statease is an R package designed to simplify statistical analysis by combining a wide range of tests with automatic plain-English interpretation of results. Whether you are a student, researcher, or educator, statease gives you numbers and meaning in one command.
Throughout this vignette we use a simulated dataset of 90 students examining the effect of teaching methods on exam performance.
set.seed(42)
tutorial_data <- data.frame(
student_id = 1:90,
method = rep(c("Traditional", "Online", "Hybrid"), each = 30),
gender = rep(c("Male", "Female"), times = 45),
exam_score = c(
round(rnorm(30, mean = 65, sd = 10)),
round(rnorm(30, mean = 72, sd = 10)),
round(rnorm(30, mean = 78, sd = 10))
),
pre_test = c(
round(rnorm(30, mean = 55, sd = 10)),
round(rnorm(30, mean = 58, sd = 10)),
round(rnorm(30, mean = 57, sd = 10))
),
age = round(rnorm(90, mean = 22, sd = 3)),
passed = rbinom(90, 1, prob = 0.7)
)
head(tutorial_data)
#> student_id method gender exam_score pre_test age passed
#> 1 1 Traditional Male 79 69 22 0
#> 2 2 Traditional Female 59 50 20 0
#> 3 3 Traditional Male 69 62 23 1
#> 4 4 Traditional Female 71 69 23 1
#> 5 5 Traditional Male 69 44 21 1
#> 6 6 Traditional Female 64 46 18 0The describe() function provides a full summary of a
numeric variable including measures of central tendency, spread, and a
normality check.
result <- describe(tutorial_data$exam_score,
var_name = "Exam Score")
print(result)
#>
#> -- statease Descriptive Report ----------------------------------
#> Variable : Exam Score
#> N : 90 | Missing: 0
#> -----------------------------------------------------------------
#> Mean : 72.10
#> Median : 74.00
#> Std Dev : 11.94
#> Min : 38.00 | Max: 93.00
#> Q1 : 64.00 | Q3: 80.00
#> IQR : 16.00
#> -----------------------------------------------------------------
#> Interpretation:
#> The distribution is approximately symmetric.
#> Spread shows moderate variability (CV = 16.6%).
#> Shapiro-Wilk test suggests non-normality (W = 0.958, p = 0.0054).
#> -----------------------------------------------------------------You can also extract individual values:
result$mean
#> [1] 72.1
result$sd
#> [1] 11.93903
result$skew_label
#> [1] "approximately symmetric"Compare exam scores between male and female students:
males <- tutorial_data$exam_score[tutorial_data$gender == "Male"]
females <- tutorial_data$exam_score[tutorial_data$gender == "Female"]
result <- ttest_interpret(
males, females,
var_name = "Exam Score by Gender"
)
print(result)
#>
#> -- statease T-Test Report ----------------------------------------
#> Test : Independent Samples T-Test
#> Variable : Exam Score by Gender
#> Groups : Group 1: n = 45 | Group 2: n = 45
#> -----------------------------------------------------------------
#> t-statistic : 0.026
#> df : 88.0
#> p-value : 0.9790
#> 95% CI : [-4.964, 5.097]
#> Cohen's d : 0.006 (negligible effect)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Normality (x) : PASSED (Shapiro-Wilk p = 0.050)
#> Normality (y) : PASSED (Shapiro-Wilk p = 0.156)
#> Equal variances : PASSED (F-test p = 0.937)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is not statistically significant (p = 0.979 > alpha 0.05).
#> Group 1 had a higher mean (72.13 vs 72.07).
#> Effect size is negligible (d = 0.006).
#> 95% CI: true difference lies between -4.964 and 5.097.
#> -----------------------------------------------------------------Test whether the average exam score is significantly different from 70:
result <- ttest_interpret(
tutorial_data$exam_score,
mu = 70,
var_name = "Exam Score"
)
print(result)
#>
#> -- statease T-Test Report ----------------------------------------
#> Test : One-Sample T-Test
#> Variable : Exam Score
#> Groups : n = 90 | Hypothesised mean (mu) = 70.00
#> -----------------------------------------------------------------
#> t-statistic : 1.669
#> df : 89.0
#> p-value : 0.0987
#> 95% CI : [69.599, 74.601]
#> Cohen's d : 0.176 (negligible effect)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Normality (x) : WARNING (Shapiro-Wilk p = 0.005, may not be normal)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is not statistically significant (p = 0.099 > alpha 0.05).
