger as more people have scores further from the mean.
together, what do the mean and standard deviation provide info about?
the way the scores are distributed.
How is the standard deviation derived?
by first calculating the variance, symbolized as s^2 and then finding the square root of the variance.
what is variance?
A measure of the variability of scores about a mean. The variance is calculated by taking the difference between each score and the group mean, squaring these differences, and dividing the sum of these squares by the number of scores.
What is an important thing to note about the calculation of standard deviation?
as with the mean, the calculation of standard deviation (and variance) uses the actual values of scores.
What is standard deviation only appropriate for?
continuous variables (i.e. interval and ratio scale variables)
What is the range? Is it a measure of variability or central tendency?
it is a measure of variability, and it is the most commonly used calculation. it is the difference between the highest score (max.) and the lowest score (min.).
After describing variables using percentages or means, what is the next step?
typically a statistical analysis to determine whether there is a statistically significant difference between nominal groups.
Why might we compare group percentages?
to see if there is a relationship between nominal variables.
Why might we compare group means?
to compare means responses to continuous variables made by participants in two or more nominal groups.
What is a common way to graph a relationship between variables when one variable is nominal?
a bar graph or a line graph.
where should the nominal data be represented on a bar graph?
on the x-axis.
When are line graphs vs bar graphs used?
bar graphs are oftne used when the valueso n the x-axis are nominal categories, line graphs are often used when the values on the x-axis are numeric.
What is a common trick used to mislead readers with bar graphs and line graphs?
exaggerating the distance between points on the y-axis to make the results appear more dramatic than they really are.
what is the effect size? What is it a general term for?
The magnitude of an effect observed, either the extent to which two variables are associated or the size of the difference in scores between groups.
general term for the indicators allowing you to describe relationships among variables in terms of size and amount of strength.
What is effect size a descriptive tool for?
help us interpret how large our effects are.
When comparing 2 groups, on their responses to a continuous variable, what is one appropriate effect size?
Cohen’s d
What is cohens d?
An effect-size estimate that is the standardized mean difference in scores between two groups.
it is the difference in means between two groups, standardized by expressing it in units of standard deviation (i.e how many standard deviations large is the difference in scores between these 2 groups.)
In a true experiment free of the threats to internal validity, what does the cohen’s d describe?
the magnitufe of the effect of the IV on the DV. In a study comparing naturally occuring groups, the cohen’s d value descrbies the magnitude of the effect of group membership on continuous variables.
How do you interpret the cohen’s d values?
because cohen’s d expresses effect size, in units of SD a d of 1.0 means that the means are 1 SD apart. and os on.
What is the smallest possible value for cohen’s d? is there a maximum value?
0 indicating no effect, but there is no maximum value
What can you add to include even more valuable information about the range of effect-sizes likely to be true?
adding confidence intervals around the effect sizes.
Look at the equations for cohen’s d in the try it out for cohen’s d
Do table 12.2 once you understand the equations for cohen’s d!
When are different analyses needed?
when you do not have distinct groups you wish to compare but instead have a range of scores ot investigate in terms of their relationship with other scores.
What is the appropriate analysis for correlational designs?
a correlation coeffecient
What is the correlation coefficient?
A statistic that describes how strongly two variables are related to one another, the degree to which they covary.
What does correlational analysis not tell us?
whether there is any causal relationship between variables.
are there many types of correlational coeffrecients? how are they calculated?
yes.
they are calculated somewhat differently and their use depends on the measurement scale of the two variables being analyzed (ordinal vs interval)
whatis the most common correlational coefficient?
the pearson’s correlational coefficient. otherwise known as pearson’s r.
When do we use pearson’s r?
when both variables have interval or ratio scale propoerties (ie continuosu variables.)
what can the pearson’s r range from? What do the values tell us?
0.00 to plus or minus 1.00, with the values teling us about the strenfth and the direction of the relationship.
What is considered a perfect relationship with the peirson’s r? Why?
plus 1.00 or minus 1.00
because changes inthe two variables follow one another in a perfect fashion.
What does the sign of the pierson’s r tell us?
whether it is a positive or negative relationship
What do we need to obtain to calculate a correlation coefficient?
we need to obtain paris of observations.
how can correlational data be visualized?
in a scatterplot
what is a scatter plot?
A graph of the relationship between two variables, in which pairs of scores are plotted on thex- and y-axes. This graph illustrates the relationship between two variables.
What is on the x and y axes for scatterplots?
values for the first variable are noted on the x axis and values for the second variable are on the y axis.
why are perfect correlations rarely seen in real life?
because all measures contain measurement error, which results in variability or differences in scores not rooted in the construct of interest. Human phenomena are also almost always caused by multiple factors so we tend not to observe just on factor predicting all of the variability in another construct.
Can you perfectly predict what the peirson’s score will be on the second variable if the relationship is not perfect?
no.
What do scatterplots allow researchers to detect?
outliers, which are scores that are extremely distant form the rest of the data. Particularly when samples are small, outliers can skew corerelation coefficients.
Is it important that the researcher smaple from the full range of possible scores for both variables? Why?
yes.
if the full range is not samples, but instead the range is restricted, the correlational coefficient produced with these data can be misleading. With a restricted range of values, there is less variability in the scores and thus less variability can be explained or predicted by the other variable.
what is the problem of restriction of range?
When only a subset of a variable’s possible values are sampled or observed, which can lead to misleading null or attenuated correlations.
