Transcript Research Methods in Psychology

Research Methods in Psychology
AS Descriptive Statistics
1
There was widespread panic
today with fans fainting as top
girl band ‘Central Tendency’
revealed their true values
mean
median
mode
Top? More
like pretty
average
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Hi! The name’s Ave Rage
and I’m a pretty MEAN
character. I get really
MEAN because people
add up all the facts about
me and then divide them
by the total number. I
suppose that makes me
an average guy most of
the time
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I’m MEAN and powerful because I make
use of all the data. Those weaklings
MEDIAN and MODE chuck most of it
away, but I can only be used to measure
data that:
1.
2.
Starts from true zero, e.g., physical quantities
such as time, height, weight
Are on a scale of fixed units separated by equal
intervals that allow us to make accurate comparisons,
e.g., someone completing a memory task in 20
seconds did it twice as fast as someone taking 40
seconds
I’m also affected by
extreme scores
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Extreme scores
•
•
•
•
•
•
Time in seconds to solve a puzzle:
135, 109, 95, 121, 140
Mean = 600 secs ÷ 5 participants =120 secs
Add a 6th participant, who stares at it for 8 mins
135, 109, 95, 121, 140, 480
Mean = 1080÷6=180 secs
Get out of here, kid!
You’re taking too long.
You’re about to wreck my
experiment!
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Median
• Middle value of scores arranged in rank order
• Half the scores will lie above the median, half below it
 Unlike the MEAN, it can be used on ranked data, e.g.,
placing a group of people in order of position on a
memory test rather than counting their actual score
 Unaffected by extremes, so can we can use it on data
with a skewed distribution where results would be a bit
one sided – if we were to plot a graph, it would look like
this:
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Do you know
where my
middle is?
Odd scores:
2, 3, 5, 6, 7, 10, 14
median=6
(middle value)
Even scores:
2, 3, 5, 6, 7, 10, 14, 15
median=6+7÷2 = 6.5
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Disadvantages of the median

1.
2.

Does not work well on small data sets, e.g.,
10, 12, 13, 14, 18, 19, 22, 22 =16
10, 12, 13, 14, 15, 19, 22, 22 = 14.5
Not as powerful as the MEAN: we can only say
one value is higher than another on ranked
data
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Mode
• Most frequently occurring value in a data set, e.g.,
2, 4, 6, 7, 7, 7, 10,12 mode = 7
 Unaffected by extremes as we’re just looking at the most
common value rather than its position
 Can be used on basic data forming nominal categories –
we could do a frequency count on these, e.g., number of
people preferring vanilla, strawberry or chocolate ice-cream
Those mongrels are just
sooooooo common
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Disadvantages of the Mode

Small
changes can make a
big difference, e.g.,
1. 3, 6, 8, 9, 10, 10 mode=10
2. 3, 3, 6, 8, 9, 10 mode=3
 Can be bi/multimodal, e.g.,
3,5,8,8,10,12,16,16,16,20
So we’re too common
for you, now? You can
calculate the MEDIAN
and MEAN if you want to
waste time…we’re off to
have fun!
But the MODE
doesn’t tell me
much. What about
the rest of the
data? There’s this
really interesting
figure…
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Measures of central tendency are always
accompanied by a measure of dispersion
When using the …
Use …
Mean
Standard deviation
Median
Interquartile range
or range
Mode
Range
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Measures of Dispersion
Describe how spread out the values in a
data set are
Standard Deviation
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• The difference between the highest and lowest
scores in a set of data
 Quick to calculate
 Gives us a basic measure of how much the
data varies
Tells us nothing about data in the
middle of a set of scores
Affected by outlying values
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Interquartile
• This measures the spread of the middle 50% of
scores
Avoids extreme scores lying in the top 25% and
bottom 25%
Still uses only half of the available data
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Standard Deviation
• Measures the variability of our data, i.e., how
scores spread out in relation to the mean score
Allows us to make statements about probability –
how likely or unlikely a given value is to occur
Most powerful measure of dispersion as
all the data is used
Data cannot be ranked or from categories
Data must form a normal distribution curve
as SD is affected by skewed data
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68%
95%
99%
-3 SD
-2 SD
-1 SD
mean
1 SD
2 SD
3 SD
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The AS syllabus doesn’t require you to
work out SD, but you must know why we
use it and what it means. However,
previous students found this much
easier to understand when they saw how
it was calculated and how it related to
data in a study, so stick with it if you can.
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Formula for calculating
standard deviation
s
d
2
N 1
18
s
d 2
I knew I
should’ve
done art
N 1
It’s really not so bad! You can do it!
S = the standard deviation we are trying to calculate
√ = square root
∑ = sum of – add up
d2 = the squared deviation from the mean for each value
N = number of scores less one for error
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The easiest way to
calculate SD is to put all
your data into a very simple
table…Come on, I don’t
think you’re even trying, but
it’s not hard.
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Let’s look at some
test scores on a
reaction time task
85 86 94 95 96 107 108 108 109 112
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Make a table like this
Test Scores
Mean
Difference (d)
Difference Squared
(d2)
85
86
94
95
96
107
108
108
109
112
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Calculate the mean of
the data set
• 85+86+94+95+96+107+108+108+109+112 =
1000
• 1000 ÷ 10 (number of participants)=100
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Test Scores
Mean
85
100
86
100
94
100
95
100
96
100
107
100
108
100
108
100
109
100
112
100
Difference (d)
Difference Squared
(d2)
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Find the difference
between your results
and the mean score
to give you column d
Then square all the
values of d to give you
the next column d2.
Add up all the figures to
give you the total sum
for use in the formula
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Test Scores
Mean
Difference (d)
Difference Squared
(d2)
85
100
-15
225
86
100
-14
196
94
100
-6
36
95
100
-5
25
96
100
-4
16
107
100
+7
49
108
100
+8
64
108
100
+8
64
109
100
+9
81
112
100
+12
144
∑d2 = 900
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You now have all the
figures you need to
place into the equation
900
s
10  1
s
d
2
N 1
900 is the sum of d2
10 is your number of participants
900
s
9
Subtract 1 from your number of
participants to allow for errors in
sampling method, then divide the
top by the bottom number
s  100
Find the square root of this figure
s  10
This will give you your figure of
standard deviation
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But what does it actually mean in terms
of the reaction time task? I’m still very
confused
The mean time taken to do the task
was 100 seconds, but our SD figure
shows us that individual performances
varied from the mean by 10 seconds.
Some people would’ve taken 90
seconds to complete the task, while
others would’ve taken 110 seconds
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Here’s an example where we can compare performance
between two differing conditions in a repeated measures design
Participant
Number
Control
Condition
(before caffeine)
Experimental
Condition
(after caffeine)
1
6
5
2
5
5
3
7
4
4
9
3
5
8
8
6
5
4
7
6
5
8
7
6
9
8
5
10
6
7
Raw scores in seconds for a reaction time task
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Summary data table of reaction time scores in control (before
caffeine) and experimental (after caffeine) conditions
Control
Condition
(time in secs)
Experimental
Condition
(time in secs)
Mean
6.7
5.2
Median
6.5
5.0
6
5
1.34
1.48
Mode
Standard
Deviation
You can see from the table that performance after
caffeine was faster compared to doing the task before
caffeine. However, the SD tells us that there was greater
variation in the scores in the experimental condition.
Scores in the control condition were closer to the mean
and therefore are more representative as there’s less
variation in them. SD provides us with detailed
information about data spread that the range cannot.30