Graph Information

Options on many / all graphs

Invert Colours

Switches the colours on the graph to the opposite colours

Gray Scale (do not use on Firefox)

Makes all of the NZGrapher interface in greyscale

Size

This adjusts the size of the graph. By default it fills the size of the graph area.

• Auto: Fills the graph area completely

• Auto - High Res: Fills the graph area completely, but the image is a high resolution image, which can be useful when printing published materials

• Standard:  800px wide by 600px high

• Short: 800px wide by 300px high

• Small: 500px wide by 400px high

Colour Scale

• Rainbow: Goes from Red through to Purple

• Viridis: Goes from Purple through to Yellow (Colourblind friendly)

Title

This is the title that ends up on the top of the graph

x-axis

This is the label that is shown next to the horizontal axis.

y-axis

This is the label that is shown next to the vertical axis.

Colour Label

This is the label that is shown next to the colour key at the top of the graph.

Show ID of Removed Points

In the top right corner shows the ID of the points that have been removed as they didn't have valid data for graphing. This is on by default.

Transparency

This slider allows you to set the transparency of the points on the graph.

About

This shows the info page about NZGrapher in the graph window (it's not really a graph).

Pairs Plot

This graph gives a quick overview of all the variables in the dataset. Note: it will not work if the first data point has any missing values.

Dot Plot (and Box and Whisker)

This graph draws dot plots and box and whisker graphs, as well as violin graphs, strip graphs, shape outline graphs and bee swarms.

Data Options

• Numerical 1: This is the variable that is plotted against the x-axis.

• Category 1 (Optional): This is the variable that is used to split the data into different box plots that are plotted on the same axis.

• Category 2 (Optional): This is the variable that splits the graph into multiple graphs side by side.

• Colour By (Optional): This is the variable that the dots are coloured by.

Summaries

Shows the summary statistics for each group including the mean, median, min, max, quartiles, standard deviation and number of points in the group.

Box Plots

Shows a box plot overlaid over the dot plot.

High Box Plot

Shows a box plot towards the top of the graph area to avoid as much as possible overlapping with the dots.

Hide Points

Hides the dots on the dot plot.

Box (No Whisker)

Just plots the middle box of a box-and whisker graph

Box (No Outlier)

Plots a box and whisker graph that doesn't extend to the outliers (no more than 1.5 times the IQR less than the LQ / more than the UQ).

C-I Limits

Displays the numbers at each end the Informal C-I lines.

C-I Highlight

Highlights above and below the informal C-I area on the graph to make it visually easier to see if they overlap.

Point Labels

Puts a number next to each of the points so you can identify which point it is in the data table.

Mean Dot

Draws a red dot on the graph where the median sits.

Stack Dots

Makes the dots all sit on top of each other in "tidy" vertical lines. This means the points may not be plotted in exactly the right location, as they are shifted slightly horizontally to allow them to stack up.

Gridlines

Draws vertical gridlines on the graph up from the axis

Thick Lines

Makes the thickness of the lines used to draw the dots much thicker.

Point Size

This slider allows you to set the size of the points on the graph.

Bar Graph

Data Options

• Category: This is the variable that become the bars.

• Split (Optional): This is the variable that splits the graph into multiple graphs that are stacked on top of each other.

• Colour By (Optional): This is the variable that the bars are split into and are coloured by.

Summaries

Shows numbers on the bars for the frequency of each group

Allow More Categories

Allows more categories to be graphed.

Note: by default the limit is 10, which doesn't work for the sum of two dice, so this allows more categories to be graphed.

Gridlines

Draws horizontal gridlines on the graph to more easily match the axis to the bars

100% Bar Graph

Makes all the bars 100% tall (only useful when you have used the 'Colour By' option or 'Relative Width' option)

Relative Freq.

Makes all the bars add up to 1, so shows probabilities rather than frequencies

Relative Width

Makes the bars relative widths based on their frequency (only  useful with the '100% Bar Graph' option)

Bar Graph - Summary Data

This is identical to the bar graph, except there is an extra option under the data so you can use summary data to draw the bar graph 

• Frequency: This is the number of each category.

Histogram

Data Options

• Numerical: This is the data that determines the buckets used on the graph.

• Split (Optional): This is the variable that splits the graph into multiple graphs that are stacked on top of each other.

Summaries

Shows numbers next to the histograms with summary statistics like mean and median.