When can the problem of restriction of range occur?
when people in your sample are all very similar on one or both of the variables you are studying.
What can restriction of range lead us to mistakenly conclude?
that there is no relationship between variables because there is insufficient variability in one of more of the variables to allow us to detect changes in one relate to changes in another.
What kind of relationship is the pearson’s r only designed to detect?
linear relationships. if the relationship is curvilinear, the correlational coefficient will fail to detect this relationship.
What would the perason’s r say about curvilinear relationships?
it would say that the persons correlation is 0
Why is it important to always inspect a scatterplot of the data before looking at the magnitude of correlation?
because the variables in your data might have a curvilinear relationship.
Are corelational coefficients indicators of effect size?
yes.
what tells us that our corerelational coefficient is what is typically observed, smaller, or larger?
bottom third f correlations re below .20, the middle third ranges from .20-.30, and the top third is greater than 3.0
what can you do to an r value to lend it to.a simple interpretation? example?
you can square it because it then relates to the proporiton of variance being explained. Ex: is r= .50 then r squared equals .25 meaning that one variable explains or account for 25% of the variance in the other variable and vice versa.
what is a squared correlational coefficient?
A correlation coefficient that has been multiplied by itself, resulting in a value that reflects the proportion of variance shared between the two variables (i.e., the amount of variance explained in one variable by the other variable, and vice versa).
What is an advanced way of examining how variables relate or covary? What is it?
regression. like a correlation, regression analyzes the relationship among variables. In fact, the calculations for correlations and regression result in the same value when there are only two variables involved.
why can the regression framework be more powerful than coefficients?
because it allows us to expand the analysis to include more variables.
what does analyzing data using regression require?
calculating regression equation which is the same as the equation for drawing a straight line.
is the regression just any line?
no. it is the line that best summarizes all of the data points.
what would we say if the line form regression had all data points fall exactly on it?
it would be a perfect summary or characterization of the data.
because we almost never have a perfect line from regression, how do we try to draw it? What can we then do with the regression equation?
we try to draw a straight line so it is as close al possible to all of the data points.
the regression equation that describes this line can then be used make specific predictions.
using regression, what can we do if we know the regression equation that summarizes the ability for self-reported feelings of health to predict life satisfaction?
we could plug in someon’s scores on the former and use it to predict the latter.
what is the general form of a regression equation?
Y = a +bX
where is the score we wish to predict (called the criterion varaible), is is the known score (the predictor variable), a is the y-intercept (a constant, where the line hits the y-axis or the value of y when x = 0), and b is the slope of the line (a weighting adjustment factor that is multiplied by X).
Think about this:
in a clincal setting, if we know the regression equation summarizing the relationship between symptom severity and treatment duration, we could measure a new clients symptom severity and use it to estimate how long that client will need treatment before symptoms are reduced.
What is the criterion variable?
The outcome variable that is being predicted in a regression analysis.
What is the predictor variable?
The variable used to predict changes in the criterion (or outcome) variable in a regression analysis.
What is multiple correlation?
A correlation between a combined set of predictor variables and one criterion variable.
Why does accounting for many predicotr variables usually permit greater accuracy of prediction than using only one predictor?
Becuae almost any human phenomenon is liekly to be detemrined y a great number of factors.
does the multiple correlation usually generate a stronger relation than the single correlation between one one of the predicotr variables and the criterion variable?
yes.
what is the squared multiple correlation? How is interpreted?
The proportion of variance in the criterion that can be explained by the combined set of predictors for multiple correlation.
the squared multiple correlation coeeficient tells you the proportion of variability in the criterion variable that is accounted for by the combined set of predictor variables.
What is the expanded multiple of regression called?
multiple regression
What is multiple regression?
An extension of the correlation technique that models the extent to which one or more predictor variables are related to one criterion variable.
how does multiple regression differ from multiple correlation?
it allows us to examine the unique relationship betwene each predictor and the criterion. This contrasts with the multiple correlation which one provides a single value for the relationship between the combined set of predictors and the criterion variable.
What does multiple regression tell us?
th relationship between each individual predictor and the criterion
What does the expanded multiple regression equation look like?
Y= a + b1X1 + b2X2 +…+ BnXn
y = crieterion variable, X1 to Xn are the predicotr variables, a is the y-intercept (a constant) and b1 to bn are the weights that are multiplied by scores on the predictor variables.
When researchers use multiple regressions to study basic research topics, what are they most interested in? does this require a different calculation for the multiple regression equation? What do these adjusted calculations do?
how eahc individual predictor relates to the outcome variable, controlling for the influence of the other predictor varaible.
yes.
make it possible to to assume all variables are measured on the same scale. When this is done, each predictors weight (symbolized by b) reflects the magnitude of the relationship between the criterion variable and the predicotr variable, holdign the other predictors constant.
When does the third variable problem occur?
when 2 varaibles are correlated but we don’t know if some third variable might be the reason they are related.
What do you need to calculate a partial correelation?
you need to have scores on the 2 primary variables of interest as well as a third variable that you want to control for
what do correlation and regression help us describe? What are they part of?
how variables relate to one another and are part of whats known as descriptive stats (along with central tendency measures, measures of variability, visualization like histograms etc ) .
After describing our data based on a sample form a population, what is common practice? What is this known as?
tring to make inferecnes abou the population from which the sample was drawn. these are knoen as inferential statistics.
