Class ChiSquareTestResult<T>

Namespace

AiDotNet.Models.Results

Assembly

AiDotNet.dll

Represents the results of a Chi-Square statistical test, which is used to determine whether there is a significant association between two categorical variables.

public class ChiSquareTestResult<T>

Type Parameters

T

The numeric type used for statistical values, typically float or double.

Inheritance

object

ChiSquareTestResult<T>

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Remarks

The Chi-Square test is a statistical hypothesis test that evaluates whether observed frequencies differ significantly from expected frequencies. It is commonly used to test the independence of two categorical variables or to assess the goodness of fit between observed data and a theoretical distribution. This class stores the results of such a test, including the test statistic, p-value, degrees of freedom, observed and expected frequencies, and whether the result is statistically significant. The class uses generic type parameter T to support different numeric types for the statistical values, such as float, double, or decimal.

For Beginners: The Chi-Square test helps determine if there's a meaningful relationship between two categorical variables.

For example, you might use this test to answer questions like:

• Is there a relationship between gender and preference for a product?
• Does treatment type affect recovery rates?
• Are survey responses distributed as expected?

The test works by:

1. Comparing observed frequencies (what you actually counted) with expected frequencies (what you would expect if there's no relationship)
2. Calculating a statistic that measures how different these frequencies are
3. Determining if this difference is statistically significant

This class stores all the information about the test results, helping you interpret whether the observed differences are likely due to chance or represent a real association.

Constructors

ChiSquareTestResult()

Initializes a new instance of the ChiSquareTestResult class with all statistical values set to zero.

public ChiSquareTestResult()

Remarks

This constructor creates a new ChiSquareTestResult instance and initializes all statistical values (ChiSquareStatistic, PValue, CriticalValue) to zero and all frequency vectors (LeftObserved, RightObserved, LeftExpected, RightExpected) to empty vectors. It uses the MathHelper.GetNumericOperations method to obtain the appropriate numeric operations for the generic type T, which allows the class to work with different numeric types such as float, double, or decimal. This initialization ensures that the statistical values start at a well-defined state before being updated with actual results from the Chi-Square test.

For Beginners: This constructor creates a new result object with all values initialized to zero.

When a new ChiSquareTestResult is created:

• All statistical values are set to zero
• All frequency vectors are initialized as empty
• The constructor uses MathHelper to handle different numeric types
• This provides a clean starting point before actual results are calculated

This initialization is important because:

• It ensures consistent behavior regardless of how the object is created
• It prevents potential issues with uninitialized values
• It makes the code more robust across different numeric types

You typically won't need to call this constructor directly, as it will be used internally by the Chi-Square test implementation.

Properties

ChiSquareStatistic

Gets or sets the Chi-Square test statistic value.

public T ChiSquareStatistic { get; set; }

Property Value

T

The calculated Chi-Square statistic, initialized to zero.

Remarks

This property represents the Chi-Square test statistic, which measures the difference between observed and expected frequencies. It is calculated as the sum of (observed - expected)²/expected across all categories. Larger values indicate greater differences between observed and expected frequencies, suggesting a stronger association between the variables or a poorer fit to the expected distribution. The Chi-Square statistic follows a Chi-Square distribution with degrees of freedom determined by the number of categories in the data. This statistic is used in conjunction with the degrees of freedom to calculate the p-value, which determines statistical significance.

For Beginners: This value measures how different your observed data is from what you expected.

The Chi-Square statistic:

• Quantifies the total difference between observed and expected frequencies
• Is always positive (or zero if observed exactly matches expected)
• Larger values indicate greater differences

This value is calculated by:

1. Finding the difference between each observed and expected frequency
2. Squaring each difference (to make all values positive)
3. Dividing by the expected frequency (to standardize)
4. Summing all these values

For example, a Chi-Square statistic of 0 means perfect agreement between observed and expected, while a value of 15.3 indicates substantial differences that may be statistically significant.

CriticalValue

Gets or sets the critical value for the Chi-Square test at the specified significance level.

public T CriticalValue { get; set; }

Property Value

T

The critical value from the Chi-Square distribution, initialized to zero.

Remarks

This property represents the critical value from the Chi-Square distribution for the given degrees of freedom and significance level (typically 0.05). The critical value is the threshold value of the Chi-Square statistic above which the null hypothesis would be rejected at the specified significance level. If the calculated Chi-Square statistic exceeds this critical value, the result is considered statistically significant. The critical value is determined by the inverse cumulative distribution function of the Chi-Square distribution, using the degrees of freedom and the complement of the significance level.

For Beginners: This value is the threshold that determines statistical significance.

The critical value:

• Is the cutoff point for the Chi-Square statistic to be considered significant
• Depends on the degrees of freedom and chosen significance level (typically 0.05)
• If the Chi-Square statistic exceeds this value, the result is statistically significant

This value is important because:

• It provides a clear threshold for decision-making
• It's directly related to your chosen significance level
• It allows for quick determination of significance without checking p-values

For example, with 2 degrees of freedom and a significance level of 0.05, the critical value is approximately 5.99. Any Chi-Square statistic above this value would be considered statistically significant.

DegreesOfFreedom

public int DegreesOfFreedom { get; set; }

Property Value

int

IsSignificant

Gets or sets a value indicating whether the Chi-Square test result is statistically significant.

public bool IsSignificant { get; set; }

Property Value

bool

True if the result is statistically significant; otherwise, false.

