diff --git a/src/AggregateFunctions/AggregateFunctionAnalysisOfVariance.cpp b/src/AggregateFunctions/AggregateFunctionAnalysisOfVariance.cpp
index ffb651b3288..9ef2d295828 100644
--- a/src/AggregateFunctions/AggregateFunctionAnalysisOfVariance.cpp
+++ b/src/AggregateFunctions/AggregateFunctionAnalysisOfVariance.cpp
@@ -18,8 +18,10 @@ AggregateFunctionPtr createAggregateFunctionAnalysisOfVariance(const std::string
     assertNoParameters(name, parameters);
     assertBinary(name, arguments);
 
-    if (!isNumber(arguments[0]) || !isNumber(arguments[1]))
-        throw Exception(ErrorCodes::BAD_ARGUMENTS, "Aggregate function {} only supports numerical types", name);
+    if (!isNumber(arguments[0]))
+        throw Exception(ErrorCodes::BAD_ARGUMENTS, "Aggregate function {} only supports numerical argument types", name);
+    if (!WhichDataType(arguments[1]).isNativeUInt())
+        throw Exception(ErrorCodes::BAD_ARGUMENTS, "Second argument of aggregate function {} should be a native unsigned integer", name);
 
     return std::make_shared<AggregateFunctionAnalysisOfVariance>(arguments, parameters);
 }
diff --git a/src/AggregateFunctions/AggregateFunctionAnalysisOfVariance.h b/src/AggregateFunctions/AggregateFunctionAnalysisOfVariance.h
index efb6426a96c..e891fb191f6 100644
--- a/src/AggregateFunctions/AggregateFunctionAnalysisOfVariance.h
+++ b/src/AggregateFunctions/AggregateFunctionAnalysisOfVariance.h
@@ -77,7 +77,7 @@ public:
     void insertResultInto(AggregateDataPtr __restrict place, IColumn & to, Arena *) const override
     {
         auto f_stat = data(place).getFStatistic();
-        if (std::isinf(f_stat) || isNaN(f_stat))
+        if (std::isinf(f_stat) || isNaN(f_stat) || f_stat < 0)
             throw Exception("F statistic is not defined or infinite for these arguments", ErrorCodes::BAD_ARGUMENTS);
 
         auto p_value = data(place).getPValue(f_stat);
diff --git a/src/AggregateFunctions/Moments.h b/src/AggregateFunctions/Moments.h
index 16279cb93a4..2dfd5bc46d6 100644
--- a/src/AggregateFunctions/Moments.h
+++ b/src/AggregateFunctions/Moments.h
@@ -482,6 +482,8 @@ struct ZTestMoments
 template <typename T>
 struct AnalysisOfVarianceMoments
 {
+    constexpr static size_t MAX_GROUPS_NUMBER = 1024 * 1024;
+
     /// Sums of values within a group
     std::vector<T> xs1{};
     /// Sums of squared values within a group
@@ -494,6 +496,10 @@ struct AnalysisOfVarianceMoments
         if (xs1.size() >= possible_size)
             return;
 
+        if (possible_size > MAX_GROUPS_NUMBER)
+            throw Exception(ErrorCodes::BAD_ARGUMENTS, "Too many groups for analysis of variance (should be no more than {}, got {})",
+                            MAX_GROUPS_NUMBER, possible_size);
+
         xs1.resize(possible_size, 0.0);
         xs2.resize(possible_size, 0.0);
         ns.resize(possible_size, 0);
diff --git a/tests/queries/0_stateless/02475_analysis_of_variance.reference b/tests/queries/0_stateless/02475_analysis_of_variance.reference
new file mode 100644
index 00000000000..e69de29bb2d
diff --git a/tests/queries/0_stateless/02475_analysis_of_variance.sql b/tests/queries/0_stateless/02475_analysis_of_variance.sql
new file mode 100644
index 00000000000..86996f784ea
--- /dev/null
+++ b/tests/queries/0_stateless/02475_analysis_of_variance.sql
@@ -0,0 +1,10 @@
+
+SELECT analysisOfVariance(number, number % 2) FROM numbers(10) FORMAT Null;
+SELECT analysisOfVariance(number :: Decimal32(5), number % 2) FROM numbers(10) FORMAT Null;
+SELECT analysisOfVariance(number :: Decimal256(5), number % 2) FROM numbers(10) FORMAT Null;
+
+SELECT analysisOfVariance(1.11, -20); -- { serverError BAD_ARGUMENTS }
+SELECT analysisOfVariance(1.11, 20 :: UInt128); -- { serverError BAD_ARGUMENTS }
+SELECT analysisOfVariance(1.11, 9000000000000000); -- { serverError BAD_ARGUMENTS }
+
+SELECT analysisOfVariance(number, number % 2), analysisOfVariance(100000000000000000000., number % 65535) FROM numbers(1048575); -- { serverError BAD_ARGUMENTS }