#> Sample mean was 72.10 vs hypothesised 70.00.
#> Effect size is negligible (d = 0.176).
#> 95% CI: true difference lies between 69.599 and 74.601.
#> -----------------------------------------------------------------Test whether students improved from pre-test to final exam:
result <- ttest_interpret(
tutorial_data$exam_score,
tutorial_data$pre_test,
paired = TRUE,
var_name = "Score Improvement"
)
print(result)
#>
#> -- statease T-Test Report ----------------------------------------
#> Test : Paired Samples T-Test
#> Variable : Score Improvement
#> Groups : n (pairs) = 90
#> -----------------------------------------------------------------
#> t-statistic : 10.296
#> df : 89.0
#> p-value : 0.0000
#> 95% CI : [13.262, 19.605]
#> Cohen's d : 1.085 (large effect)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Normality (x) : WARNING (Shapiro-Wilk p = 0.005, may not be normal)
#> Normality (y) : PASSED (Shapiro-Wilk p = 0.282)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is statistically significant (p = 0.000 < alpha 0.05).
#> Group 1 had a higher mean (72.10 vs 55.67).
#> Effect size is large (d = 1.085).
#> 95% CI: true difference lies between 13.262 and 19.605.
#> -----------------------------------------------------------------Test whether teaching method affects exam scores:
result <- anova_interpret(
exam_score ~ method,
data = tutorial_data
)
print(result)
#>
#> -- statease ANOVA Report -----------------------------------------
#> Outcome : exam_score
#> Group : method (3 levels)
#> -----------------------------------------------------------------
#> Group Means:
#> Hybrid : Mean = 79.90 (n = 30)
#> Online : Mean = 70.77 (n = 30)
#> Traditional : Mean = 65.63 (n = 30)
#> -----------------------------------------------------------------
#> F-statistic : 14.267
#> df : 2, 87
#> p-value : 0.0000
#> Eta squared : 0.2470 (large effect)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Normality (Group: Hybrid): PASSED (Shapiro-Wilk p = 0.226)
#> Normality (Group: Online): PASSED (Shapiro-Wilk p = 0.074)
#> Normality (Group: Traditional): PASSED (Shapiro-Wilk p = 0.340)
#> Equal variances : WARNING (Bartlett's p = 0.042 (unequal variances))
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The overall ANOVA result is statistically significant (p = 0.0000 < alpha 0.05).
#> Group differences explain 24.7% of variance
#> (eta^2 = 0.2470, large effect).
#> WARNING: Bartlett's test suggests unequal variances (p = 0.0421).
#>
#> -- Post-Hoc Tukey HSD --------------------------------------------
#> Online-Hybrid
#> Mean diff = -9.133 | p adj = 0.0031 | [significant]
#> Traditional-Hybrid
#> Mean diff = -14.267 | p adj = 0.0000 | [significant]
#> Traditional-Online
#> Mean diff = -5.133 | p adj = 0.1456 | [not significant]
#> -----------------------------------------------------------------
#> Note: Tukey HSD controls for family-wise error rate.
#> -----------------------------------------------------------------Test the effect of both teaching method and gender on exam scores:
result <- anova2_interpret(
exam_score ~ method * gender,
data = tutorial_data
)
print(result)
#>
#> statease Two-Way ANOVA Report
#> Outcome : exam_score
#> Factor 1 : method
#> Factor 2 : gender
#> N : 90
#> SS Type : Type-II
#>
#> Means by method:
#> Hybrid : 79.90
#> Online : 70.77
#> Traditional : 65.63
#>
#> Means by gender:
#> Female : 72.07
#> Male : 72.13
#>
#> Interaction Means:
#> Female Male
#> Hybrid 81.27 78.53
#> Online 71.60 69.93
#> Traditional 63.33 67.93
#>
#> ANOVA Results:
#> method : F = 14.123 df = 2,84 significant (p = 0.0000) eta^2 = 0.2470 (large)
#> gender : F = 0.001 df = 1,84 not significant (p = 0.9761) eta^2 = 0.0000 (negligible)
#> Interaction : F = 1.061 df = 2,84 not significant (p = 0.3506) eta^2 = 0.0186 (small)
#>
#> Assumption Checks:
#> Normality (residuals) : PASSED (Shapiro-Wilk p = 0.181)
#> Equal variances (cells) : PASSED (Bartlett's p = 0.104)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#>
#> Interpretation:
#> Main effect of method is significant (p = 0.0000).