High Box Plot

Draws a box and whisker graph above the histogram

Gridlines

Draws horizontal and vertical gridlines on the graph to more easily match the axis to the bars

Relative Freq.

Changes the scale on the left from frequency to the proportion of the data that is in each bucket.

Normal Dist.

Overlays a normal distribution onto the histogram so it can be easily compared.

Rectangular Dist.

Overlays a rectangular distribution onto the histogram so it can be easily compared.

Triangular Dist.

Overlays a triangular distribution onto the histogram so it can be easily compared.

Poisson Dist.

Overlays a poisson distribution onto the histogram so it can be easily compared.

Binomial Dist.

Overlays a binomial distribution onto the histogram so it can be easily compared.

Intervals Slider

Adjusts the number of intervals displayed in the histogram

Histogram - Summary Data

This is identical to the histogram, except there is an extra option under the data so you can use summary data to draw the bar graph 

• Frequency: This is the number of each category.

Pie Chart

A Pie Chart is a circular graphic divided into slices to illustrate numerical proportions or relative frequencies of categorical data. Each slice's arc length (and central angle) is proportional to the quantity or frequency it represents, allowing viewers to easily visualize the relative size of each category as a part of a whole.

Data Options

Category 1: This is the variable that determines the slices of the pie.

Category 2 (Optional): This is the variable that splits the graph into multiple separate pie charts.

Frequency (Optional): The number in each group, if blank then it defaults to 1

Summaries

Displays the data values, percentages, or frequencies directly on or next to each slice of the pie chart, making exact figures easy to read at a glance.

Donut

Transforms the standard solid pie chart into a donut chart by cutting out the center, leaving a hollow space in the middle.

Scatter Graph

Regression Line

Fits a least squared regression line to the data, and displays the equation. If your variable names are long, you can alter what shows on the graph under the "more options" button in the bottom right corner.

Point Labels

Shows numbers next to the points that correspond to the point ID in the data list.

Mean Dot

Places a dot at the mean point of both variables. A normal regression line will always pass through this point.

Quadrant Count

The Quadrant Count Ratio is a measure of association between paired numerical variables. You divide the scatter plot into 4 sections by plotting the mean point and placing a vertical and horizontal line through it.

The QCR = (Number of Points in Q1 and Q3) - (Number of points in Q2 and Q4)
                                (total number of points)

The QCR is always between -1 and +1, and can be converted to a percentage. If the QCR is > 20% then it suggests a positive association, and < -20% suggests a negative association.

More details on Quadrant Count Ratio and how it can be used in teaching can be found in Pip Arnold's book Statistical Investigations (page 325-326) or GAISE II (pages 60-61).

Show Ratio

Shows the quadrant count ratio on the graph.

Bootstrap Trendline

Bootstraps the data 1000 times, and shows a trendline for each bootstrap sample, allowing you to see how stable the trendline is.

Jitter

Adjusts each point by a random amount left to right and up and down, which is useful for showing how many points there are when lots of points are in the same location.

Quadratic

Fits a quadratic trendline to the data

Cubic

Fits a cubic trendline to the data.

y=a*exp(b*x)

Fits an exponential trendline to the data.

y=a*ln(x)+b

Fits a logarithmic trendline to the data.

y=a*x^b

Fits a power trendline to the data.

y=x

Draws a dotted line along the line y=x

Colour by Dist.

This uses the Mahalanobis distance to colour points based on their distance from the bulk of the data, which makes it useful for identifying outliers. I've done a video explainer on the Mahalanobis distance. You can also play with the tool in the video here.

When you use the Limit option, it only highlights the number of points chosen that are have the largest Mahalanobis distance.

Stack Graphs

Instead of drawing the graphs separately, it stacks them on top of each other, allowing you to easily compare trends.

Gridlines

Shows gridlines on the scatter graphs

Thick Lines

Makes the lines thicker

Add Cust. Line 1/2/3

Allows you to add up to three custom lines onto the graph by dragging points around to fit the lines by eye.

Show Eqn

Shows the equation of the custom lines

Horizontal / Vertical Error Bars

Allows you to add error bars to the datapoints, based on the variable you select

Grid Density Plot

A Grid Density Plot displays the distribution and concentration of data points across a two-dimensional grid space. Rather than just showing individual markers or a standard scatter plot, it divides the graphing area into a grid matrix where the shading or density of each cell represents the frequency or concentration of data points falling within that specific region. This helps visualize dense clusters and overall patterns in bivariate data more clearly when dealing with large sample sizes.

