Table of Contents

Class TTestResult<T>

Namespace
AiDotNet.Models.Results
Assembly
AiDotNet.dll

Represents the results of a t-test, which is a statistical hypothesis test used to determine if there is a significant difference between the means of two groups.

public class TTestResult<T>

Type Parameters

T

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

Inheritance
TTestResult<T>
Inherited Members

Remarks

The t-test is one of the most commonly used statistical tests for comparing means. This class stores the results of such a test, including the t-statistic, degrees of freedom, p-value, and whether the result is statistically significant. The t-test is used when the test statistic follows a t-distribution under the null hypothesis, which typically occurs when comparing means from normally distributed populations with unknown variances. The class uses generic type parameter T to support different numeric types for the statistical values, such as float, double, or decimal.

For Beginners: This class stores the results of a t-test, which helps determine if the difference between two groups is statistically significant.

For example, you might use a t-test to answer questions like:

  • Is there a significant difference in test scores between two teaching methods?
  • Does a new medication significantly change blood pressure compared to a placebo?
  • Are the average sales before and after a marketing campaign significantly different?

The t-test works by:

  1. Calculating a t-statistic based on the difference between group means
  2. Determining how likely this t-statistic would occur by chance
  3. Producing a p-value that represents this probability

This test is particularly useful when:

  • You're comparing means between two groups
  • Your data approximately follows a normal distribution
  • You have relatively small sample sizes

This class stores all the information about the test results, helping you interpret whether the observed difference is statistically significant.

Constructors

TTestResult(T, int, T, T)

Initializes a new instance of the TTestResult class with the specified test statistics and parameters.

public TTestResult(T tStatistic, int degreesOfFreedom, T pValue, T significanceLevel)

Parameters

tStatistic T

The t-statistic value.

degreesOfFreedom int

The degrees of freedom for the t-test.

pValue T

The p-value associated with the t-test.

significanceLevel T

The significance level used for the test.

Remarks

This constructor creates a new TTestResult instance with the specified test statistics and parameters. It initializes all properties of the class and calculates the IsSignificant property by comparing the p-value to the significance level. The IsSignificant property is set to true if the p-value is less than the significance level, indicating that the test result is statistically significant. This constructor provides a convenient way to create a complete TTestResult object in a single step after performing a t-test.

For Beginners: This constructor creates a new result object with all the t-test statistics and parameters.

When a new TTestResult is created with this constructor:

  • All the test statistics and parameters are set to the values you provide
  • The IsSignificant property is automatically calculated by comparing the p-value to the significance level

This constructor is useful because:

  • It creates a complete result object in one step
  • It automatically determines statistical significance
  • It ensures all the related test information is kept together

The IsSignificant calculation uses MathHelper to compare the p-value to the significance level, which works regardless of what numeric type T is (float, double, decimal, etc.).

Properties

DegreesOfFreedom

Gets or sets the degrees of freedom for the t-test.

public int DegreesOfFreedom { get; set; }

Property Value

int

An integer representing the degrees of freedom.

Remarks

This property represents the degrees of freedom for the t-test, which is a parameter that determines the shape of the t-distribution used to calculate the p-value. The degrees of freedom is typically related to the sample sizes of the groups being compared. For an independent samples t-test, it is often calculated as the sum of the sample sizes minus 2, though more complex formulas may be used for Welch's t-test or other variants. For a paired t-test, it is typically the number of pairs minus 1. As the degrees of freedom increases, the t-distribution approaches the normal distribution.

For Beginners: This value helps determine the shape of the t-distribution used to calculate the p-value.

The degrees of freedom:

  • Is related to your sample size
  • Affects the critical values used to determine significance
  • Influences how conservative the test is

For common t-tests:

  • Independent samples t-test: df = n1 + n2 - 2 (where n1 and n2 are the sample sizes)
  • Paired t-test: df = n - 1 (where n is the number of pairs)
  • Welch's t-test: uses a more complex formula that accounts for unequal variances

As degrees of freedom increase:

  • The t-distribution becomes closer to a normal distribution
  • The test becomes more powerful (better at detecting real differences)

IsSignificant

Gets or sets a value indicating whether the t-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 t-test result is statistically significant at the specified significance level. A result is considered significant if the p-value is less than the significance level. Statistical significance suggests that the observed difference between the groups is unlikely to have occurred by chance alone, leading to the rejection of the null hypothesis that the means are equal. This property provides a convenient boolean indicator of significance without requiring the user to compare the p-value to the significance level.

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 difference between groups is statistically significant
  • False means the difference could reasonably be due to random chance

This is determined by:

  • Comparing the p-value to the significance level

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.

PValue

Gets or sets the p-value associated with the t-test.

public T PValue { get; set; }

Property Value

T

The calculated p-value.

Remarks

This property represents the p-value of the t-test, which is the probability of observing a t-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 difference between the means of the groups being compared. A small p-value (typically = 0.05) suggests that the observed difference is unlikely under the null hypothesis, leading to its rejection in favor of the alternative hypothesis that the means differ. The p-value is calculated from the t-statistic and the degrees of freedom using the cumulative distribution function of the t-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 the groups are actually the same

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 a difference as large as yours if the groups truly have the same mean, suggesting the difference is likely real and not due to random chance.

SignificanceLevel

Gets or sets the significance level used for the test.

public T SignificanceLevel { get; set; }

Property Value

T

The significance level, typically 0.05.

Remarks

This property represents the significance level used for the t-test, which is the threshold p-value below which the result is considered statistically significant. Common values are 0.05 (5%), 0.01 (1%), and 0.001 (0.1%). The significance level represents the probability of rejecting the null hypothesis when it is actually true (Type I error). A lower significance level reduces the risk of Type I errors but increases the risk of Type II errors (failing to reject a false null hypothesis).

For Beginners: This value is the threshold that determines when a result is considered statistically significant.

The significance level:

  • Is typically set to 0.05 (5%) by convention
  • Represents your tolerance for false positives
  • Lower values (like 0.01) make the test more conservative
  • Higher values (like 0.10) make the test more lenient

This value is important because:

  • It directly determines whether a result is considered "significant"
  • It represents the risk you're willing to take of finding a difference when none exists

For example, with a significance level of 0.05, you're accepting a 5% chance of incorrectly concluding there's a difference when there's actually none.

TStatistic

Gets or sets the t-statistic value.

public T TStatistic { get; set; }

Property Value

T

The calculated t-statistic.

Remarks

This property represents the t-statistic, which is a measure of the difference between the groups being compared, scaled by the variability in the data. The t-statistic is calculated by dividing the difference between the means by the standard error of the difference. A larger absolute value of the t-statistic indicates a greater difference between the groups relative to the variability within the groups. The sign of the t-statistic indicates the direction of the difference (positive if the first group mean is larger, negative if the second group mean is larger).

For Beginners: This value measures how different your groups are, taking into account the variability in your data.

The t-statistic:

  • Measures the size of the difference between groups relative to the variation within groups
  • Larger absolute values indicate stronger evidence of a real difference
  • The sign (+ or -) indicates which group has the higher mean

For example, a t-statistic of 2.5 suggests the difference between groups is 2.5 times larger than what you might expect from random variation alone.

This value is important because:

  • It's used to calculate the p-value
  • It indicates both the direction and magnitude of the effect
  • It can be compared to critical values from t-distribution tables
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