Fathom Features

Data Sources

Use data from one of the many sample documents that come with Fathom.
Enter your own data by typing into a case table.
Paste data from other applications.
Import text files.
Import data from the Internet.
Generate data by formula.
Import U.S. Census Microdata from IPUMS (more than 50 attributes available; includes historical data as old as 1850).

Plot Types

Dot plot (stacked or unstacked): May be split by adding one or more numeric attributes to the same axis or by dropping a categorical attribute on the other axis. May display dots shaped according to a legend.
Line plot: May be split by a categorical attribute on the vertical axis and may display dots shaped according to a legend. You can add attributes to the vertical axis.
Histogram (equal width bars): May be split by adding numeric attributes to the same axis or by dropping a categorical attribute on the other axis. May show Frequency (the default), Relative Frequency, Relative Percentage, or Density.
Ntigram (equal area histogram): May be split by adding numeric attributes to the same axis or by dropping a categorical attribute on the other axis.
Box plot: May be split by adding more numeric attributes to the same axis or by dropping a categorical attribute on the other axis.
Percentile plot: May be split by adding more numeric attributes to the same axis or by dropping a categorical attribute on the other axis. May display dots shaped according to a legend.
Normal quantile plot: May be split by adding more numeric attributes to the same axis or by dropping a categorical attribute on the horizontal axis. May display dots shaped according to a legend.
Bar chart: May be split by adding one more categorical attribute to the axis of a bar chart or by dropping another categorical attribute in the plot area. May display shaded regions according to a legend.
Ribbon chart: May be split by dropping another categorical attribute in the plot area. May display shaded regions according to a legend.
Breakdown plot: May be split by dropping a categorical attribute on each axis. May display dots shaped according to a legend.
Scatter plot: You can add more numeric attributes to one of the axes or drop any attribute in the plot area. May display dots shaped or colored according to a legend.
Line scatter plot: You can add more numeric attributes to one of the axes or drop any attribute in the plot area. May display dots shaped or colored according to a legend.
Function Plot: Use sliders in the formulas to manipulate the functions dynamically.
Fathom also displays the Test Statistic Distribution for hypothesis tests.

Plotting Values and Functions

Plotted values: Display any number of computed values with a line perpendicular to the numeric attribute axis of a univariate plot.
Plotted functions: Display any functions, f(x), on a graph that has two continuous attributes. For univariate graphs, the x-axis is the axis corresponding to the attribute.

Statistical Tests

t-test to test the mean of a sample against a hypothesized population mean when the population standard deviation is not known. Compute either from summary or raw data.
t-test to test the hypothesis that two means from independent samples are equal.
Choose either an un-pooled or a pooled estimate of population standard deviation.
Compute either from summary or raw data.
One-way ANOVA tests the null hypothesis that means of a continuous attribute, when grouped by a single categorical attribute, are independent of each other. Compute from raw data.
Test proportion of a sample against a hypothesized population proportion. Uses exact binomial computation when np or n(1– p) is less than five; otherwise, uses normal approximation. Compute either from summary or raw data.
Compare two proportions against the null hypothesis that the two population proportions are equal. Uses the normal approximation and requires that the number of successes and failures in each of the two attributes be greater than or equal to 5. Compute either from summary or raw data.
Chi-square goodness of fit tests the null hypothesis that each of n categories is equally likely or that each has a specified probability of occurrence. Compute either from summary or raw data.
Chi-square test for independence tests the null hypothesis that two categorical attributes are independent of each other. Compute either from summary or raw data. Displays expected values for each cell.
Test the slope of a least squares regression line against the null hypothesis that the slope is zero. Uses student’s t as the test statistic. Can only be computed from raw data.
Test the correlation coefficient between two attributes against the null hypothesis that the correlation coefficient is zero. Uses student’s t as the test statistic. Compute either from summary or raw data.

Estimates of Population Parameters

Given a confidence level, compute the confidence interval for the mean of a population when the standard deviation of the population is unknown. Compute either from summary or raw data.
Given a confidence level, compute the confidence interval for a population proportion. Compute either from summary or raw data.
Estimate the difference of two means. Given a confidence level, compute the confidence interval for the difference of means for two groups where the groups are specified either by two continuous attributes or by one continuous and one categorical attribute. Compute either from summary or raw data.
Estimate the difference of two proportions. Given a confidence level, compute the confidence interval for the difference of proportions. Compute either from summary or raw data.

Linear Models

Simple linear regression: Estimate the slope, intercept, and correlation coefficient for paired, continuous observations. Given a confidence level, compute the confidence intervals for each of these. Given a value for the independent attribute, compute the predicted value and its confidence interval at a specified confidence level.
Multiple linear regression: Estimate regression coefficients and their standard errors, tstatistics, p-values, and contributions to R-squared for multiple predictor attributes’ contributions to a model of a response attribute.

Dynamic Dragging

The following can be dragged in Fathom. All dependent objects update during the drag.