Data Options

Variable 1: The "x" axis variable.

Variable 2: The "y" axis variable.

Variable 3: Splits the graph by this variable

Gridlines

Draws horizontal and vertical reference lines across the grid density plot area, making it easier to trace specific points or dense regions back to the numerical values on the x- and y-axes.

Viridis

A perceptually uniform, colourblind-friendly colour palette that transitions smoothly from purple (representing lower data density) through green to yellow (representing higher data density). This ensures that variations in concentration are accurately interpreted and easily distinguishable for all viewers. When off the graph is displayed as a grey scale.

Residuals Plot

A Residuals Plot is used in regression analysis to evaluate the goodness-of-fit of a linear model. It plots the independent variable (or fitted values) on the x-axis against the residuals (the differences between the observed values and the values predicted by the model) on the y-axis.

• Fitted Values: The predicted y-values generated by the linear regression line.

• Residuals: Calculated as Observed - Predicted. A random, even scatter of points centered around the horizontal line at zero indicates that a linear model is appropriate for the data. Patterns, curves, or funnel shapes in a residuals plot suggest that a linear relationship may not be the best fit.

FAQ: Why does residuals plots have 'fitted' on the x axis?

Data Options

Variable 1: The "x" axis variable.

Variable 2: The "y" axis variable.

Point Labels

Shows numbers next to the points that correspond to the point ID in the data list.

Weighted Average

Toggles a smoothed trend line through the residuals. This helps visually identify whether the residuals remain evenly centered around zero across the entire range of the plot, or if there is a hidden non-linear trend or systematic bias that the linear model missed.

Change X Axis

Allows you to switch the variable displayed on the horizontal axis of the residuals plot. Instead of plotting the residuals against the fitted values, you can toggle it to plot against the independent variable. This is useful for checking variance consistency and spotting funnel shapes or heteroscedasticity.

Regression Type

Lets you change the underlying mathematical model used to fit the data before generating the residuals (such as Linear, Quadratic, Exponential, or Power). Changing the regression type instantly updates the residuals plot, allowing you to compare how effectively different models capture the patterns in the data and minimize residual error.

Running Proportion

A Running Proportion graph plots the cumulative relative frequency (or proportion) of an event or outcome against the number of trials or sample size. As the sample size increases, the line fluctuates significantly at the beginning before stabilizing and converging toward the true underlying probability, illustrating the Law of Large Numbers. This graph is commonly used in probability simulations and experiments to show how experimental probability approaches theoretical probability over time.

Data Options

Event: The column containing the event you are trying to track

Point Labels

Shows numbers next to the points that correspond to the point ID in the data list.

Success

Allows you to select which specific outcome from the variable is counted as the "success" or event of interest.

Bootstrap Single Variable - To Be Completed

Bootstrap Confidence Interval - (Median or Mean) - To Be Completed

Re-Randomisation - (Median or Mean) - To Be Completed

Paired Experiment Dot Plot (and Arrows Graph)

A Paired Experiment Dot Plot (and the associated Arrows Graph) is designed for dependent or matched-pairs data where two measurements are taken from the same subject or item (such as "Before" and "After" conditions). It allows you to visualize both the individual changes using connecting arrows and the overarching distribution of the paired numerical values.

Data Options

Numerical 1: The first numerical variable representing the initial measurement or baseline condition.

Numerical 2: The second numerical variable representing the subsequent measurement or follow-up condition.

Arrows

Toggles the display of directed lines connecting the two paired values for each individual subject, visually highlighting the direction and magnitude of change.

Colour by Difference

Colours the points or arrows based on whether the paired difference is positive or negative, making it easy to distinguish increases from decreases.

These options are the same as on the dot plot graph:

• Summaries

• Box Plots

• High Box Plot

• Strip Graph

• Box (No Whisker)

• Box (No Outlier)

• Informal C-I

• C-I Limits

• C-I Highlight

• Point Labels

• Mean Dot

• Stack Dots

• Gridlines

Time Series

FAQ: How does NZGrapher produce its time series graphs?

Time Series Data Types:

• Yearly: Simple numbers representing years alone (e.g., 2015, 2016, 2017).

• Quarterly (4 Seasons): Year followed by the letter "Q" and a single-digit quarter number from 1 to 4 (e.g., 2015Q1, 2015Q2).

• Monthly (12 Seasons): Year followed by the letter "M" and a two-digit month number from 01 to 12 (e.g., 2015M01, 2015M12).

