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.
