Complete revision and summary notes for Data Concepts & Data Analysis for BSc Psychology: Research Methods 1 Module.
Written by a straight A* King's College London student set for a 1st.
Well organised and in order. Includes diagrams and full reference section and collated information from lec...
4PAHPRM1 Research Methods 1 Data Concepts & Data Analysis
BSc Psychology Year 1
DESCRIPTIVE STATISTICS
MEASURES OF CENTRAL TENDENCY
Mode
• The score that appears the greatest number of times
Median
• The “middle score” in an ordered list of scores
𝑛+1
𝑀𝑒𝑑𝑖𝑎𝑛 𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛 =
2
Mean
• The sum of scores
• The mean of a sample is an unbiased estimator of the mean of the population
∑"
Χ# (𝜇) = # where 𝑋 is the data values, and 𝑁 is the number of scores
Calculating the Measures of Central Tendency
Analyze > Descriptive Statistics > Explore
• Enter relevant variable(s) into the relevant boxes
• Click OK (this will only show the mean and median)
OR
Analyze > Descriptive Statistics > Frequencies...
• Add relevant variables into the Variable(s) box
• Click Statistics and tick Mean, Median and Mode
• Click Continue, then OK
Trimmed Mean
• Calculates the average of a dataset after removing a percentage of the highest and lowest values
• For a 5% trimmed mean, remove the highest 5% and lowest 5% of scores
• For a 20% trimmed mean, remove the highest 20% and lowest 20% of scores
Sample of 40 scores
5% trimmed mean
• 5% of 40 = 2
• Take 2 scores from the top and bottom
20% trimmed mean
• 20% of 40 = 8
• Take 8 scores from the top and bottom
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,4PAHPRM1 Research Methods 1 Data Concepts & Data Analysis
BSc Psychology Year 1
Calculating a 5% Trimmed Mean
Analyze > Descriptive Statistics > Explore
• Enter relevant variable(s) into the relevant boxes
• Click OK
You cannot compute trimmed means with different percentages on SPSS
MEASURES OF DISPERSION (VARIABILITY)
Minimum Score and Maximum Score
• The lowest and highest scores within a data set
Lower Quartile (25th Percentile)
𝑛+1
𝐿𝑜𝑤𝑒𝑟 𝑄𝑢𝑎𝑟𝑡𝑖𝑙𝑒 𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛 =
4
Interquartile Range
𝑈𝑝𝑝𝑒𝑟 𝑄𝑢𝑎𝑟𝑡𝑖𝑙𝑒 − 𝐿𝑜𝑤𝑒𝑟 𝑄𝑢𝑎𝑟𝑡𝑖𝑙𝑒
• The interquartile range can be recorded as a size (e.g. “18”) or a pair (e.g. “(2, 20)”)
Range
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑠𝑐𝑜𝑟𝑒 − 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑠𝑐𝑜𝑟𝑒
• The range can be recorded as a size (e.g. “18”) or a pair (e.g. “(2, 20)”)
Calculating the Measures of Dispersion
Analyze > Descriptive Statistics > Explore
• Enter relevant variable(s) into the relevant boxes
• Click OK
OR
Analyze > Descriptive Statistics > Frequencies...
• Add relevant variables into the Variable(s) box
• Click Statistics and tick any of the Minimum, Maximum, Quartiles, Range
• Click Continue, then OK
OR
Analyze > Compare Means and Proportions > Means...
• Add relevant variables into the Variable(s) box
• Click Options and tick any of the Minimum, Maximum, Quartiles, Range
• Click Continue, then OK
2
,4PAHPRM1 Research Methods 1 Data Concepts & Data Analysis
BSc Psychology Year 1
VARIANCE AND STANDARD DEVIATION
Sample Variance
• Computes the deviation from the mean for each score
• The sample mean and sample variance are “unbiased estimators” of the corresponding
population parameters
%("'"( )!
𝑠$ = where 𝑋 are the data values, 𝑋@ is the mean, and 𝑁 is the number of scores
#'*
OR
𝑠! = 𝜎!
Standard Deviation
"($%$&)!
𝜎 =B (%)
OR
𝜎 = √𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒
Calculating Variance and Standard Deviation
Analyze > Descriptive Statistics > Explore
• Enter relevant variable(s) into the relevant boxes
• Click OK
OR
Analyze > Compare Means and Proportions > Means...
• Add relevant variables into the Variable(s) box
• Click Options and tick any of the Variance or Standard Deviation
• Click Continue, then OK
Pooled Standard Deviation
• Used for when there is no population or control standard deviation for calculating the effect size of
a mean difference
*"! %*!!
𝑃𝑜𝑜𝑙𝑒𝑑 𝑆𝐷 = B !
where 𝜎) and 𝜎! are the standard deviations of two groups
MEASUREMENT DATA AND CATEGORICAL DATA
Scales of Measurement
Nominal
• Data is categorised without any order or ranking
• Categories are mutually exclusive (e.g., Male, Female)
• Statistical operations include mode and frequency counts
3
, 4PAHPRM1 Research Methods 1 Data Concepts & Data Analysis
BSc Psychology Year 1
Ordinal
• Data is ranked in order, but intervals between ranks are not equal
• Examples include education levels (e.g., Bachelor’s, Master’s)
• Statistical operations include median and percentiles
Interval
• Data is ranked with equal intervals, but no true zero point
• Examples include temperature in Celsius or Fahrenheit
• Statistical operations include mean, standard deviation, and correlations
Ratio
• Data has equal intervals and a true zero point
• Examples include height, weight, and time
• Statistical operations include all arithmetic and geometric calculations
MATCHING THE SCALES OF MEASUREMENT
• It is valuable to summarise a sample by reporting both central tendency and variability because it
provides a more complete picture of the data
• Central tendency measures indicate the typical value within the sample
• Variability measures reveal the spread or dispersion of the data around the central value
Advantages and Disadvantages
Measure Advantages Disadvantages
Mean • Most informative for central • Can be skewed by outliers (using
tendency a trimmed mean can negate this)
Median • When there are outliers • Time consuming with lots of data
Mode • The only one that can be used for • Not always representative of the
nominal data data
Quartiles • Resistant to outliers • Ignores extreme values, so can
be misleading
Range • Easy to calculate • Susceptible to outliers
Standard Deviation • Shows data distribution • Time consuming to calculate
• Not affected by outliers • Assumes normal distribution
When to Use Each Measure
Scale of Measurement Measure of Central Tendency Measure of Dispersion
Nominal Mode N/A
Ordinal Median Quartiles/Range
Interval Mean Range/Standard deviation
Ratio Mean Range/Standard deviation
FREQUENCY DISTRIBUTIONS
• Shows every score in order and indicates how often each has been obtained
Cumulative Frequency
• The total of all frequencies in a frequency distribution
• Calculated by adding each frequency to the sum of those that came before it
4
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