#> Main effect of gender is not significant (p = 0.9761).
#> Interaction (method x gender) is not significant (p = 0.3506).
#>
#> -- Post-Hoc Tukey HSD (method) ------------------------------
#> Online-Hybrid : diff = -9.133 p adj = 0.0033 [significant]
#> Traditional-Hybrid : diff = -14.267 p adj = 0.0000 [significant]
#> Traditional-Online : diff = -5.133 p adj = 0.1485 [not significant]
#> -----------------------------------------------------------------Test the combined effect of teaching method on both exam score and pre-test score simultaneously:
result <- manova_interpret(
cbind(exam_score, pre_test) ~ method,
data = tutorial_data
)
print(result)
#>
#> -- statease MANOVA Report ----------------------------------------
#> Outcomes : exam_score, pre_test
#> Group : method (3 levels)
#> N : 90
#> -----------------------------------------------------------------
#> Group Means:
#>
#> exam_score:
#> Hybrid : 79.90
#> Online : 70.77
#> Traditional : 65.63
#>
#> pre_test:
#> Hybrid : 56.87
#> Online : 55.37
#> Traditional : 54.77
#> -----------------------------------------------------------------
#> Multivariate Test Results:
#> Pillai's Trace : 0.2565
#> Wilks' Lambda : 0.7435
#> F-statistic : 6.400 (df = 4, 174)
#> p-value : 0.0001
#> Effect size : small (Pillai = 0.2565)
#> -----------------------------------------------------------------
#> Interpretation:
#> The overall MANOVA result is statistically significant (p = 0.0001 < alpha 0.05).
#> Pillai's Trace = 0.2565 indicates a small effect.
#> -----------------------------------------------------------------
#> Follow-Up Univariate ANOVAs:
#>
#> exam_score
#> F = 14.267 (df = 2, 87) p = 0.0000 [significant]
#>
#> pre_test
#> F = 0.403 (df = 2, 87) p = 0.6695 [not significant]
#>
#> Note: Follow-up ANOVAs identify which outcomes
#> differ significantly across groups.
#>
#> WARNING: 'exam_score' may not be normally distributed (Shapiro-Wilk p = 0.0054).
#> -----------------------------------------------------------------Test whether there is an association between teaching method and pass/fail outcome:
tutorial_data$passed_label <- ifelse(tutorial_data$passed == 1,
"Pass", "Fail")
result <- chisq_interpret(
tutorial_data$method,
tutorial_data$passed_label
)
print(result)
#>
#> -- statease Chi-Square Test Report ------------------------------
#> N : 90
#> -----------------------------------------------------------------
#> Contingency Table (Observed):
#> y
#> x Fail Pass
#> Hybrid 6 24
#> Online 8 22
#> Traditional 10 20
#>
#> Expected Frequencies:
#> y
#> x Fail Pass
#> Hybrid 8 22
#> Online 8 22
#> Traditional 8 22
#>
#> -----------------------------------------------------------------
#> Chi-square : 1.364
#> df : 2
#> p-value : 0.5057
#> Cramer's V : 0.123 (small effect)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Expected cell frequencies : PASSED (all cells >= 5)
#> Sample independence : NOTE (assumed from study design, not testable from data)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is not statistically significant (p = 0.5057 > alpha 0.05).
#> There is no significant association between the two variables.
#> Effect size is small (V = 0.123).
