diff --git a/Cargo.lock b/Cargo.lock
index 33f32d9..bb17d58 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -81,6 +81,15 @@ dependencies = [
  "windows-sys 0.52.0",
 ]
 
+[[package]]
+name = "approx"
+version = "0.5.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "cab112f0a86d568ea0e627cc1d6be74a1e9cd55214684db5561995f6dad897c6"
+dependencies = [
+ "num-traits",
+]
+
 [[package]]
 name = "async-stream"
 version = "0.3.6"
@@ -504,6 +513,18 @@ version = "3.16.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "79296716171880943b8470b5f8d03aa55eb2e645a4874bdbb28adb49162e012c"
 
+[[package]]
+name = "bytemuck"
+version = "1.19.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "8334215b81e418a0a7bdb8ef0849474f40bb10c8b71f1c4ed315cff49f32494d"
+
+[[package]]
+name = "byteorder"
+version = "1.5.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1fd0f2584146f6f2ef48085050886acf353beff7305ebd1ae69500e27c67f64b"
+
 [[package]]
 name = "bytes"
 version = "1.7.2"
@@ -537,6 +558,7 @@ dependencies = [
  "serde",
  "serde_json",
  "static_assertions",
+ "statrs",
  "thiserror",
  "tokio",
  "tokio-stream",
@@ -1036,6 +1058,12 @@ version = "0.2.161"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "8e9489c2807c139ffd9c1794f4af0ebe86a828db53ecdc7fea2111d0fed085d1"
 
+[[package]]
+name = "libm"
+version = "0.2.8"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "4ec2a862134d2a7d32d7983ddcdd1c4923530833c9f2ea1a44fc5fa473989058"
+
 [[package]]
 name = "linux-raw-sys"
 version = "0.4.14"
@@ -1058,6 +1086,16 @@ version = "0.4.22"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "a7a70ba024b9dc04c27ea2f0c0548feb474ec5c54bba33a7f72f873a39d07b24"
 
+[[package]]
+name = "matrixmultiply"
+version = "0.3.9"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "9380b911e3e96d10c1f415da0876389aaf1b56759054eeb0de7df940c456ba1a"
+dependencies = [
+ "autocfg",
+ "rawpointer",
+]
+
 [[package]]
 name = "memchr"
 version = "2.7.4"
@@ -1116,6 +1154,44 @@ dependencies = [
  "windows-sys 0.52.0",
 ]
 
+[[package]]
+name = "nalgebra"
+version = "0.32.6"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7b5c17de023a86f59ed79891b2e5d5a94c705dbe904a5b5c9c952ea6221b03e4"
+dependencies = [
+ "approx",
+ "matrixmultiply",
+ "nalgebra-macros",
+ "num-complex",
+ "num-rational",
+ "num-traits",
+ "rand",
+ "rand_distr",
+ "simba",
+ "typenum",
+]
+
+[[package]]
+name = "nalgebra-macros"
+version = "0.2.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "254a5372af8fc138e36684761d3c0cdb758a4410e938babcff1c860ce14ddbfc"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "num-complex"
+version = "0.4.6"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "73f88a1307638156682bada9d7604135552957b7818057dcef22705b4d509495"
+dependencies = [
+ "num-traits",
+]
+
 [[package]]
 name = "num-conv"
 version = "0.1.0"
@@ -1131,6 +1207,16 @@ dependencies = [
  "num-traits",
 ]
 
+[[package]]
+name = "num-rational"
+version = "0.4.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f83d14da390562dca69fc84082e73e548e1ad308d24accdedd2720017cb37824"
+dependencies = [
+ "num-integer",
+ "num-traits",
+]
+
 [[package]]
 name = "num-traits"
 version = "0.2.19"
@@ -1138,6 +1224,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "071dfc062690e90b734c0b2273ce72ad0ffa95f0c74596bc250dcfd960262841"
 dependencies = [
  "autocfg",
+ "libm",
 ]
 
 [[package]]
@@ -1196,6 +1283,12 @@ dependencies = [
  "windows-targets 0.52.6",
 ]
 
+[[package]]
+name = "paste"
+version = "1.0.15"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "57c0d7b74b563b49d38dae00a0c37d4d6de9b432382b2892f0574ddcae73fd0a"
+
 [[package]]
 name = "percent-encoding"
 version = "2.3.1"
@@ -1220,6 +1313,15 @@ version = "0.2.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "439ee305def115ba05938db6eb1644ff94165c5ab5e9420d1c1bcedbba909391"
 
