diff --git a/tests/unit/test_parameters/test_process_parameter_data.py b/tests/unit/test_parameters/test_process_parameter_data.py
index 9352894c5c..6767ee8358 100644
--- a/tests/unit/test_parameters/test_process_parameter_data.py
+++ b/tests/unit/test_parameters/test_process_parameter_data.py
@@ -2,57 +2,57 @@
 # Tests for the parameter processing functions
 #
 
-
 import os
 import numpy as np
 import pybamm
-
 import pytest
 
 
-class TestProcessParameterData:
-    def test_process_1D_data(self):
-        name = "lico2_ocv_example"
-        path = os.path.abspath(os.path.dirname(__file__))
-        processed = pybamm.parameters.process_1D_data(name, path)
-        assert processed[0] == name
-        assert isinstance(processed[1], tuple)
-        assert isinstance(processed[1][0][0], np.ndarray)
-        assert isinstance(processed[1][1], np.ndarray)
+@pytest.fixture
+def path():
+    return os.path.abspath(os.path.dirname(__file__))
 
-    def test_process_2D_data(self):
-        name = "lico2_diffusivity_Dualfoil1998_2D"
-        path = os.path.abspath(os.path.dirname(__file__))
-        processed = pybamm.parameters.process_2D_data(name, path)
-        assert processed[0] == name
-        assert isinstance(processed[1], tuple)
-        assert isinstance(processed[1][0][0], np.ndarray)
-        assert isinstance(processed[1][0][1], np.ndarray)
-        assert isinstance(processed[1][1], np.ndarray)
+@pytest.fixture(params=[
+    ("lico2_ocv_example", pybamm.parameters.process_1D_data),
+    ("lico2_diffusivity_Dualfoil1998_2D", pybamm.parameters.process_2D_data),
+    ("data_for_testing_2D", pybamm.parameters.process_2D_data_csv),
+    ("data_for_testing_3D", pybamm.parameters.process_3D_data_csv),
+])
+def parameter_data(request, path):
+    name, processing_function = request.param
+    processed = processing_function(name, path)
+    return name, processed
 
-    def test_process_2D_data_csv(self):
-        name = "data_for_testing_2D"
-        path = os.path.abspath(os.path.dirname(__file__))
-        processed = pybamm.parameters.process_2D_data_csv(name, path)
 
+class TestProcessParameterData:
+    def test_processed_name(self, parameter_data):
+        name, processed = parameter_data
         assert processed[0] == name
-        assert isinstance(processed[1], tuple)
-        assert isinstance(processed[1][0][0], np.ndarray)
-        assert isinstance(processed[1][0][1], np.ndarray)
-        assert isinstance(processed[1][1], np.ndarray)
-
-    def test_process_3D_data_csv(self):
-        name = "data_for_testing_3D"
-        path = os.path.abspath(os.path.dirname(__file__))
-        processed = pybamm.parameters.process_3D_data_csv(name, path)
 
-        assert processed[0] == name
+    def test_processed_structure(self, parameter_data):
+        """
+        Test that the processed data has the correct structure.
+        
+        Args:
+            parameter_data: A tuple containing the name and processed data.
+        
+        Asserts:
+            - The second element of the processed data is a tuple.
+            - The first element of the second item in the processed data is a numpy array.
+            - Additional checks based on the shape of the processed data.
+        """
+        name, processed = parameter_data
         assert isinstance(processed[1], tuple)
         assert isinstance(processed[1][0][0], np.ndarray)
-        assert isinstance(processed[1][0][1], np.ndarray)
-        assert isinstance(processed[1][0][2], np.ndarray)
         assert isinstance(processed[1][1], np.ndarray)
 
+        if len(processed[1][0]) > 1:
+            assert isinstance(processed[1][0][1], np.ndarray)
+        
+        elif len(processed[1]) == 3:  
+            assert isinstance(processed[1][0][1], np.ndarray)
+            assert isinstance(processed[1][0][2], np.ndarray)
+
     def test_error(self):
         with pytest.raises(FileNotFoundError, match="Could not find file"):
             pybamm.parameters.process_1D_data("not_a_real_file", "not_a_real_path")