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University of Toronto St. George
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Psychology
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PSY201H1
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Alison Luby
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Lecture 2

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Psychology

PSY201H1

Alison Luby

Fall

Description

PSY201H1F L2 Sept 21, 2011 ○ List of x values is way too long for simple
presentation of data
Frequency Distributions, Tables vs. ○ Use a Grouped Freq Distr Table
Graphs X column lists class intervals: grps of
• Frequency distribution: Organized scores
○ Guidelines:
tabulation of entire set of scores allowing to
see big picture in data at a glance Select intervals so have about 10
○ Shows where each indiv is located relative class intervals
to others in the distr Class interval width should be
○ Shows whether scores are high or low, simple number (2, 5, 10, multiples of
concentrated in centre or spaced apart 5 or 10)
Bottom score in each class
• Places raw scores in order from highest to
lowest interval should b multiple of width
○ For nominal, any order • Ex. If width is 5 then bottom score
• Group together everyone w same scores is multiple of 5: 5,10,15,20
get sense of patterns Intervals have same width, cover
• Chart, table, graph, always presents 2 complete range of scores, each
score belongs in 1 interval
elements:
○ Cats that make up the original • Ex. Time to complete puzzle: 23 213 range
measurement scale (128,99,213,117,83,201,79,156,88,91,23,65,1
○ Record of the frequency (# of indiv in each 41,43,52,81,126,113,166,142)
cat) ○ X column (top to bottom): 200-219, 180-
199,160-179,140-159,120-139,100-
Freq Distr Tables 119,80-99,60-79,40-59,20-39
• Consist of at least 2 columns:
○ X column (raw scores) measurement cats ○ Start at multiple of width, don’t leave
○ F (frequency) column out intervals even if f=0
○ Ex. Number of cars ppl have: ○ Less groups more info you lose,
less you know about your data
1,2,1,0,3,4,0,1,1,1,2,2,3,2,3,2,1,4,0,0 • Continuous var have an infinite number
X F
4 2 of possible values, so in 200-219 a could
3 3 have X = 201.9
2 5 • Measurements indicate an interval not a
1 6 single pt
○ Ex. If X = 10 then the score was btwn 9.5
0 4 & 10.5
○ Tally freqs for each X
How often each X occurs • Grouped Freq Distr Table:Values listed in
Σf = N the intervals are called Apparent Limits
Ex. Above: Σ f = 20 of the interval
• But upper & lower boundaries involve
• If you are asked for ΣX, do not add up the Real Limits
values in the X column so don’t use the freq ○ Ex. For X=20-39, lower & upper real limits
dirt table
○ Add up all of the raw scores for X instead are 19.5 & 39.5, apparent limits are 20 &
○ ΣX = ΣfX 39
○ Or just add fX ex. 2(4) + 3(3) … = ΣfX Freq Distr Graphs
• Pic (graphical representation) of info in a freq
○ ΣX = 33 distr table
○ Use the same method to calculate ΣX 2
• Calculate proportions&percentages to • All graphs have 2 perpendicular lines called
describe distr axes which typically meet at 0
○ Proportion (aka Relative Freq) ○ X axis = Abscissa: Lists the
measurement scale (the set of X values)
measures fraction of total grp ○ Y axis = Ordinate: Lists the freqs
associated w each score ○ General rule: Y axis height = approx 2/3
p= f/N
Σp = 1.00 - 3/4 length of X axis
○ Percentage = p(100) = f/N x (100) • When score cats consist of numerical
scores from interval or ratio scale, graph
Σpercentage column = 100% should be histogram or polygon
• If many X values:
○ Don’t want many rows • When the scores r measured on a nominal or • Polygons:
ordinal scale, the freq distr should be ○ Centre a dot above each score so
displayed in a bar graph height of dot correspond to freq
• Histograms ○ Join dots w straight lines
○ List cats of measurement along X axis ○ Additional line drawn @ each end to
○ Draw a bar about each X value so: bring graph back to 0 freq
Height of bar corresponds to freq Usually reach the x axis at a pt 1 cat
for that cat below lowest score on left & 1 cat
Width of bar extends to real limits above highest score on right
of the cat ○ For Grouped Distr, position each dot
• No space btwn bars directly above midpt of the Class
When data grouped into class
Interval
intervals, draw bar above each interval Find midpt by avging highest & lowest
so width of bar extends to real limits of score for the interval
the interval ○ Similar to freq histogram
○ Ex. Freq of quiz scores – Use Reg Freq Appropriate for plotting freq of
Distr Table continuous vars
Communicates same info
Distr shape may be easier to see
using polygon
○ Using Reg Freq Distr Table:
○ Ex. Freq of children’s height w class
intervals – Use Grouped Freq Distr Table
○ Using Grouped Freq Distr Table - dots @
midpts
○ Could be made for puzzle scores from
earlier
Usually label x axis at the
midpoint of each interval
• Simple & quick representation
• Ex. for class scores - don’t need Ex. For previous puzzle scores: No 0
to label each bar freq in end cats so would hit 0 in new
end cats
○ To make freq chart from polygon:
Start w the dot w the highest x
value
○ Usually data written in histogram forms
• Nom or ord scales:
○ Score cats &X values not continuous
○ Use Bar Graph: Like histogram but
spaces/gaps btwn bars
Indicate the scale is made up of
distinct cats
○ Can’t assume all cats r same size ○ Ex. Number of cars ppl have – discrete not
continuous, can’t have 2.5 cars so X can’t
be 2.5
Shapes of Freq Distrs, Symmetrical vs.
Skewed
• Many pops are so large we can’t know
exact # of indivs (freq) for any specific
cat: Percentiles + [Percentile] Ranks +
○ So pop distr can be shown

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