Remarks

This property indicates whether the Chi-Square test result is statistically significant at the specified significance level (typically 0.05). A result is considered significant if the p-value is less than or equal to the significance level, or equivalently, if the Chi-Square statistic is greater than or equal to the critical value. Statistical significance suggests that the observed differences between the observed and expected frequencies are unlikely to have occurred by chance alone, leading to the rejection of the null hypothesis. This property provides a convenient boolean indicator of significance without requiring the user to compare the p-value or Chi-Square statistic to thresholds.

For Beginners: This tells you whether your result is statistically significant or not.

The significance indicator:

• Provides a simple yes/no answer about statistical significance
• True means the relationship or difference is statistically significant
• False means the result could reasonably be due to random chance

This is determined by:

• Comparing the p-value to the significance level (typically 0.05)
• Or comparing the Chi-Square statistic to the critical value

This value makes it easy to interpret your results without having to manually check if the p-value is below the significance threshold. It's particularly useful when automating analysis or presenting results to non-statisticians.

LeftExpected

Gets or sets the expected frequencies for the left variable or category.

public Vector<T> LeftExpected { get; set; }

Property Value

Vector<T>

A vector of expected frequencies, initialized to an empty vector.

Remarks

This property represents the expected frequencies for the left variable or category in the Chi-Square test. Expected frequencies are the counts that would be expected if the null hypothesis were true (i.e., if there were no association between the variables or if the data followed the expected distribution). In a test of independence, expected frequencies are calculated based on the marginal totals of the contingency table. These expected frequencies are compared with the observed frequencies to calculate the Chi-Square statistic.

For Beginners: This contains the counts you would expect for the first variable if there's no relationship.

The left expected frequencies:

• Represent what you would expect to see if the null hypothesis is true
• Are calculated based on the marginal totals and sample size
• The difference between these and observed frequencies drives the Chi-Square statistic

For example, in a gender and product preference test, this might contain the expected counts of males and females based on the overall proportions in your sample.

LeftObserved

Gets or sets the observed frequencies for the left variable or category.

public Vector<T> LeftObserved { get; set; }

Property Value

Vector<T>

A vector of observed frequencies, initialized to an empty vector.

Remarks

This property represents the observed frequencies for the left variable or category in the Chi-Square test. Observed frequencies are the actual counts or occurrences of each category in the sample data. In a test of independence, this might represent the counts for different categories of one variable, while in a goodness-of-fit test, it might represent the observed counts for each category being tested against an expected distribution. These observed frequencies are compared with the expected frequencies to calculate the Chi-Square statistic.

For Beginners: This contains the actual counts you observed in your data for the first variable.

The left observed frequencies:

• Represent the actual counts from your data collection
• Are compared against expected frequencies to calculate the Chi-Square statistic
• For a contingency table, these would be the counts for one of the variables

For example, if testing the relationship between gender and product preference, this might contain the counts of males and females in your sample.

PValue

Gets or sets the p-value associated with the Chi-Square test.

public T PValue { get; set; }

Property Value

T

The calculated p-value, initialized to zero.

Remarks

This property represents the p-value of the Chi-Square test, which is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true. The null hypothesis typically states that there is no association between the variables or that the data follows the expected distribution. A small p-value (typically = 0.05) suggests that the observed data is unlikely under the null hypothesis, leading to its rejection in favor of the alternative hypothesis. The p-value is calculated from the Chi-Square statistic and the degrees of freedom using the cumulative distribution function of the Chi-Square distribution.

For Beginners: This value tells you how likely your results could occur by random chance.

The p-value:

• Ranges from 0 to 1
• Smaller values indicate stronger evidence against the null hypothesis
• Represents the probability of seeing your results (or more extreme) if there's no real relationship

Common interpretation:

• p = 0.05: Results are statistically significant (commonly used threshold)
• p = 0.01: Results are highly significant
• p > 0.05: Results are not statistically significant

For example, a p-value of 0.03 means there's only a 3% chance of seeing your results if there's no real relationship between the variables, suggesting the relationship is likely real and not due to random chance.

RightExpected

Gets or sets the expected frequencies for the right variable or category.

public Vector<T> RightExpected { get; set; }

Property Value

Vector<T>

A vector of expected frequencies, initialized to an empty vector.

Remarks

This property represents the expected frequencies for the right variable or category in the Chi-Square test. Expected frequencies are the counts that would be expected if the null hypothesis were true (i.e., if there were no association between the variables or if the data followed the expected distribution). In a test of independence, expected frequencies are calculated based on the marginal totals of the contingency table. These expected frequencies are compared with the observed frequencies to calculate the Chi-Square statistic.

For Beginners: This contains the counts you would expect for the second variable if there's no relationship.

The right expected frequencies:

• Represent what you would expect to see if the null hypothesis is true
• Are calculated based on the marginal totals and sample size
• The difference between these and observed frequencies drives the Chi-Square statistic

For example, in a gender and product preference test, this might contain the expected counts for each product option based on the overall proportions in your sample.

RightObserved

Gets or sets the observed frequencies for the right variable or category.

public Vector<T> RightObserved { get; set; }

Property Value

Vector<T>

A vector of observed frequencies, initialized to an empty vector.

Remarks

This property represents the observed frequencies for the right variable or category in the Chi-Square test. Observed frequencies are the actual counts or occurrences of each category in the sample data. In a test of independence, this might represent the counts for different categories of the second variable. These observed frequencies are compared with the expected frequencies to calculate the Chi-Square statistic.

For Beginners: This contains the actual counts you observed in your data for the second variable.

The right observed frequencies:

• Represent the actual counts from your data collection
• Are compared against expected frequencies to calculate the Chi-Square statistic
• For a contingency table, these would be the counts for the other variable

For example, if testing the relationship between gender and product preference, this might contain the counts of people preferring each product option.