PSYC*1010 Chapter 2: Frequency Distributions Flashcards
What is a frequency distribution?
An organized tabulation of the number of individuals located in each category on a scale of measurement
What are three things that frequency distributions provide information about?
- Whether scores are generally high or low
- Whether scores are concentrated in one area or spread out across the entire scale
- The location of any individual score relative to others in the set
What two elements are presented in both frequency distribution tables and frequency distribution graphs?
- The set of categories that make up the original scale of measurement
- A record of the frequency/ number of individuals in each category
How can the number of participants be calculated with the information provided by a frequency distribution?
By adding all the frequencies in a distribution
How is the sum of scores obtained from a frequency distribution?
Each X value is multiplied by its frequency and the products are totalled
What are the two most common measures that describe distribution of scores and can be incorporated into a frequency distribution table?
Proportion and percentage
What does proportion measure?
The fraction of the total group associated with each score
How is proportion most frequently expressed?
Proportion is most frequently expressed as a decimal rather than a fraction
How is the proportion of a score in a frequency distribution calculated?
Proportion of a score is calculated by dividing its frequency by the total number of scores
How is the percentage of a score in a frequency distribution calculated?
The percentage associated with each score is the product of the proportion multiplied by 100
What is a grouped frequency distribution?
A frequency distribution where scores are grouped into intervals rather than listed as individual values
What is range, and how is it calculated?
- Range: the distance between the absolute highest and lowest points in a distribution
- Range = highest score - lowest score
What is a class interval?
The group of scores in a grouped frequency distribution
What are the five guidelines for creating class intervals?
- There should be about 10 intervals
- The width should be a relatively simple number
- The bottom score of each interval should be a multiple of the width
- All intervals should be the same width
- The intervals should completely cover the range of scores with no gaps or overlaps
How are the sizes of class intervals determined?
Calculate the (range + 1)/10 and chose a convenient interval size as close to that value as possible
What type(s) of limits do continuous variables have?
- Real limits
- Apparent limits
What are the apparent limits of a class interval?
The score values that appear to be the lowest and highest of an interval
What are the real limits of a class interval?
The upper real limit of the first score in a class interval and the lower real limit of the last score in a class interval
When are real limits used to describe class intervals?
When measuring and organizing continuous variables
What is the abscissa of a graph?
The x-axis
What is the ordinate of a graph?
The y-axis
What are two guidelines that help avoid creating misleading graphs?
- The point of intersection of both axes has a score of zero
- The y-axis is approximately two-thirds to three-quarters the length of the x-axis
What is a histogram?
- A graph showing a bar above each score or interval corresponding to their frequencies
- There are no gaps between bars
What do the heights and widths of bars in histograms correspond to?
- Height = Frequency
- Width = class interval size, extending to real limits
What is a modified histogram?
Instead of drawing a bar above each score, a stack of “blocks” is used to represent the number of individuals
T or F: Modified histograms can be used as a substitute for regular histograms.
- False
- A modified histogram is not a substitute for an accurately drawn histogram with two labelled axes
What is a polygon?
A graph consisting of a line that connects a series of dots
What does the height of a dot in a polygon correspond to?
The height of each dot placed above intervals/scores corresponds to the frequency of that interval/score
How is nominal and ordinal data typically displayed?
A bar graph
What is a bar graph?
- A graph showing a bar above each score or interval corresponding to their frequencies
- There are gaps between adjacent bars
What do the spaces between adjacent bars in a bar graph represent when displaying nominal data?
For a nominal scale, the space between bars emphasizes that the scale consists of separate and distinct categories
What do the spaces between adjacent bars in a bar graph represent when displaying ordinal data?
For an ordinal scale, the space between bars are present because it cannot be assumed that all categories are the same size/have the same sized intervals
What are the two special features of graphs for population distributions?
- Relative frequencies
- Smooth curves
What is a relative frequency?
A proportion of the total distributor rather than the absolute frequency
When are relative frequencies used?
When the total number of individuals is unknown for each category
How can relative frequencies be presented/ displayed?
By using a relative frequency graph that does not display absolute numbers, simply the proportions of a category relative to each other
What does a smooth curve demonstrate?
The relative changes that occur from one score to the next in a population
What are the characteristics of a normal distribution curve?
Symmetrical, with the greatest frequency in the middle and relatively smaller frequencies toward either extreme
Which three characteristics completely describe any distribution?
- Central tendency
- Variability
- Shape
How is the shape of a distribution technically defined?
By an equation that describes the exact relationship between each X and Y value on the graph
How is the shape of a distribution classified?
The shape of nearly all distributions can be classified as either symmetrical or skewed
What is a symmetrical distribution?
If a vertical line was drawn through the distribution curve, each side would be a mirror image of the other
What is a skewed distribution?
Occurs when the scores pile up toward one end of the scale and taper off gradually at the other end
What is the tail of distribution?
The section where the scores taper off toward one end of a distribution
What does a positively skewed distribution look like?
The tail points toward the positive end of the x-axis (on the right-hand side)
What does a negatively skewed distribution look like?
The tail points toward the negative end of the x-axis (on the left-hand side)
What is the floor effect?
A situation in which a constraint prevents a variable from taking values below a certain point
How might the floor effect influence distribution?
It may lead to a positively skewed distribution
What is the ceiling effect?
A situation in which a constraint prevents a variable from taking on values above a given number
How might the ceiling effect influence a distribution?
It may lead to a negatively skewed distribution
What are stem and leaf displays?
A technique for organizing data that requires each score be separated into two parts
What do the “stem” and “leaf” in a stem and leaf display represent?
- Stem: the first digit(s) of a score
- Leaf: the last digit of a score
What does each stem in a stem and leaf display correspond to?
Each stem corresponds to a class interval
What does the number of leafs in a stem and leaf display correspond to?
The number of leafs shows the frequency associated with each stem
What is the advantage of a stem and leaf display over a traditional grouped frequency distribution?
Stem and leaf displays allow you to identify each individual score in the data
What factors need to be considered when determining the type of statistical analyses needed in a study?
- The type of study (correlational, experimental, quasi-experimental)
- What type of variables are being used (nominal, ordinal, interval, ratio)