+[[package]]
+name = "ppv-lite86"
+version = "0.2.20"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "77957b295656769bb8ad2b6a6b09d897d94f05c41b069aede1fcdaa675eaea04"
+dependencies = [
+ "zerocopy",
+]
+
 [[package]]
 name = "pretty_assertions"
 version = "1.4.1"
@@ -1248,6 +1350,52 @@ dependencies = [
  "proc-macro2",
 ]
 
+[[package]]
+name = "rand"
+version = "0.8.5"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "34af8d1a0e25924bc5b7c43c079c942339d8f0a8b57c39049bef581b46327404"
+dependencies = [
+ "libc",
+ "rand_chacha",
+ "rand_core",
+]
+
+[[package]]
+name = "rand_chacha"
+version = "0.3.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "e6c10a63a0fa32252be49d21e7709d4d4baf8d231c2dbce1eaa8141b9b127d88"
+dependencies = [
+ "ppv-lite86",
+ "rand_core",
+]
+
+[[package]]
+name = "rand_core"
+version = "0.6.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ec0be4795e2f6a28069bec0b5ff3e2ac9bafc99e6a9a7dc3547996c5c816922c"
+dependencies = [
+ "getrandom",
+]
+
+[[package]]
+name = "rand_distr"
+version = "0.4.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "32cb0b9bc82b0a0876c2dd994a7e7a2683d3e7390ca40e6886785ef0c7e3ee31"
+dependencies = [
+ "num-traits",
+ "rand",
+]
+
+[[package]]
+name = "rawpointer"
+version = "0.2.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "60a357793950651c4ed0f3f52338f53b2f809f32d83a07f72909fa13e4c6c1e3"
+
 [[package]]
 name = "redox_syscall"
 version = "0.5.7"
@@ -1355,6 +1503,15 @@ version = "1.0.18"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "f3cb5ba0dc43242ce17de99c180e96db90b235b8a9fdc9543c96d2209116bd9f"
 
+[[package]]
+name = "safe_arch"
+version = "0.7.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c3460605018fdc9612bce72735cba0d27efbcd9904780d44c7e3a9948f96148a"
+dependencies = [
+ "bytemuck",
+]
+
 [[package]]
 name = "schannel"
 version = "0.1.26"
@@ -1467,6 +1624,19 @@ dependencies = [
  "libc",
 ]
 
+[[package]]
+name = "simba"
+version = "0.8.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "061507c94fc6ab4ba1c9a0305018408e312e17c041eb63bef8aa726fa33aceae"
+dependencies = [
+ "approx",
+ "num-complex",
+ "num-traits",
+ "paste",
+ "wide",
+]
+
 [[package]]
 name = "slab"
 version = "0.4.9"
@@ -1510,6 +1680,18 @@ version = "1.1.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "a2eb9349b6444b326872e140eb1cf5e7c522154d69e7a0ffb0fb81c06b37543f"
 
+[[package]]
+name = "statrs"
+version = "0.17.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f697a07e4606a0a25c044de247e583a330dbb1731d11bc7350b81f48ad567255"
+dependencies = [
+ "approx",
+ "nalgebra",
+ "num-traits",
+ "rand",
+]
+
 [[package]]
 name = "strsim"
 version = "0.11.1"
@@ -1902,6 +2084,16 @@ version = "0.2.95"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "65fc09f10666a9f147042251e0dda9c18f166ff7de300607007e96bdebc1068d"
 
+[[package]]
+name = "wide"
+version = "0.7.28"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b828f995bf1e9622031f8009f8481a85406ce1f4d4588ff746d872043e855690"
+dependencies = [
+ "bytemuck",
+ "safe_arch",
+]
+
 [[package]]
 name = "windows-core"
 version = "0.52.0"
@@ -2071,6 +2263,27 @@ version = "1.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "cfe53a6657fd280eaa890a3bc59152892ffa3e30101319d168b781ed6529b049"
 
+[[package]]
+name = "zerocopy"
+version = "0.7.35"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1b9b4fd18abc82b8136838da5d50bae7bdea537c574d8dc1a34ed098d6c166f0"
+dependencies = [
+ "byteorder",
+ "zerocopy-derive",
+]
+
+[[package]]
+name = "zerocopy-derive"
+version = "0.7.35"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "fa4f8080344d4671fb4e831a13ad1e68092748387dfc4f55e356242fae12ce3e"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
 [[package]]
 name = "zeroize"
 version = "1.8.1"
diff --git a/Cargo.toml b/Cargo.toml
index 8c03e5b..215f36e 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -25,6 +25,7 @@ futures-util = "0.3.31"
 miette = { version = "7", features = ["fancy"] }
 serde = { version = "1.0", features = ["derive"] }
 serde_json = "1.0"
+statrs = "0.17.1"
 thiserror = "1.0.61"
 tokio = { version = "1.37.0", features = ["full"] }
 tokio-stream = { version = "0.1", features = ["time"] }
diff --git a/src/pipeline/mod.rs b/src/pipeline/mod.rs
index 786d3db..b1de561 100644
--- a/src/pipeline/mod.rs
+++ b/src/pipeline/mod.rs
@@ -42,7 +42,7 @@ pub fn repeat_query<T: Observer>(
         //   be moved between iterations.
         pin!(timer);
         // Each iteration of the loop represents one unit of tiem.
-        while let Some(_) = timer.next().await {
+        while timer.next().await.is_some() {
             // • We perform the query then dump the results into the stream.
             let items = observer.query().await;
             for item in items {
diff --git a/src/stats/chi.rs b/src/stats/chi.rs
index 7d42862..fccf035 100644
--- a/src/stats/chi.rs
+++ b/src/stats/chi.rs
@@ -1,33 +1,40 @@
 use std::collections::{HashMap, HashSet};
 use std::hash::Hash;
+use std::num::NonZeroU64;
 