#> -----------------------------------------------------------------Test the relationship between pre-test scores and exam scores:
result <- cor_interpret(
tutorial_data$pre_test,
tutorial_data$exam_score,
var1_name = "Pre-Test Score",
var2_name = "Exam Score"
)
print(result)
#>
#> -- statease Correlation Report -----------------------------------
#> Method : Pearson Product-Moment Correlation
#> Variables : Pre-Test Score & Exam Score
#> N : 90 | Missing: 0
#> -----------------------------------------------------------------
#> r : -0.0038
#> p-value : 0.9720
#> 95% CI : [-0.2107, 0.2035]
#> Strength : negligible
#> Direction : negative (as one variable increases, the other tends to decrease)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Normality (x) : PASSED (Shapiro-Wilk p = 0.282, Pearson only)
#> Normality (y) : WARNING (Shapiro-Wilk p = 0.005, Pearson only, may not be normal)
#> Linearity : NOTE (visual inspection is recommended, not testable numerically)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The correlation is not statistically significant (p = 0.9720 > alpha 0.05).
#> The relationship between Pre-Test Score and Exam Score is
#> negligible and negative (as one variable increases, the other tends to decrease) in direction.
#>
#> WARNING: One or both variables may not be normally distributed. Consider using method = 'spearman' instead.
#> -----------------------------------------------------------------result <- cor_interpret(
tutorial_data$pre_test,
tutorial_data$exam_score,
method = "spearman",
var1_name = "Pre-Test Score",
var2_name = "Exam Score"
)
#> Warning in cor.test.default(x, y, method = method, conf.level = conf.level):
#> Cannot compute exact p-value with ties
print(result)
#>
#> -- statease Correlation Report -----------------------------------
#> Method : Spearman Rank Correlation
#> Variables : Pre-Test Score & Exam Score
#> N : 90 | Missing: 0
#> -----------------------------------------------------------------
#> r : 0.0750
#> p-value : 0.4826
#> Strength : negligible
#> Direction : positive (as one variable increases, the other tends to increase)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Linearity : NOTE (visual inspection is recommended, not testable numerically)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The correlation is not statistically significant (p = 0.4826 > alpha 0.05).
#> The relationship between Pre-Test Score and Exam Score is
#> negligible and positive (as one variable increases, the other tends to increase) in direction.
#> -----------------------------------------------------------------Predict exam score from pre-test score:
result <- reg_interpret(
exam_score ~ pre_test,
data = tutorial_data
)
print(result)
#>
#> -- statease Simple Linear Regression Report ---------------------
#> Outcome : exam_score
#> Predictor : pre_test
#> N : 90
#> -----------------------------------------------------------------
#> Model Equation:
#> exam_score = 72.369 + -0.005 * pre_test
#> -----------------------------------------------------------------
#> Coefficients:
#> Intercept : 72.369
#> Slope : -0.005 (SE = 0.137)
#> t-statistic : -0.035
#> p-value : 0.9720
#> 95% CI : [-0.278, 0.268]
#> -----------------------------------------------------------------
#> Model Fit:
#> R-squared : 0.0000
#> Adj R-squared: -0.0113
#> F-statistic : 0.001 (df = 1, 88) p = 0.9720
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Normality (residuals) : WARNING (Shapiro-Wilk p = 0.006, may not be normal)
#> Homoscedasticity : PASSED (non-constant variance test p = 0.413)
#> Residual independence : WARNING (Durbin-Watson DW = 1.47, p = 0.010, possible autocorrelation)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The predictor pre_test is not statistically significant (p = 0.9720 > alpha 0.05).
#> The slope is negative - as pre_test increases by 1 unit, exam_score decreases by 0.005 units.
#> R-squared = 0.0000: pre_test explains 0.0% of the
#> variance in exam_score (negligible effect).
#> -----------------------------------------------------------------Predict exam score from both pre-test score and age:
result <- mlr_interpret(
exam_score ~ pre_test + age,
data = tutorial_data
)
print(result)
#>
#> -- statease Multiple Linear Regression Report -------------------
#> Outcome : exam_score
#> Predictors : pre_test, age
#> N : 90
#> -----------------------------------------------------------------
#> Model Equation:
#> exam_score = 70.019 + 0.001*pre_test + 0.093*age
#> -----------------------------------------------------------------
#> Overall Model Fit:
#> R-squared : 0.0005 (negligible effect)
#> Adj R-squared: -0.0225
#> F-statistic : 0.022 (df = 2, 87) p = 0.9782
#> The overall model is not statistically significant (p = 0.9782 > alpha 0.05).
