diff --git a/.idea/pydantic.xml b/.idea/pydantic.xml
index e6e3ec67b..abaa51442 100644
--- a/.idea/pydantic.xml
+++ b/.idea/pydantic.xml
@@ -1,6 +1,8 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <project version="4">
   <component name="PydanticConfigService">
+    <option name="mypyInitTyped" value="true" />
+    <option name="mypyWarnUntypedFields" value="true" />
     <option name="warnUntypedFields" value="true" />
   </component>
 </project>
\ No newline at end of file
diff --git a/cli/codeflash/verification/statistical_analysis.py b/cli/codeflash/verification/statistical_analysis.py
new file mode 100644
index 000000000..5c11c59f4
--- /dev/null
+++ b/cli/codeflash/verification/statistical_analysis.py
@@ -0,0 +1,41 @@
+from __future__ import annotations
+
+import math
+from typing import TYPE_CHECKING
+
+import numpy as np
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+
+TWO_SIGMA = 2
+
+
+def bootstrap_minima(series: list[int], bootstrap_size: int) -> npt.NDArray[np.int64]:
+    rng = np.random.default_rng()
+    return np.array([np.min(rng.choice(series, len(series), replace=True)) for _ in range(bootstrap_size)])
+
+
+def bootstrap_noise_floor(series: list[int], bootstrap_size: int) -> np.float64:
+    return np.std(bootstrap_minima(series, bootstrap_size))
+
+
+def combined_series_noise_floor(series1: list[int], series2: list[int], bootstrap_size: int) -> float:
+    noise_floor1 = bootstrap_noise_floor(series1, bootstrap_size)
+    noise_floor2 = bootstrap_noise_floor(series2, bootstrap_size)
+    return math.sqrt(noise_floor1 * noise_floor1 + noise_floor2 * noise_floor2)
+
+
+def series2_faster_95_confidence(
+    series1: list[int], series2: list[int], bootstrap_size: int
+) -> tuple[float, float] | None:
+    min1 = min(series1)
+    min_diff = min1 - min(series2)
+    if min_diff <= 0:
+        return None
+    combined_noise_floor = combined_series_noise_floor(series1, series2, bootstrap_size)
+    percent_diff = 100 * min_diff / min1
+    uncertainty = TWO_SIGMA * combined_noise_floor / min1
+    if combined_noise_floor == 0 or min_diff / combined_noise_floor > TWO_SIGMA:
+        return percent_diff, uncertainty
+    return None
diff --git a/cli/codeflash/verification/test_results.py b/cli/codeflash/verification/test_results.py
index 3dfbca120..9ec406efd 100644
--- a/cli/codeflash/verification/test_results.py
+++ b/cli/codeflash/verification/test_results.py
@@ -1,9 +1,10 @@
 from __future__ import annotations
 
 import sys
+from collections.abc import Iterator
 from enum import Enum
 from pathlib import Path
-from typing import Iterator, Optional, cast
+from typing import Optional, cast
 
 from pydantic import BaseModel
 from pydantic.dataclasses import dataclass
@@ -151,22 +152,30 @@ class TestResults(BaseModel):
             )
         return tree
 
+    def usable_runtime_data_by_test_case(self) -> dict[InvocationId, list[int]]:
+        for result in self.test_results:
+            if result.did_pass and not result.runtime:
+                logger.debug(
+                    f"Ignoring test case that passed but had no runtime -> {result.id}, Loop # {result.loop_index}"
+                )
+        usable_runtimes = [
+            (result.id, result.runtime) for result in self.test_results if result.did_pass and result.runtime
+        ]
+        return {
+            usable_id: [runtime[1] for runtime in usable_runtimes if runtime[0] == usable_id]
+            for usable_id in {runtime[0] for runtime in usable_runtimes}
+        }
+
     def total_passed_runtime(self) -> int:
         """Calculate the sum of runtimes of all test cases that passed, where a testcase runtime
         is the minimum value of all looped execution runtimes.
 
         :return: The runtime in nanoseconds.
         """
-        for result in self.test_results:
-            if result.did_pass and not result.runtime:
-                logger.debug(
-                    f"Ignoring test case that passed but had no runtime -> {result.id}, Loop # {result.loop_index}"
-                )
-        usable_results = [result for result in self.test_results if result.did_pass and result.runtime]
         return sum(
             [
-                min([result.runtime for result in usable_results if result.id == invocation_id])
-                for invocation_id in {result.id for result in usable_results}
+                min(usable_runtime_data)
+                for invocation_id, usable_runtime_data in self.usable_runtime_data_by_test_case().items()
             ]
         )
 
diff --git a/cli/tests/test_statistical_analysis.py b/cli/tests/test_statistical_analysis.py
new file mode 100644
index 000000000..e15f15e24
--- /dev/null
+++ b/cli/tests/test_statistical_analysis.py
@@ -0,0 +1,18 @@
+import numpy as np
+from codeflash.verification.statistical_analysis import series2_faster_95_confidence
+
+
+def create_timing_series(size: int, mean: int, std_dev: int) -> list[int]:
+    mu = np.log(mean**2 / np.sqrt(std_dev**2 + mean**2))
+    sigma = np.sqrt(np.log(1 + (std_dev**2 / mean**2)))
+    rng = np.random.default_rng()
+    return np.round(rng.lognormal(mu, sigma, size)).astype(int).tolist()
+
+
+def test_compare_timing_series() -> None:
+    original_timing_series = create_timing_series(50000, 2000, 100)
+    optimized_timing_series = create_timing_series(50000, 1700, 85)
+    result = series2_faster_95_confidence(original_timing_series, optimized_timing_series, 5000)
+    assert result is not None
+    assert 12 < result[0] < 18
+    assert 0.01 < result[1] < 0.1