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# PSYB01 - Chapter 12 notes.doc

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University of Toronto Scarborough

Psychology

PSYB01H3

Anna Nagy

Summer

Description

Chapter 12 - Understanding research results: description and correlation
• Stats are used for describing data and making inferences on sample data
Scales of Measurement: a review
• Levels of a variable can be decribed by 4 scales
o Nominal: no numerical, quantitative properties
o Ordinal: rank order
o Interval: quantitative properties, no absolute 0
o Ratio: quantitative properties, has an absolute 0
Analyzing the results if research investigation
• Depending on the way the variables are studied there are 3 basic ways of describing the
results
o Comparing group percentages
o Correlating scores of individuals on two variables
o Comparing group means
Comparing group percentages
• Example: studying if which females or males like traveling more
o Lets say out of 50 females and 50 males
• 80% of females like to travel
• 60% of males like to travel
o Need to focus on % because of variable of liking travel or disliking travel is
nominal
Correlating individual scores
• Used when you do not have distinct subject groups
• Individuals are measured on 2 variables
o Each variable has a range of numerical values
•
Example: do people who sit near the front receive higher grades?
Comparing group means
• Example: studying effect of exposure to an aggressive adult on children's play
o On average how many aggressive acts did the children perform during play in both
groups?
• Aggression is a ratio scale variable because there is a true zero and equal intervals
Frequency distributions
• When analyzing results it is useful to start by making a frequency distribution of the data
• Frequency Distribution: indicates the number of individuals that receive each possible
score on a variable
o Useful to look at this in terms of %s
• Example: how many students in a class received a specific score on an exam
Graphing frequency Distributions • Pie Charts: divide a whole circle or pie into slices that represent relative percentages
o
Useful when representing nominal scale information
• Bar graphs: use a separate and distinct bar for each piece of information
o X-axis is the independent variable
o y-axis is the dependent variable
• Frequency polygons: use a line to represent frequencies
o Useful when representing interval or ratio scales
o Can have more then one line to represent more then one group
• Histograms: uses bars to display a frequency distribution for a quantitative variable
o
Scale values are continuous and show increasing amounts on a variable such as age,
blood pressure or stress
o Bars are drawn next to each other since values are continuous
• Looking at frequency distributions allows you to directly observe how your participants
responded
o Can look at what scores are most frequent and the shape of the distribution of
scores
o Find "outliers" or unusual, unexpected scores
Descriptive statistics
• Descriptive statistics allow researchers to make precise statements about the data
o Two statistics are needed to describe the data
o
One number can be used to describe the central tendency or how participants scored
overall while another number describes the variability or how widely the distribution of
scores is spread
• These 2 numbers summarize the information contained in a frequency
distribution
Central tendency
• Central tendency: a central tendency statistic tells us what the sample as a whole or on the
average is like
o
Three measures of central tendency:
• Mean: the average
Abbreviated as "M"
Indicator of central tendency only when scores are measured on an
interval or ratio scale
• Median: the score that divides the group in half
Abbreviated as "Mdn"
Indicator of central tendency only when scores are measured on an
ordinal scale
Also useful with interval and ratio scale variables
• Mode: the most frequent score
Only measure of central tendency that is appropriate if a nominal
scale is used
o The median or mode can be a better indicator of central tendency than the mean if a
few unusual scores bias the mean Variability
• A measure of variability is a number that characterizes the amount of spread in a
distribution of scores
o Standard deviation
• Symbolized as "s" or "SD"
• Indicates the average deviation of scores from the mean
• Standard deviation is first derived by first calculating the variance;
symbolized as s²
Standard deviation is the square root of the variance
• Only appropriate for interval and ratio scale variables
o Range: the difference between the highest score and the lowest score
Graphing relationships
•
You can graph relationships between variables by using a bar graph or a line graph
o Bar graphs are used when the values on the x-axis are nominal categories
o Line graphs are used the values on the x-axis are numeric
o If the distance between the points on the measurement scale is exaggerated, it
makes the results appear more dramatic than they really are
Correlation coefficients: describing the strength of relationships
• Important to know whether a relationship between variables is weak or strong
• Correlation Coefficient: a statistic that describes how strongly variables are related to one
another
o Pearson product-moment correlation coefficient
• Used when both variables have interval or ratio scale properties
• Called the Pearson r
• Values can range from 0.00 to ± 1.00
• Provides information on the strength and the direction of the relationship
o Perfect relationships are rarely if ever observed
o If the relationships are not perfect you can

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