Points in plots, bars in histograms and Ntigrams, all portions of a box plot. Dragging changes values of data.
Numeric axes. Dragging changes scale or translates axis.
Categorical axes. Dragging changes the category order.
Slider. Dragging changes slider value. Whatever formula the slider is used in updates. (See Parameterization.)
Edges of bars in histograms and Ntigrams. Dragging changes widths of bins.
Edges of bars in bar charts. Dragging changes the width of the bar.
Movable lines in univariate plots and in scatter plots. Dragging moves lines and shows changed value or equation.

Simulation Capabilities

Fathom supports several different kinds of simulation.

Sampling

Given a collection, generate a new collection whose cases are drawn at random from the original:

with or without replacement
with or without animation
may be triggered on response to source change
choice of whether to empty collection when starting a new sampling process
sample a given number of cases or sample until a condition is met

Collecting Measures

The source collection may be an:

ordinary collection, in which case any values defined by random functions will be regenerated before each iteration of collecting measures
sample collection, in which case the sample will be taken again before each iteration of collecting measures
summary table
statistical test or estimate

Copy the measures defined in one collection into a single case in a new collection:

with or without animation
may be triggered on response to source change
choice of whether to empty collection before collecting more measures
repeat the collection process a specified number of times or until a given condition is met

Scrambling

Given a collection, form a new collection in which the values for a specified attribute have been randomly shuffled.

Parameterization

Sliders provide manipulatable parameters that can be referenced in formulas for:

attributes and measures
plotted values
plotted functions
formulas in summary tables
parameters for sampling and collecting measures
filters
numeric parameters for statistical tests and estimates

Dragging the slider causes all aspects of the model to recompute dynamically. Sliders can be animated to move continuously from the lower to the upper bounds of their axes. Slider values can be restricted to multiples of an input value (for example, restrict to multiples of 1 for an integer slider). Slider values can be defined by formula.

Control Over Appearance of Cases

The appearance of cases in a collection may be changed either directly or through formulas.

The “display” attributes over which the user has control are:

caption
x-position
y-position
width
height
icon image (by default, a little gold ball)

Flexible Layout

All objects may be laid out in a single document and saved, restored, or printed as such.
Individual objects may be viewed in a separate window if desired.
Text objects of any length can be placed anywhere in the document. Text objects support full character formatting and insertion of a suite of mathematical and statistical symbols.
Objects may copied as pictures and pasted into other applications, or pasted back into the document as a static record.

Functions

Statistical Functions

bin
correlation
count
covariance
first quartile
first value
interquartile range
last value
linear regression intercept
linear regression predicted value
linear regression residual
linear regression slope
linear regression standard error of the slope
maximum
mean
median
minimum
next value
percentile
population covariance
population standard deviation
population variance
population z-score
previous value
product
proportion
R-squared
rank
run length
sample covariance
sample standard deviation
sample variance
sample z-score
standard error
sum
third quartile
unique rank
unique values
variance

Distributions

For each of the distributions listed below, Fathom provides functions to compute the probability density, cumulative probability and inverse cumulative probability (quantiles).

beta
binomial
Cauchy
chi-square
exponential
F
gamma
geometric
hypergeometric
normal
Poisson
student’s t
uniform
uniform lattice

Random Functions

random integer between a defined minimum and maximum
random integer from a binomial distribution
random integer from a geometric distribution
random number between 0 and 1
random number between 0 and a defined maximum
random number between a defined minimum and maximum
random number from a beta distribution
random number from a Cauchy distribution
random number from a chi-square distribution
random number from an exponential distribution
random number from an F-distribution
random number from a gamma distribution
random number from a hypergeometric distribution
random number from a normal distribution
random number from a Poisson distribution
random number from a t-distribution
random number from a uniform distribution
random number from a uniform lattice distribution
random pick from a defined list of elements

Trigonometric Functions

cosecant
cosine
cotangent
hyperbolic cosecant
hyperbolic cosine
hyperbolic cotangent
hyperbolic secant
hyperbolic sine
hyperbolic tangent
inverse cosecant
inverse cosine
inverse cotangent
inverse hyperbolic cosecant
inverse hyperbolic cosine
inverse hyperbolic cotangent
inverse hyperbolic secant
inverse hyperbolic sine
inverse hyperbolic tangent
inverse secant
inverse sine
inverse tangent
inverse tangent with two numeric arguments
secant
sine
tangent

Functions for Dealing with Text

begins with
character to number
concatenate
ends with
find string
includes
left string
mid-string
number to character
repeat string
replace characters
replace string
right string
string length
string to number

Arithmetic, Logical, and Other Functions

absolute value
bin width
card icon
case index
ceiling
column proportion
column total
combinations
common logarithm
concatenate
even
exists
expected
exponential
false value
floor
grand total
if
includes
index of category
in range
is number
is prime
look up value by index
look up value by key
missing
modulo
natural logarithm
number of bins
number of digits in common between two arguments
odd
pi
round
row proportion
row total
scalar
signum
square root
switch (nested if statements)
true value
truncate
unit of

Units

Fathom recognizes and performs unit algebra on dozens of built-in units in the following dimensions:

Acceleration
Angle
Area
Capacitance
Charge
Conductance
Current
Data
Density
Electrical Potential
Force
Frequency
Important Constants
Inductance
Length
Magnetic Flux
Magnetic Flux Density
Mass
Power/Energy
Pressure
Resistance
Speed
Time
Volume
Work