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Psychology
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PSYB01H3
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David Nussbaum
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Chapter 10

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Psychology

PSYB01H3

David Nussbaum

Fall

Description

Chapter 10- Quantitative Data Analysis
Does Spending Money on Others Promote Happiness
Statistical Approach
o Descriptive Statistics: describe variables in a study; one at a time and in relation to another
o Inferential statistics: used to estimate characteristics of a population from those found in a
random sample of the population; can be used to test hypotheses about the relationship between
variables; likelihood of results due to chance
Levels of Measurement Matters
o Nominal, ordinal, interval, ratio: determines which ties of statistic analyses you can use (see
chapter 4)
Univariate Distributions
o Univariate distribution: a probability or frequency distribution of only one variable
Frequency Distributions: shows the number of cases and/or % of cases who receive each possible score
on a variable
o Many require grouping of some values so it can fit on a table and so distribution will be clearer
and more meaningful
o Categories should be logically defensible and preserve distribution shape and should be mutually
exclusive and exhaustive
o Preferable to graphing when exact number of cases has to be stated or when lots of distributions
have to be shown in compact form
Graphing: to depict frequency distributions
o Bar chart: solid bars separated by spaces; good for nominal level
o Histogram: shows frequency distribution of a quantitative variable
Beware of Deceptive Graphs
o
Guidelines
Begin graph of quantitative variables at 0 on both axes; can break this rule at times ex. Age
distribution of adults; should show break clearly
Always use bars of equal width
Two axes should be of approximately equal length
Done have chart 'junk' that can obscure distribution shape
Descriptive Statistics
o Important features of shape: central tendency, variability, and skewness
o Statistic for skewness is only appropriate for quantitative variables but is rarely used and isnt
discussed
Measures of Central Tendency
o To choose which consider level of measurement, skewness of distribution and purpose of statistic
o Mode/probability average: most frequent value; used least often as it can be misleading
Bimodal vs unimodal
Might fall far from main cluster of cases in distribution
o Median: position average; cant be done in nominal
In frequency distribution determine it by identifying the value corresponding to a
cumulative % of 50 o Mean: arithmetic average; sum of value of all cases/# of cases; only in interval or ratio or if ordinal
treat as an interval?
o Median vs. Mean
Mean is technically inappropriate for ordinal but in practice is used
If symmetric use either, if skewed use median
Most important consideration is purpose of statistical summary
Neither is appropriate at nominal level
Measures of Variation
o Must be at interval or ratio level although some argue they can be used with ordinal-level
measures
o Range: highest value-lowest value +1; not great as can be affected by outliers
o Varianc2: average2squared deviation of each case from the mean
σ = Σ(yi- i) /N
o Standard deviation: square root of the variance; when calculated from sample data denominator
is supposed to be N-1 not N (no effect when N is large)
Can show how much variation, dispersion, or spread there is in a set of scores, numbers or
data points and how far from the average a particular score is
Sampling Distributions
o Value of mean or any other statistic from random sample is not likely equal to population
parameter
o Sampling distribution: distribution of the means of all the possible samples from the population;
mean is population mean
o Standard error to the mean: statistic that indicated the degree to which the means of the samples
vary from the population mean; estimate of stdev of sampling distribution
Inferential Statistics
o Confidence limits: assume normal distribution; probability that sample statistic falls in certain
range of population parameter
Normal distribution: from chance variation around the mean
-1stdev<65%

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