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Research Methods & Design in PsychologyPowerPoint Presentation

Research Methods & Design in Psychology

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Lecture 3 Descriptives & Graphing Lecturer: James Neill Research Methods & Design in Psychology Overview Univariate descriptives & graphs Non-parametric vs. parametric Non-normal distributions Properties of normal distributions Graphing relations b/w 2 and 3 variables

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Research Methods & Design in Psychology

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Lecture 3

Descriptives & Graphing

Lecturer: James Neill

Univariate descriptives & graphs

Non-parametric vs. parametric

Non-normal distributions

Properties of normal distributions

Graphing relations b/w 2 and 3 variables

A positivistic approach ASSUMES:

the world is made up of bits of data which can be ‘measured’, ‘recorded’, & ‘analysed’

Interpretation of data can lead to valid insights about how people think, feel and behave

Distributional properties of variables:

Central tendency(ies)

Shape

Spread / Dispersion

Central tendency

Mode

Median

Mean

Spread

- Interquartile Range
- Range
- Standard Deviation
- Variance

Shape

- Skewness
- Kurtosis

Bar Graph – Pie Chart

Stem & Leaf Plot

Boxplot

Histogram

Statistics to represent the ‘centre’ of a distribution

Mode (most frequent)

Median (50th percentile)

Mean (average)

Choice of measure dependent on

Type of data

Shape of distribution (esp. skewness)

Mode

Median

Mean

Nominal

X

Ordinal

X

X

Interval

X

X

X

Ratio

X?

X

X

Measures of deviation from the central tendency

Non-parametric / non-normal:range, percentiles, min, max

Parametric:SD & properties of the normal distribution

Range, Min/Max

Percentiles

SD

Nominal

Ordinal

X

Interval

X

X

X?

Ratio

X

X

X

Frequencies

Most frequent?

Least frequent?

Percentages?

Bar graphs

Examine comparative heights of bars – shape is arbitrary

Consider whether to use freqs or %s

Number of individuals obtaining each score on a variable

Frequency tables

graphically (bar chart, pie chart)

Can also present as %

Most common score - highest point in a distribution

Suitable for all types of data including nominal (may not be useful for ratio)

Before using, check frequencies and bar graph to see whether it is an accurate and useful statistic.

Conveys order but not distance (e.g., ranks)

Descriptives as for nominal (i.e., frequencies, mode)

Also maybe median – if accurate/useful

Maybe IQR, min. & max.

Bar graphs, pie charts, & stem-&-leaf plots

- Useful for ordinal, interval and ratio data
- Alternative to histogram

- Useful for interval and ratio data
- Represents min. max, median and quartiles

Conveys order and distance, but no true zero (0 pt is arbitrary).

Interval data is discrete, but is often treated as ratio/continuous (especially for > 5 intervals)

Distribution (shape)

Central tendency (mode, median)

Dispersion (min, max, range)

Can also use M & SD if treating as continuous

Numbers convey order and distance, true zero point - can talk meaningfully about ratios.

Continuous

Distribution (shape – skewness, kurtosis)

Central tendency (median, mean)

Dispersion (min, max, range, SD)

Mean

<-Kurt->

<-SD->

<-Skew

Skew->

Four mathematical qualities (parameters) allow one to describe a continuous distribution which as least roughly follows a bell curve shape:

- 1st = mean (central tendency)
- 2nd = SD (dispersion)
- 3rd = skewness (lean / tail)
- 4th = kurtosis (peakedness / flattness)

- Average score
- Mean = X / N
- Use for ratio data or interval (if treating it as continuous).
- Influenced by extreme scores (outliers)

- SD = square root of Variance
= (X - X)2

N – 1

- Standard Error (SE) = SD / square root of N

- Lean of distribution
- +ve = tail to right
- -ve = tail to left
- Can be caused by an outlier
- Can be caused by ceiling or floor effects
- Can be accurate (e.g., the number of cars owned per person)

- Negative skew

- Positive skew

- Flatness or peakedness of distribution
- +ve = peaked
- -ve = flattened
- Be aware that by altering the X and Y axis, any distribution can be made to look more peaked or more flat – so add a normal curve to the histogram to help judge kurtosis

Red = Positive (leptokurtic)

Blue = negative (platykurtic)

- For normal distributions, approx. +/- 1 SD = 68%+/- 2 SD ~ 95%+/- 3 SD ~ 99.9%

- Bi-modal
- Multi-modal
- Positively skewed
- Negatively skewed
- Flat (platykurtic)
- Peaked (leptokurtic)

- View histogram with normal curve
- Deal with outliers
- Skewness / kurtosis <-1 or >1
- Skewness / kurtosis significance tests

+vely skewed mode < median < mean

Symmetrical (normal) mean = median = mode

-vely skewed mean < median < mode

Graphs:

Reveal data

Communicate complex ideas with clarity, precision, and efficiency

Show the data

Substance rather than method

Avoid distortion

Present many numbers in a small space

Make large data sets coherent

- Encourage eye to make comparisons
- Reveal data at several levels
- Purpose: Description, exploration, tabulation, decoration
- Closely integrated with statistical and verbal descriptions

Some lapses intentional, some not

Lie Factor = size of effect in graph size of effect in data

Misleading uses of area

Misleading uses of perspective

Leaving out important context

Lack of taste and aesthetics

Trade-off between amount of information, simplicity, and accuracy

“It is often hard to judge what users will find intuitive and how [a visualization] will support a particular task” (Tweedie et al)

- Presenting Data – Statistics Glossary v1.1 - http://www.cas.lancs.ac.uk/glossary_v1.1/presdata.html
- A Periodic Table of Visualisation Methods - http://www.visual-literacy.org/periodic_table/periodic_table.html
- Gallery of Data Visualization
- Univariate Data Analysis – The Best & Worst of Statistical Graphs - http://www.csulb.edu/~msaintg/ppa696/696uni.htm
- Pitfalls of Data Analysis – http://www.vims.edu/~david/pitfalls/pitfalls.htm
- Statistics for the Life Sciences –http://www.math.sfu.ca/~cschwarz/Stat-301/Handouts/Handouts.html