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Normality (residuals) : WARNING (Shapiro-Wilk p = 0.005, may not be normal)
#> Homoscedasticity : PASSED (non-constant variance test p = 0.105)
#> Residual independence : WARNING (Durbin-Watson DW = 1.48, p = 0.010, possible autocorrelation)
#> Multicollinearity (VIF) : PASSED (max VIF = 1.0, threshold = 5)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#>
#> pre_test
#> Coefficient : 0.001 (SE = 0.141)
#> t-statistic : 0.008
#> p-value : 0.9936 [not significant]
#> 95% CI : [-0.279, 0.282]
#> Direction : positive (b = 0.001)
#>
#> age
#> Coefficient : 0.093 (SE = 0.447)
#> t-statistic : 0.207
#> p-value : 0.8366 [not significant]
#> 95% CI : [-0.796, 0.982]
#> Direction : positive (b = 0.093)
#> -----------------------------------------------------------------
#> Interpretation:
#> The model explains 0.1% of the variance in exam_score
#> (R-squared = 0.0005, negligible effect).
#> Adjusted R-squared = -0.0225 accounting for
#> the number of predictors in the model.
#> Non-significant predictors: pre_test, age
#> -----------------------------------------------------------------Predict pass/fail outcome from pre-test score and age:
result <- logistic_interpret(
passed ~ pre_test + age,
data = tutorial_data
)
#> Waiting for profiling to be done...
print(result)
#>
#> -- statease Logistic Regression Report --------------------------
#> Outcome : passed
#> Predictors : pre_test, age
#> N : 90
#> -----------------------------------------------------------------
#> Overall Model Fit:
#> Chi-square : 3.668 (df = 2) p = 0.1598
#> Nagelkerke R2: 0.0582 (small effect)
#> The overall model is not statistically significant (p = 0.1598 > alpha 0.05).
#> -----------------------------------------------------------------
#> Individual Predictors:
#>
#> pre_test
#> Coefficient : -0.050 (SE = 0.027)
#> z-statistic : -1.842
#> p-value : 0.0655 [not significant]
#> Odds Ratio : 0.951
#> 95% CI (OR) : [0.899, 1.002]
#> Interpretation: each unit increase in pre_test decreases the odds by 4.9%.
#>
#> age
#> Coefficient : -0.006 (SE = 0.086)
#> z-statistic : -0.065
#> p-value : 0.9482 [not significant]
#> Odds Ratio : 0.994
#> 95% CI (OR) : [0.838, 1.180]
#> Interpretation: each unit increase in age decreases the odds by 0.6%.
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Multicollinearity (VIF) : PASSED (max VIF = 1.1, threshold = 5)
#> Complete separation : PASSED (no obvious numerical evidence of separation)
#> Linearity of the logit : NOTE (not automatically tested; consider a diagnostic such as the Box-Tidwell test or component-plus-residual plots for continuous predictors)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The model is not statistically significant (p = 0.1598 > alpha 0.05).
#> Nagelkerke R2 = 0.0582 suggests a small amount of
#> variance in passed is explained by the predictors.
#> Non-significant predictors: pre_test, age
#> -----------------------------------------------------------------Non-parametric alternative to the independent samples t-test:
result <- mannwhitney_interpret(
males, females,
var_name = "Exam Score by Gender"
)
print(result)
#>
#> -- statease Mann-Whitney U Test Report --------------------------
#> Variable : Exam Score by Gender
#> Group 1 : n = 45 | Median = 74.00
#> Group 2 : n = 45 | Median = 75.00
#> -----------------------------------------------------------------
#> W statistic : 1026.500
#> p-value : 0.9132
#> 95% CI : [-5.000, 5.000]
#> Effect size : 0.011 (negligible)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Sample size (Group 1) : NOTE (n = 45)
#> Sample size (Group 2) : NOTE (n = 45)
#> Test method used : NOTE (Wilcoxon rank sum test with continuity correction)
#> Independence : NOTE (assumed from study design, not testable from data)
#>
#> NOTE: These are contextual notes rather than pass/fail checks.
#> They describe aspects of the data and test method relevant to
#> interpretation, but are not automatically verifiable by the
#> package.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is not statistically significant (p = 0.9132 > alpha 0.05).
