Presenting data

Scientific research – have a hypothesis and use scientific methods to draw a conclusion 

Variable – anything that varies 

Data – values that variables recieve in measurements  

Results – systematic variation in the data that relates to the hypothesis and research question  

Analysis – reveals or tests patterns in data, produces results  

Three ways of presenting results: 

Text – verbal description. Establish unambigous meaning and logical relationship but risk to get lost in details 

Table – spatially organised representation of single, precise specifications. Communicate a larger number of specific details but meaning/logical relationships aren’t communicated 

Graphics – visualisation of data patterns.  

Focus and highlight on main pattterns in the data and communicate different kinds of information in parallel.   

But specific details get lost and visual interpretation may depend on veiwer 

Two main uses:

•  to assess quality of data (detects faults in your experiment, characterise data distribution and identifying outliers)

• visualise results  (highlights and explains main results)

When making graphics need to focus on dimensionality and format 

• How to use graphical tools? 

  1. How many variables  

     • One variable (univariate) data quality, distribution, outliers 

     • Two variable (bivariate) independent/dependent vriable, simple relationshops  

     • More than 2 variables (multivariate) complex relationships (interaction) 

   

  1. Types of variation. Independent variation, dependent variation and other variation(noise) which is not part of testing logic, but intertefers with the tested vairation and defines reliability of results. Other variation (noise) typically error bars, independent variable on X axis and dependent variable on Y axis 

    

  1. Types of scales: 

  Nominal scale – in graphic distances are unrelated 

  Ordinal scale - oriented 

  Interval scale - distances 

  Ratio scale – ratios 

   

   

  1. Resolution – put screenshot.  

  Decrease resoultion through aggregation (eg by categorising for nominal data or for quantative data using mean and standard deviation) to avoid clutter 

   

  1. Pattern- different kinds of diagrams to reveal different patterns and relationships 

  Freedom rating – more freedom, more versatile so describes more complex relationships but also less organised 

   

  Pie chart has low freedom rating  

  Variable 1 – a continous, ratio-scaled axis is represented as a circle 

  Variable 2 – discrete data is show as wedges 

  Advantage – Part-whole relationships – relate parts to the whole  

  But limited scope – limited to 2 sources of variation (no error bars) and requires ratio-scale and finite data 

   

  Bar chart has higher freedom rating  

  Variable 1 – discrete, more intuitve with regular steps  

  Variable 2 – quantative scale along 

  Can add error bars 

  Advantage: grouping – highlight distance from zero/another baseline and highlight differences across groups/conditions and visualise different groups/conditiions 

  Disadvantage: useless for continous data along both axes. Risks clutter when many data points 

   

  Line chart has even higher freedom rating  

  Variable 1 – continous, at least ordinal scale (otherwise connecting line misleading) 

  Variable 2 – continous, at least ordinal scale  

  Error bars 

  Additional continous variables: grouping of ata by seperate lines identified by visual appearance 

  Advantage: 

  Disadvantage: 

   

  Scatter chart higher freedom rating  

  Variable 1 and 2 – continous X and Y-axis, at least interval scale  

  Error bars possible along both axis  

  Additional varibales – identify by visual appearance 

  Advantage: covariation  

  Disadvantage: lacks structure, risks clutter  

Typically use graphics to see whether it is nominal or skew distribution  

Also typically used to highlight main results for comparison and references 

Aggregation by counting each value and summing up a binary variable (frequency) 

aggregate by frequency to visualise the distribution  

Proportion – a part, share or number considered in comparative relation to a whole (fraction) = relative frequency 

Percentage – per 100, where 100 is the full set 

In frequency charts we have dependent variable on X-axis and frequency on Y-axis 

• Nominal scale use a pie chart, can also use a bar chart. 

   But would be misleading (it would look like there is a trend when there is not) on line chart and not clear on scattergram 

   

  Ordinal scale would be good on a bar chart 

  But would not be clear on pie, line or scatter 

   

  Ratio scale but discrete is good on a scattergram  

   

  Continous data aggregation by frequency is useless  

  So we use binning which is transforming continuous data into discrete data by allocating the continous data to intervals (the bins) SCREENSHOT 

  Using the stem and leaf display forms a histogram  

  Histogram – a bar chart using bins to display continuous data  

  Highlight difference from zero on Y-axis 

  Frequency density – frequency of data per equal interval (frequency/bin size) 

  Probability density – probability of dara per value 

  Frequency desnity allows estimation of probabiklity density, which is fundamental for statistical testing 

  Assess the shape of distribution on histogram: symetrical (no tail or 2 tails), negative skew (left tail) or positive skew (right tail) 

   

  Cumulation – a collection of objects laid on top of each other  

  Cumulative sum or running total: sum up progressively 

  Gives cumulative histogram with cumulative frequency 

  Cumulative frequencies are an estimate of cumulative probabilities 

   

  Can simplify data by only analysing whats changed 

   

  Standard deviation of binary variable only depends on proportions 

   

  Aggregation by central tendency by obtaining the mean and standard deviation. Can plot the mean and standard deviation in bar chart making it much more simple 

  But mean and standard deviation can only be used for symmetrical distribution 

  Mean and SD misrepresent asymmetrical distribution 

  median and quartiles do not assume symmetry 

  Boxplot does not assume symmetry. Shows outliers and interquartile range (which is the width of the box) 

   

  When the IV and DV are both qualitative and nominal/ordinal date: 

  Use bar chart 

   

  When IV is qualitative and nominal/ordinal and DV is quantative and interval/ratio data that is discrete use bar or boxplot 

   

   

  When the dependent and independent variable is both quantative and continous: 

  • Use line chart because better highlights trends 

   

  For bivariate distribution use scattergram