## Description

Are you working with directional data measured in degrees? Perhaps your research involves looking at patterns in the time of day of events, or things that occur in weekly, monthly or yearly cycles. These are circular data and they require special types of statistics. If you want to analyse this type of data, then Oriana is just what you need. Oriana is a program written for Microsoft Windows. It calculates the special forms of sample and inter-sample statistics required for circular data. It also graphs your data in a variety of ways, allowing you to easily demonstrate patterns. These analyses and graphs are rarely found in other statistical packages. Oriana is designed to be full featured and powerful, but also intuitive and easy to use.

# Features of Oriana 4

**Data Handling**

- Built-in spreadsheet-like data editor; supports cut and paste between applications.
- Circular data types:
- Angles (unidirectional and bidirectional [axial])
- Time of day
- Compass direction
- Day of week
- Month of year
- Week of year
- Day of year
- Proportional and percentage (like Angles, but scaled 0-1 or 0-100 rather than 0-360)
- Lunar cycle

- Non-circular data types:
- Date
- Linear numerical
- Label
- Subgroups

- Flexible data handling; sets of data can be entered as separate columns (the old Oriana ver. 1 method) or can be entered pairwise with other data (linear, dates, labels, other circular data).
- With the paired method a file can also have one or more grouping variables added to allow for analysis of subgroups of data. Subgrouping can also be performed on existing data (such as the date, summarized in different ways).
- Frequency data can be entered either directly into the spreadsheet as a frequency table or through a special frequency editing mode that expands the frequencies into a single column of raw data.
- Data can be filtered, restricting analyses and graphs to just cases that meet a certain criterion (e.g. Angle > 90 or Month = June).
- Circular data can be entered as x/y coordinates defining the beginning and ending point of a vector. They can then be converted to vectors (angle and length) for analysis.
- Variables can be automatically filled with identical, incrementing or random (uniform or von Mises) data.
- An optional file creation wizard aids in the process of setting up new data files.
- Dates can be summarized into day of week, month of year, week of year or day of year.
- Data transformation:
- Data entered or imported in radians can be converted to degrees for analysis.
- Linear data can be standardized and log or square root transformed.

- A Find and Replace facility lets you search for particular data points and make global changes.
- Data can be sorted.
- Grouped circular data (data recorded approximately to the nearest interval, such as every 20° or every hour, rather than exactly) are automatically detected and flagged (with user confirmation) so that statistical analyses are adjusted accordingly, where relevant.
- Missing data capability with pairwise deletion where required.
- Several Oriana data files can be merged into a single file.
- Import and export from/to Excel (both .XLS and .XLSX), Lotus 123, Quattro, dBase, Paradox, ASCII text.
- Number of cases and variables limited only by available memory and disk space.

**Statistics**

- Basic statistics
- circular mean,
- length of mean vector (r),
- median angle
- circular variance, standard deviation and standard error
- 95% and 99% confidence interval for the mean vector.
- mean weighted by linear variable, plus basic statistics for the linear variable itself
- means and mean vector lengths can be saved to a file for further second order analysis.

- One-sample tests
- Rayleigh’s test of uniformity
- Hotelling’s test for weighted data
- Moore’s modified Rayleigh test for weighted data
- Rao’s spacing test
- Chi-Squared
- V-Test
- Watson’s U²
- Kuiper’s.

The last two can be used for tests against both the uniform and von Mises distribution.

- Two-sample tests
- Watson-Wheeler F-test
- Chi-squared test
- Mardia-Watson-Wheeler test
- Watson’s U² test.
- Hotelling’s paired multisample test
- Moore’s paired multisample test (nonparametric)

- Multisample tests – The first three two-sample tests above can also be performed as multi-sample tests.
- Circular-circular and circular-linear correlations.
- Second order statistical analysis:
- Grand mean angle, length and confidence limits
- Hotelling’s one sample second order test
- Moore’s modified Rayleigh test for second order analyses
- Hotelling’s two sample second order test
- Mardia’s two sample second order test (nonparametric)
- Hotelling’s paired sample second order test
- Moore’s paired sample second order test (nonparametric)

- All analyses can be performed on subgroups of data as well as the whole data set.

