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PS296
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Max Gwynn
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Chapter 3

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Psychology

PS296

Max Gwynn

Winter

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January 14 & 16 th th
Chapter 3: Displaying Data 01/21/2014
Collection of #’s – to be interpretable, must first be organized in some sort of logical
order
3.1 – Plotting Data
simplest way to reorganize data is to plot them in graphical form
frequency distributions, histograms, bar graphs, stem-and-leaf displays
Frequency Dist. – distribution where values of DV are plotted against their frequency of
occurrence
Real Lower Limit – point halfway between the bottom of one interval & top of the one
below it
Real Upper Limit – point halfway between the top of one interval & the bottom of the
one above it
Midpoint – center of the interval
Histograms – collapse data into intervals
Optimal # of intervals to use when grouping data follows the:
Goldilocks Principle – neither too many nor too few
3.3 Reading Graphs
Histogram
DV is on X axis Frequency on Y axis
Bar Graph – frequency of occurrence of different values of X is represented by the
height of the bar
Uses vertical bards to represent whatever is being measured
IV on X axis
DV on Y axis
Line Graph – Y values corresponding to values of X are connected by line
- most important thing in making sense of a graph is to:
first identify what is plotted on each axis
identify IV & DV
look for patterns
3.5 – Describing Distributions
Symmetric – distribution with same shape on both sides of the center
Bimodal – any distribution with 2 predominant peaks
Unimodal – any distribution with only 1 major peak
Modality – number of meaningful peaks in a distribution
Positively Skewed – distribution trails off to the right
Negatively Skewed – distribution trails off to left
Skewness – measure of the degree to which a distribution is asymmetrical Chapter 4: Measures of Central Tendency 01/21/2014
Central Tendency – measures that relate to the center of a distribution of scores Chapter 4: Measures of Central Tendency 01/21/2014
4.1 – The Mode
(Mo)
least useful measure
most common score
is the value of X – the dependent variable that corresponds to the highest point on the
distribution
Modal Interval – 1.50-1.59 occurred 50 times (most common interval)
If two adjacent times occur with equal frequency
Take average of the 2 values mode
If two nonadjacent times occur with equal (near equal) frequency – bimodal
distribution (2 distinct peaks)
4.2 – The Median
(Mdn)
middle score in an ordered set or data
th
50 percentile
Median Location – location of the median in an ordered series
(N+1)/2
4.3 – The Mean
(X) X bar OR (M) Chapter 4: Measures of Central Tendency 01/21/2014
most common measure of central tendency
known as the average
the sum of all scores divided by the number of scores in the data
mean & median are same in number when the distribution is symmetric
nearly symmetric and unimodal distribution – mean, median, mode same
Asymmetric Distributions – different mean, median, mode
4.4 – Advantages & Disadvantages of Mean, Median, Mode
Mode
Score that actually occurred
Advantages
Represents the largest number of people having same score
Applicable to nominal data
Disadvantages
Depends on how we group data
Not representative of the entire collection of numbers
Median
Advantage
Major – unaffected by extreme score
Doesn’t require any assumptions about the interval properties of the scale
Disadvantage Chapter 4: Measures of Central Tendency 01/21/2014
Major – does not enter readily into equations
More difficult to work with than mean
Not as stable from sample to sample
Mean
Advantage
Gives a more stable estimate of the central tendency of a population
Can be manipulated algebraically
Disadvantages
Influenced by extreme scores
Value may not exist in the data
Interpretation requires at least some faith in the interval properties of the data
Trimmed Means
Mean that results from trimming away a percentage of the extreme observations
Usually 10% or 20% from each side
Used to eliminate extreme scores
Common in treating skewed data
For a 10% trimmed mean, we would set aside the largest 10% and smallest 10%
remaining mean would be the 10% trimmed mean Chapter 5: Measures of Variability 01/21/2014
Dispersion (Variability) – degree to which individual data points are distributed around
the mean
The difference in variability is a focus
Groups could have different levels of variability even if the means are comparable
5.1 – Range
Range – measure of distance (from lowest to highest score)
Will suffer if there are unusually extreme values that stand out in the data set
(outliers)
5.2 – Interquartile Range & Other Range Statistics
Interquartile Range – the range of the middle 50% of the observations
Is obtained by discarding the upper & lower 25% of the distribution & taking the range of
whatever remains
The range of a 25% trimmed sample
The difference between 75 & 25 percentile
Plays important role in graphical method boxplot
Trimmed Samples – samples that have a certain percentage of the extreme scored
removed from each tail
Trimmed Statistics – statistics calculated on trimmed samples
5.3 – Average Deviation
(X-X) deviations Chapter 5: Measures of Variability 01/21/2014
positive & negative deviations will balance each other out (sum of the deviations will
always equal to 0)
5.4 – The Variance
to eliminate the problem of (+)/(-) deviations balancing each other out would be to use
absolute deviations – simply removing the sign in front of the deviation
Variance is one of the most commonly used statistics
Sample Variance (S2) – sum of the squared deviations about the mean divided by N-1
Divide by N-1 because it leaves you with a sample variance that is a better estimate of
the corresponding population variance
A different approach to the problem of the deviations averaging out to 0
Population Variance (Q2) – variance of a population; usually estimate, rarely
computed
Take advantage of the fact that the square of a negative number is positive
We sum the squared deviations rather than the deviations themselves
We then divide the sum by a function of N
5.5 – The Standard Deviation
Standard Deviation – the positive square root of the variance; (s)
when used in a psychological report, the symbol SD is used
the notation Q is used only in reference to a population standard deviation
always round to 2 decimal places
how many scored fall no more than a standard deviation above or below the mean Chapter 5: Measures of Variability 01/21/2014
For normal distribution, approx. two thirds of observations lie within one standard
deviation of the mean
5.6 – Computational Formulae for the Variance and the Standard Deviation
Computational Formulae (Calculational)
Algebraically equivalent to definitional formula’s, but require less effort
EX – sum of all sc

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