• Daily (7 Days): Week or period identifier followed by the letter "D" and a single-digit day number from 1 to 7 (e.g., 2001D1, 2001D7).

• Daily (5 Days / Work Week): Week or period identifier followed by the letter "W" and a single-digit day number from 1 to 5 (e.g., 2001W1, 2001W5).

• Hourly (24 Hours): Day or period identifier followed by the letter "H" and a two-digit hour number from 01 to 24 (e.g., 2001H01, 2001H24).

Time Series

A Time Series graph plots data points sequentially over equally spaced intervals of time on the horizontal axis. It allows you to track changes over time, identify overall long-term trends, observe seasonal patterns, and spot irregular fluctuations or turning points in historical data.

Data Options

Variable 1: The time or date variable (such as months, quarters, or years) plotted on the horizontal axis.

Variable 2: The numerical measurement or quantitative variable being analysed over time.

Variable 3: An extra numerical measurement or quantitative variable being analysed over time.

Point Labels

Shows numbers next to the points that correspond to the point ID in the data list.

Show Dots

Toggles the visibility of individual data point markers along the plotted lines.

Seasonal

Toggles the display of the seasonal component to the right of the main graph.

Different Axis

Puts the variable 3 on it's own axis to the right of the graph so you can look at variable on different scales.

Long Term Trend (STL)

Applies a Seasonal and Trend decomposition using Loess (STL) algorithm to isolate the smooth, long-term underlying trend of the data.

Seasonal (STL)

Toggles the display of the seasonal component to the right of the main graph. This is done using the STL decomposition method.

Start / End Points

Highlights the first and last data points of the long term trend, showing their values.

Gridlines

Draws horizontal and vertical reference lines across the graph area, making it easier to trace specific points back to the numerical values on the axes.

Type

Lets you select the underlying model type (Additive or Multiplicative) used for analyzing or decomposing the time series.

Add Cust. Line

Allows you to draw a custom reference line on the graph at a specified value to highlight particular thresholds or benchmarks.

Show Eqn

Displays the equation associated with the custom line directly on the graph.

Re-Composition

A Time Series Re-Composition graph takes the isolated components of a time series model—the trend, seasonal effect, and residuals (remainder)—and combines them (either by adding or multiplying) to reconstruct the original time series data. This allows you to verify how well the chosen model fits and explains the original observed values.

Data Options

Variable 1: The time or date variable (such as months, quarters, or years) plotted on the horizontal axis.

Variable 2: The numerical measurement or quantitative variable being analyzed.

Point Labels

Shows numbers next to the points that correspond to the point ID in the data list.

Start / End Points

Highlights the first and last data points of the long term trend, showing their values.

Gridlines

Draws horizontal and vertical reference lines across the graph area, making it easier to trace specific points back to the numerical values on the axes.

Type

Lets you select the underlying model type (Additive or Multiplicative) used to recompose the time series.

Seasonal Effects

A Time Series Seasonal Effects graph extracts and displays the recurring, predictable cyclical patterns that occur within a fixed period (such as months, quarters, or weeks). It isolates how much each specific time period deviates above or below the overall trend line, allowing you to examine seasonal variations independently from long-term trends.

Data Options

Variable 1: The time or date variable (such as months, quarters, or years) plotted on the horizontal axis.

Variable 2: The numerical measurement or quantitative variable being analyzed for seasonal patterns.

Point Labels

Shows numbers next to the points that correspond to the point ID in the data list.

Forecasts

A Time Series Forecast graph extends historical time series data into the future by combining trend and seasonal components to project expected values. It plots future predictions alongside prediction intervals (represented by shaded bands that widen over time), allowing analysts to visualize both expected future trends and increasing uncertainty further out.

Data Options

Variable 1: The time or date variable (such as months, quarters, or years) plotted on the horizontal axis.

Variable 2: The numerical measurement or quantitative variable being modeled and forecast.

Forecast output

When ticked, displays a data table showing the projected forecast values alongside their lower and upper bounds for upcoming time periods rather than the graph of the data.

Point Labels

Shows numbers next to the points that correspond to the point ID in the data list.

Type

Lets you select the underlying model type (Additive or Multiplicative) used to decompose the historical data and generate the forecast calculations.

Change Log

This allows you to see a list of all the changes that have been made to NZGrapher.

Update

This allows schools that are hosting themselves to show the current version of the site and update if there is a newer version available.