**Graphics**

- Graph types include
- Rose diagrams
- Circular histograms
- Linear histograms
- Arrow graphs – like a histogram, but an arrow is used for each class rather than a bar or wedge
- Raw data plots
- Distribution graphs – plot data against expected distribution for either uniform or von Mises distributions.
- Stacked and stepped circular histograms/rose diagrams- bars or wedges divided into segments to reflect the proportions of each subgroup within the data.
- Stacked raw data plots – points representing each data point are colored according to their subgroup
- Two-variable circular histograms – segments of each bar represents the classes of a second circular or linear variable (e.g. wind speed plotted as segments on bars representing wind direction)
- Circular-linear plots – these incorporate linear data along with your circular data. An arrow, bar or wedge is drawn for each case, with the length representing the linear data.
- Circular scatterplots – these also plot linear and circular data, with each data pair being plotted as points on a circular plot
- X/Y Scatterplots – can plot any circular or linear variable on X/Y Cartesian axes.
- Q-Q plot – compare distributions of two circular samples to assess whether they have the same distribution

- Mean and confidence limits can be shown on histograms. Mean can alternatively be represented by a mean vector, where the length of the arrow reflects the mean vector length (r).
- Circular graphs can have a circle showing the critical value of the Rayleigh test. The length of the r vector can then be compared to this circle to assess its significance.
- With paired vector data (consisting of angle and length) the mean vector can be weighted by the vector lengths.
- Axes can be extensively customized with regard to number of grid lines, scaling (linear, percentage or logarithmic), format and orientation of labels.
- Circular graphs can be drawn with the 0°/N point at user chosen position on the circle, and oriented either clockwise or counter-clockwise.
- Doubled-angle plots, which plot only the data between 0-180°, but spread around the full circumference of the circle, can be produced. This type of graph is used in fields such as ophthalmology.
- Circular-linear plots can have a standard deviation ellipse plotted (also used in opthalmology).
- Division of segments in two-variable histograms can be customized or manually defined.
- Bar width of histograms and rose diagrams can be changed.
- Rose diagrams can have frequency depicted by either radius or area of wedge.
- Linear histograms can be plotted as double width plots to emphasise cyclicity in data.
- Table of frequencies used to produce histograms can be displayed in the Results window.
- Graph types and options can be modified without having to create a new graph window.
- Graph appearance can be customized (fonts, color of axes, thickness of lines and grids, color of background of various sections, series of colors, patterns and symbols for stacked and subgrouped diagrams).

**User Interface**

- Written specifically for Microsoft Windows. Follows the normal Windows conventions, making it easy to learn and use alongside your other Windows applications. Intuitive menu structure and quick-access toolbar buttons.
- Uses the KCS desktop metaphor. All results and graphs for a single project can be spread out on screen. Contents and arrangement of windows can then be saved and recalled later, letting you pick up where you left off. Different projects can be saved in separate desktop files.
- Graphs and results appear in two tabbed notebooks (one for each), with each graph or page of results on separate pages.
- Results and graphs can be exported for inclusion in reports or manuscripts, using cut and paste. Results can also be saved to text files or Excel spreadsheets, and graphs can be saved in a variety of formats, including EMF, WMF, BMP, PNG, GIF and JPG.
- Data, results and graphs can be printed to any Windows printer or plotter. Different devices can be used for text and graphics.
- Results and graphs can be exported or printed individually or all at once.
- Inclusion of a notepad allows you to make notes about your analyses. These are saved along with the graphs and results in a desktop file, and can be copied or exported to your word processor.
- Customizable toolbars – you can arrange the toolbars at any point around the margin of the window or floating over the window, and you can choose which buttons to display on each toolbar.
- User can select from a number of different color schemes, many with attractive gradient effects.
- Automatically uses local language (as set in Windows) for names of months and days, and local format for times and dates. Compass direction abbreviations can be customized manually.
- Full on-line help and a comprehensive manual with tutorial.

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