-/// A ContingencyTable expresses the frequency with which a category was observed.
-/// Usually, it tracks the number of observations in ecah category, but when the
+use statrs::distribution::{ChiSquared, ContinuousCDF};
+
+/// A ContingencyTable expresses the frequency with which a group was observed.
+/// Usually, it tracks the number of observations in ecah group, but when the
 /// number is already known (i.e. its fixed, like a fair dice or coin), it can
-/// expose just the frequencies for each category.
+/// expose just the frequencies for each group.
 pub trait ContingencyTable<Group> {
-    /// return the frequency of the provided category as a number in the range [0, 1].
-    /// If this is an empirical table (i.e. its values were from observations),
-    /// then this is the number of times the category was observed
-    /// divided by the total number of observations.
-    fn group_count(&self, cat: &Group) -> usize;
+    /// return the number of observations of the in the provided group.
+    fn group_count(&self, cat: &Group) -> u64;
 
+    /// Return the set of groups that serve as columns of the contingency table.
     fn groups(&self) -> Box<dyn Iterator<Item = Group>>;
 
-    /// returns the number of degrees of freedom for this table.
-    /// This is typically the number of groups minus one.
-    fn degrees_of_freedom(&self) -> usize {
-        self.groups().count() - 1
-    }
-
     // returns the total number of observations made. This should be the sum
     // of the group count for every group.
-    fn total_count(&self) -> usize {
+    fn total_count(&self) -> u64 {
         self.groups()
             .fold(0, |sum, group| sum + self.group_count(&group))
     }
 }
 
+/// returns the number of degrees of freedom for this table.
+/// This is typically the number of groups minus one.
+/// # Panics
+/// This method panics if the number of groups returned by `groups` is less than 2.
+fn degrees_of_freedom<Cat: EnumerableCategory>(table: &impl ContingencyTable<Cat>) -> NonZeroU64 {
+    let group_count = table.groups().count() as u64;
+    if group_count < 2 {
+        panic!("The experiment must have at least two groups. Only {group_count} groups provided");
+    }
+    NonZeroU64::new(group_count - 1).unwrap()
+}
+
 /// This helper trait identifies a category with a known set of groups.
 /// For example, if modeling bools, the groups are True and False. If modeling
 /// a six sided die, the groups would be 1 through 6.
@@ -68,7 +75,7 @@ pub struct FixedContingencyTable<C>
 where
     C: EnumerableCategory + Hash + Eq,
 {
-    counts: HashMap<C, usize>,
+    counts: HashMap<C, u64>,
 }
 
 impl<C> FixedContingencyTable<C>
@@ -87,12 +94,13 @@ where
     }
 
     /// Sets the expected count of the category to the value provided.
-    pub fn set_group_count(&mut self, cat: C, count: usize) {
+    pub fn set_group_count(&mut self, cat: C, count: u64) {
         self.counts.insert(cat, count);
     }
 
-    /// Returns the frequency of the provide category.
-    pub fn group_count(&self, cat: &C) -> usize {
+    /// Returns the number of observations that were classified as
+    /// having this group/category.
+    pub fn group_count(&self, cat: &C) -> u64 {
         self.counts[cat]
     }
 }
@@ -101,14 +109,7 @@ impl<C> ContingencyTable<C> for FixedContingencyTable<C>
 where
     C: EnumerableCategory + Hash + Eq,
 {
-    /// Return the number of degrees of freedom, which is the number of
-    /// groups minus 1.
-    fn degrees_of_freedom(&self) -> usize {
-        // The number of degrees of freedom is the number of groups minus one.
-        self.counts.len() - 1
-    }
-
-    fn group_count(&self, cat: &C) -> usize {
+    fn group_count(&self, cat: &C) -> u64 {
         // delegate to the method on the base class.
         Self::group_count(self, cat)
     }
@@ -119,10 +120,31 @@ where
     }
 }
 
