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PSYC 2360
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Dan Meegan
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Psychology

PSYC 2360

Dan Meegan

Summer

Description

Chapter 12: Understanding Research Results: Description and Correlation
Statistics helps us understand the data collected in research investigations.
Statistics are used to describe a data
Statistics are used to make inferences, on the basis of sample data, about a population
Scales of Measurements: A Review
Variables can be described using one of four scales of measurements:
1. Nominal
o Have no numerical, quantitative properties. The levels are simply
different categories or groups
o Most independent variables such as gender, eye colour, and hand
dominance are nominal
2. Ordinal
o Involve minimal quantitative distinctions. The levels are rank
ordered from lowest to highest.
o For example rank-ordered judgements of most important problems
facing your state today. Although you may get an order (1 crime,
2 health, 3 crime) but, you do not know how strongly people
feel about the problems; the intervals between each of the
problems are probably not equal
3. Interval
o More detailed quantitative properties. The intervals between levels
are equal in size. The difference between 1 and 2 is the same as the
difference between 2 and 3.
o There is no absolute zero point that indicates an “absence” of the
variable being measured.
4. Ratio
o More detailed quantitative properties. The intervals between levels
are equal in size and there is an absolute zero point that indicates
an absence of the variable being measured. Example would be
time, weight, length and other physical measures.
The scale used determines the type of statistics that are appropriate when the results of a
study are analyzed. The meaning of a particular score on a variable depends on which
type of scale was used when variable was measured or manipulated.
Analyzing the Results of Research Investigations
Most research focuses on the study of relationships between variables. Depending on
the way that the variable are studied, there are three basic ways of describing the
results:
1. Comparing Group Percentages
o For example when trying to find a relationship between gender and travel.
The percentage of males who like travelling is compared to percentage of
females who like travelling.
Note: We are focusing on percentage because the travel variable is
nominal: Liking and disliking are simply two different categories 2. Correlating Individual Scores
o A second type of analysis is needed when you do not have distinct groups
of subjects. Instead, individuals are measured on two variables, and each
variable has a range of numerical value.
Relationship between location in a classroom and grades in the
class.
3. Comparing Group Means
o Used in research to compare the mean responses of participants in two or
more groups. For example studying the effect of exposure to an
aggressive adult.
One group of children get exposure and the other does not and both
groups are left to play alone and aggressive behaviour is recorded
during observation.
Aggression as a ratio scale because there are equal intervals and a
true zero on the scale
Frequency Distributions
A frequency distribution indicates the number of individuals that receive each of the
possible score on a variable.
Graphing Frequency distributions
1. Pie Charts
o Divide a whole circle or “pie” into “slices” that represent relative
percentages
o Useful when representing nominal scale information
o Are frequently used in applied research reports and in articles in
newspapers and magazines.
2. Bar Graphs
o Use a separate and distinct bar for each piece of information
3. Frequency Polygons
o Use a line to represent frequencies.
o Useful when the data represent interval or ratio scales
4. Histograms
o Uses bars to display a frequency distribution for a quantitative variable.
o The scale values are continuous and show increasing amounts on a
variable (e.g. age, blood pressure), and because the values are continuous,
the bars are drawn next to each other
o By looking at histogram you can tell: the number of respondents, frequent
scores, shape of the distribution of the scores and outliers (scores that are
unusual, unexpected, or very different from the scores of other
participants.
Descriptive Statistics
o Descriptive statistics allows researchers to make precise statements about the data and
two statistics are needed to describe the data: 1. Central Tendency
A single number can be used to describe the central tendency, or how participants
scored overall, the sample as a whole.
There are three measures of central tendency:
Mean
Is obtained by adding all the scores and dividing by the number of
scores
It is an appropriate indicator of central tendency only when scores are
measured on an interval or ratio scale, because the actual values of the
numbers are used in calculating the statistic
Median
Is the score that divides the group in half (with 50% scoring below and
50% scoring above the median)
It is an appropriate indicator of central tendency when scores are on an
ordinal scale because it takes into account only the rank order of the
scores. It is also useful with interval and ratio scale variables
Mode
Is the most frequent score
It is an appropriate indicator of central tendency if a nominal scale is
used. The mode does not use the actual values on the scale, but simply
indicates the most frequently occurring value
Median and mode are better indicators of central tendency when few unusual
scores bias the mean
2. Variability
A measure of variability is a number that characterizes the amount of spread in a
distribution of scores.
Standard deviation (SD) indicates the average deviation of scores from
the mean. SD is appropriate only for interval and ratio scale variables
The SD of a set of scores is small when most people have similar
scores close to the mean and becomes larger as more people have
scores that lie further from the mean value.
SD is the square root of variance
Variance is the measure of variability of scores about the mean
Range is the difference between the highest score and the lowest score
o These two numbers (central tendency and variability) summarize the information
contained in a frequency distribution
Graphing Relationships
A common way to graph relationships between variables is to use 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 when the values on the x axis are numeric
Correlation Coefficients: Describing the Strength of Relationships
A correlation coefficient is a statistic that describes how strongly variables are related

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