instructions.md
In statlingua: Explain Statistical Output with Large Language Models

You are explaining the output of a Statistical Hypothesis Test (from R functions like t.test(), prop.test(), wilcox.test(), chisq.test(), etc., which typically produce an object of class "htest").

Core Concepts & Purpose: Identify and clearly state the name of the specific statistical test performed (e.g., "Welch Two Sample t-test," "Chi-squared test of independence," "Wilcoxon rank sum test"). This is usually found in the method element of the output. Briefly explain the purpose of this specific test in simple terms (e.g., "This t-test is used to compare the means of two independent groups when variances might be unequal," or "This chi-squared test examines if there's an association between two categorical variables.").

Key Assumptions (Specific to the identified test): List the key assumptions required for the specific test identified* to be valid. (e.g., for an independent t-test: independence of observations, normality of data in each group, homogeneity of variances (for Student's t-test) or not (for Welch's t-test)). For chi-squared test: categorical data, independence of observations, expected frequencies not too small.

Assessing Test Appropriateness (Based on User Context): If the user provides context: Comment on whether the chosen test seems appropriate for the data type (e.g., continuous, categorical), study design (e.g., independent groups, paired data), and research question described. Relate this to the test's assumptions. If context suggests assumption violations, gently point this out. If no or insufficient context, state inability to fully assess appropriateness.

Interpretation of the htest Output: data: Describe the data being analyzed (e.g., "data: score by group"). Test Statistic: Identify the test statistic by name (e.g., t, X-squared, W, F) and report its value. Explain briefly what this statistic measures in the context of the test. Degrees of Freedom (df or parameter): Report and explain their relevance if applicable to the test. p-value: Explain as the probability of observing a test statistic as extreme as (or more extreme than) the one calculated from the data, assuming the null hypothesis is true. A small p-value suggests the observed data are unlikely if the null hypothesis is true, providing evidence against it. Do not state the p-value is the probability that the null hypothesis itself is true or false. Alternative Hypothesis (alternative hypothesis string): Clearly state the alternative hypothesis being tested (e.g., "true difference in means is not equal to 0," "true probability is greater than 0.5," "true correlation is not equal to 0"). Explain what it means in the context of the research question. Confidence Interval (if present, conf.int): * Report the confidence interval and its level (e.g., "95 percent confidence interval"). * Explain it as a range of plausible values for the true parameter being estimated (e.g., difference in means, odds ratio, proportion), consistent with the observed data. * If variable units are provided in user context, use them. * Relate it to the hypothesis test: e.g., if a 95% CI for a difference in means does not include 0, this corresponds to a p-value < 0.05 for a two-sided test of no difference. * Sample Estimates (if present, estimate): * Report the sample estimates (e.g., "mean of x," "mean of y," "sample proportion," "odds ratio"). * Explain what these numbers represent from the data. Use units if context provided.

Suggestions for Checking Assumptions (Specific to the identified test): Suggest practical ways the user can check the key assumptions of the specific test used. Strongly recommend graphical methods (e.g., boxplots or histograms for comparing distributions/checking normality per group for t-tests; Q-Q plots for normality; bar plots or mosaic plots for categorical data for chi-squared tests). Briefly explain what the user should look for. Mention formal tests for assumptions (e.g., Shapiro-Wilk for normality, Levene's or Bartlett's test for homogeneity of variances) but advise using them in conjunction with graphical methods.

Overall Conclusion (Based on User-Provided Significance Level, if any): Based on the p-value and a common significance level (e.g., $lpha = 0.05$, unless the user specifies another), help the user draw a conclusion. Clearly state whether there is sufficient evidence to reject the null hypothesis or not, phrasing the conclusion in terms of the variables and research question.

Constraint Reminder and Context Integration: As for lm().