HelixTree can perform or output the following statistical tests with the appropriate genetic model/test.

Correlation/Trend Test

The correlation/trend test is available for both case/control and quantitative dependent variables for every genetic model except the genotypic model. Also, this is the only test which is available if Principal Components Analysis (PCA) is used on the input data for stratification correction.

This test will show the p-value for the (possibly PCA-corrected) dependent variable value having any correlation with or “trend” which depends upon the (possibly PCA-corrected) count value of the genotype.

See the Formulas and Theories chapter of the HelixTree Manual for a more comprehensive explanation of this statistic.

Armitage Trend Test

This test is available specifically under the additive model for a case/control dependent variable when missing data is dropped.

The test is performed of “case” vs. “control” having a “trend” which depends upon the count of the minor allele D, which is zero within genotype dd, one within genotype Dd, and two within genotype DD.

See the Formulas and Theories chapter of the HelixTree Manual for a more comprehensive explanation of this statistic.

Exact Form of Armitage Test

This test is also available specifically under the additive model for a case/control dependent variable when missing data is dropped.

The exact form of this test yields the exact probability under the null hypothesis of having a “trend” at least as extreme as the one observed, assuming an equal probability of any permutation of the dependent variable. This form, which is more computationally expensive than is the normal Armitage Trend Test, avoids the chi-square approximation used in that test.

See the Formulas and Theories chapter of the HelixTree Manual for a more comprehensive explanation of this statistic.

Pearson Chi-Squared Test

The Pearson Chi-Squared test is available for a case/control dependent variable for all genetic models and tests except the Additive Model.

This test is on the observed contingency table vs. the expected contingency table created with all the possible variations of the selected model in one direction vs. “case” vs. “control” in the other direction, keeping the margins constant.

The respective contingency tables are as follows:

Genetic Model or Test	Contingency Table
Basic Allelic Test	(Case/Control) vs (D vs d)
Genotypic Test	(Case/Control) vs (DD vs dd vs Dd)
Dominant	(Case/Control) vs ((DD or Dd) vs dd)
Recessive	(Case/Control) vs (DD vs (Dd or dd))

See the Formulas and Theories chapter of the HelixTree Manual for a more comprehensive explanation of this statistic.

Fisher’s Exact Test

The Fisher’s exact test is also available for a case/control dependent variable for all genetic models and tests except the Additive Model.

This test yields the exact probability under the null hypothesis of having a contingency table at least as extreme as the one observed, assuming an equal probability of any permutation of the dependent variable. This form, which is more computationally expensive than the Pearson Chi-squared test, avoids the chi-square approximation altogether.

See the Formulas and Theories chapter of the HelixTree Manual for a more comprehensive explanation of this statistic.

Odds Ratio with Confidence Limits

If you have a case/control dependent variable, you are dropping missing data, and you are using any model or test other than the Genotypic Test, you may select to output odds ratios and the lower and upper 95% confidence bound for each under the following models:

• Basic Allelic Tests: The odds ratio for the minor allele enhancing the effect and the odds ratio for the major allele enhancing the effect.
• Dominant or Recessive: The odds ratio for enhancing the effect and the odds ratio for inhibiting the effect.
• Additive: The odds ratio for (Dd) vs. (dd) (heterozygous vs. homozygous major allele) enhancing the effect and the odds ratio for (DD) vs. (Dd) (homozygous minor allele vs. heterozygous) enhancing the effect.

NOTE: Under this model, the two odds ratios may be thought of as a check on the validity of the model itself in describing the effect, as well as indicators of the intensity of the association. If the two odds ratios are approximately the same, then the additive model may be considered valid. If the two odds ratios are very different, then there may be some other model that better describes the data. For instance, a high and significant odds ratio for (Dd) vs. (dd) and a low or insignificant odds ratio for (DD) vs. (Dd) may be an indicator that the Dominant model really better describes the effect.

NOTE: An odds ratio is generally considered significant if both the lower and the upper 95% confidence bounds
are greater than one (or both less than one for an odds ratio less than one).

See the Formulas and Theories chapter of the HelixTree Manual for a more comprehensive explanation of this statistic.

Analysis of Deviance

Analysis of Deviance is available for a case/control dependent variable for all genetic models and tests except the Additive Model.

This test is a first-order equivalent alternative statistic for testing an observed contingency table vs. expected contingency table created with all the possible variations of the selected model in one direction vs. “case” vs. “control” in the other direction. (See Pearson's Chi-Square Test above for a listing of the possible contingency tables.

This test has somewhat more theory in its foundation than does the Pearson test as it is a likelihood ratio test, to which the Pearson test is a first-order approximation.

See the Formulas and Theories chapter of the HelixTree Manual for a more comprehensive explanation of this statistic.

F-Test

This is one of the two tests available for a quantitative dependent variable. (The other is the correlation/trend test.) The F-Test is available for all genetic models and tests except the Additive Model.

This test is on whether the distributions of the dependent variable within each category are significantly different between the various categories of the predictor variable.

See the Formulas and Theories chapter of the HelixTree Manual for a more comprehensive explanation of this statistic.