+/// Alpha represents the alpha cutoff, expressed as a floating point from [0, 1] inclusive.
+/// For example, 0.95 is the standard 5% confidency interval.
+pub fn chi_square_test<Cat>(
+    observed: &impl ContingencyTable<Cat>,
+    expected: &impl ContingencyTable<Cat>,
+    alpha: f64,
+) -> bool
+where
+    Cat: EnumerableCategory + Hash + Eq,
+{
+    assert!(alpha < 1.0);
+    assert_eq!(
+        degrees_of_freedom(observed),
+        degrees_of_freedom(expected),
+        "Expected the degrees of freedom from both groups to be the same."
+    );
+    let stat = test_statistic(expected, observed);
+    let pval = p_value(stat, degrees_of_freedom(observed));
+    pval < alpha
+}
+
 // calculate the chi square test statistic using the provided contingency tables.
 fn test_statistic<Cat: EnumerableCategory + Hash + Eq>(
-    control: impl ContingencyTable<Cat>,
-    experimental: impl ContingencyTable<Cat>,
+    control: &impl ContingencyTable<Cat>,
+    experimental: &impl ContingencyTable<Cat>,
 ) -> f64 {
     // • First, get the set of groups. We can't assume that
     //   both table have the same groups, so we deduplicate them using
@@ -142,12 +164,18 @@ fn test_statistic<Cat: EnumerableCategory + Hash + Eq>(
     })
 }
 
+fn p_value(test_statistic: f64, degrees_of_freedom: NonZeroU64) -> f64 {
+    let freedom = u64::from(degrees_of_freedom) as f64;
+    let distribution = ChiSquared::new(freedom).expect("Degrees of freedom must be >= 0");
+    1.0 - distribution.cdf(test_statistic)
+}
+
 #[cfg(test)]
 mod tests {
 
-    use std::collections::HashSet;
+    use std::{collections::HashSet, num::NonZeroU64};
 
-    use crate::stats::chi::FixedContingencyTable;
+    use crate::stats::chi::{degrees_of_freedom, p_value, FixedContingencyTable};
 
     use super::{test_statistic, ContingencyTable, EnumerableCategory};
     use pretty_assertions::assert_eq;
@@ -176,7 +204,7 @@ mod tests {
     #[test]
     fn enumerable_table() {
         let mut table = FixedContingencyTable::new();
-        let groups = [(true, 30), (false, 70)];
+        let groups = [(true, 30u64), (false, 70u64)];
         // Put the values into the table.
         for (group, freq) in groups {
             table.set_group_count(group, freq);
@@ -188,7 +216,7 @@ mod tests {
             assert_eq!(expected, observed);
         }
         // Demonstrate the number of degrees of freedom matches expectations.
-        assert_eq!(table.degrees_of_freedom(), 1);
+        assert_eq!(degrees_of_freedom(&table), NonZeroU64::new(1).unwrap());
     }
 
     /// Scenario: You flip a coin 50 times, and get 21 Heads and 29 Tails.
@@ -202,12 +230,21 @@ mod tests {
         let mut experimental_group = FixedContingencyTable::new();
         experimental_group.set_group_count(true, 21);
         experimental_group.set_group_count(false, 29);
-        assert_eq!(control_group.degrees_of_freedom(), 1);
-        assert_eq!(experimental_group.degrees_of_freedom(), 1);
-        let stat = test_statistic(control_group, experimental_group);
+        assert_eq!(
+            degrees_of_freedom(&control_group),
+            NonZeroU64::new(1).unwrap()
+        );
+        assert_eq!(
+            degrees_of_freedom(&experimental_group),
+            NonZeroU64::new(1).unwrap()
+        );
+        let stat = test_statistic(&control_group, &experimental_group);
         // Round the statistic to two decimal places.
         let observed = (stat * 100.0).round() / 100.0;
         let expected = 1.28;
         assert_eq!(observed, expected);
+        // Now, calculate the p-value using the test statistic.
+        let pval = p_value(stat, degrees_of_freedom(&control_group));
+        assert!(0.25 < pval && pval < 0.30);
     }
 }
diff --git a/src/stats/mod.rs b/src/stats/mod.rs
index f218db7..e6b530a 100644
--- a/src/stats/mod.rs
+++ b/src/stats/mod.rs
@@ -20,6 +20,12 @@ pub struct ChiSquareEngine {
     alpha_cutoff: f64,
 }
 
+impl Default for ChiSquareEngine {
+    fn default() -> Self {
+        Self::new()
+    }
+}
+
 impl ChiSquareEngine {
     pub fn new() -> Self {
         Self {