lecture 3- data visualisation

Stem and leaf plots

• stems- represent the tens

• Leaf- the units

• Scores are ordered from smallest to largest

• Can be used to compare 2 data sets.

• Can calculate mean, median, mode

• Histograms are better

Boxplots

• useful for showing median, range, IQR, skewness, etc.

How do you visualise data for frequency distribution?

Histograms

• individual bars give the frequency of a given value within a range

How do you visualise data for probability distribution?

Bell curves

• smooth, but segmented by standard deviations

• Area under the curve is the probability that value occurs

• E.g. can work out likelihood of a person having a health heart rate

What is skewness?

• deviation from symmetry

• Histogram shows big difference between mean, median and mode

• Some extreme scores are affecting the mean, but not the median

What is kurtosis and what are the 3 types?

• measure of the tailedness of a distribution

• Tailedness (pointiness)= how often outliers occur

• Mesokurtic (normal)

• Leptokurtic (positive)- high peak, skinny in middle, fat tails due to outliers

• Platykurtic (negative)- flatter distribution, broad in middle, skinny tails due to fewer and less extreme outliers

Which descriptive statistics do you report it data is parametric/ normally distributed?

Mean/ standard deviation

Which descriptive stats do you report when data is non-parametric/ skewed?

Median/range or IQR

What are the ways to determine skewness in R?

• skewness statistic

• Histogram with normality curve (represents a smoothed distribution)

• Probability density curve (follows individual data more closely)

What is a skewness statistic?

A value showing how skewed data is.

• 0= perfectly normal

• Further from 0 a value is, the more skewed it is

• If the skewness statistic is less than -1 or more than 1, we conclude data is skewed

• -1 to +1 = normal range

How is data illustrated to help others understand it?

• tables- good for comparing data. Typically used for descriptive stats.

• Figures- e.g. bar charts, scatter plots

What are error bars?

Visual representation of variability within data on bar charts.

• 95% confidence intervals are the most commonly presented error bars

• 95% CI- the percentage of times you expect to produce an estimate within the range E.g. confident that 95 out of 100 times, estimate will fall within upper and lower values specified by CI

• When error bars overlap, there is no significant difference between conditions. When they don’t, there is.

Where do figures go that are used to assess data?

In the appendix.

E.g. stem and leaf plots, boxplots

Where do figures go that are used to visually present data analysis for others?

The results section of report.

E.g. bar graphs, scatterplots.

What is a truncated graph?

When writers skew how data is perceived by making the baseline of a graph a difference number. (Baseline is usually 0). This can be misleading and starting at 0 offers a more accurate depiction of data.

Types of misleading figures

• omitting baseline

• Manipulating y axis to make data seem more or less significant than it is.

• Cherry picking data e.g. using a small date range

• Going against conventions e.g. using lighter shades on map to depict higher population density