#> Values in Group 2 appear stochastically greater than values in Group 1. (Reported medians: Group 1 = 74.00, Group 2 = 75.00)
#> Effect size is negligible (r = 0.011).
#> Note: Mann-Whitney tests stochastic superiority,
#> not differences in medians.
#> -----------------------------------------------------------------Non-parametric alternative to the paired t-test:
result <- wilcoxon_interpret(
tutorial_data$exam_score,
tutorial_data$pre_test,
var_name = "Score Improvement"
)
print(result)
#>
#> -- statease Wilcoxon Signed Rank Test Report --------------------
#> Variable : Score Improvement
#> N (pairs) : 90
#> Pre Median : 55.00
#> Post Median : 74.00
#> -----------------------------------------------------------------
#> V statistic : 3711.500
#> p-value : 0.0000
#> 95% CI : [14.000, 20.500]
#> Effect size : 0.737 (large)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Sample size (pairs) : NOTE (n = 90)
#> Test method used : NOTE (Wilcoxon signed rank test with continuity correction)
#> Independence of pairs : NOTE (assumed from study design, not testable from data)
#>
#> NOTE: These are contextual notes rather than pass/fail checks.
#> They describe aspects of the data and test method relevant to
#> interpretation, but are not automatically verifiable by the
#> package.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is statistically significant (p = 0.0000 < alpha 0.05).
#> Post-measurement values appear stochastically greater than pre-measurement values. (Reported medians: Post = 74.00, Pre = 55.00)
#> Effect size is large (r = 0.737).
#> Note: Wilcoxon test compares groups using ranked values.
#> A significant result suggests one group tends to have larger or smaller observation than the other.
#> This can be interpreted as evidence of stochastic superiority, but only under typical distribution assumptions.
#> It does not specifically test differences in medians.
#> -----------------------------------------------------------------Non-parametric alternative to one-way ANOVA:
result <- kruskal_interpret(
exam_score ~ method,
data = tutorial_data
)
print(result)
#>
#> -- statease Kruskal-Wallis Test Report --------------------------
#> Outcome : exam_score
#> Group : method (3 levels)
#> N : 90
#> -----------------------------------------------------------------
#> Group Medians:
#> Hybrid : Median = 81.00 (n = 30)
#> Online : Median = 73.50 (n = 30)
#> Traditional : Median = 64.00 (n = 30)
#> -----------------------------------------------------------------
#> H statistic : 23.052
#> df : 2
#> p-value : 0.0000
#> Eta squared : 0.2420 (large effect)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Minimum group size : NOTE (smallest group n = 30; consider this when assessing the chi-square approximation)
#> Independence : NOTE (assumed from study design, not testable from data)
#>
#> NOTE: These are contextual notes rather than pass/fail checks.
#> They describe aspects of the data and test method relevant to
#> interpretation, but are not automatically verifiable by the
#> package.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is statistically significant (p = 0.0000 < alpha 0.05).
#> Effect size is large (eta^2 = 0.2420).
#> Note: Kruskal-Wallis test compares multiple groups using ranked values
#> not differences in medians.
#> Medians are reported for descriptive purposes only.
#>
#> -- Post-Hoc Pairwise Comparisons (Wilcoxon) ---------------------
#> Hybrid vs Online
#> p = 0.0006 [significant]
#> Hybrid vs Traditional
#> p = 0.0000 [significant]
#> Online vs Traditional
#> p = 0.0653 [not significant]
#>
#> Note: Pairwise Wilcoxon tests used for post-hoc comparisons.
#> -----------------------------------------------------------------Interpret any p-value in plain English:
result <- interpret_p(
0.03,
context = "teaching method effect on exam scores"
)
print(result)
#>
#> -- statease P-Value Interpretation ------------------------------
#> Context : teaching method effect on exam scores
#> P-value : 0.0300
#> Alpha : 0.05
#> -----------------------------------------------------------------
#> Decision : REJECT the null hypothesis at alpha = 0.05
#> Evidence : There is moderate evidence against the null hypothesis.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is statistically significant. The observed data is unlikely to have occurred by chance if the null hypothesis were true.
#>
#> Note: Statistical significance does not imply practical importance. Always consider effect size alongside the p-value.
#> -----------------------------------------------------------------The analyze() function automatically detects the right
test based on your input — no need to remember which function to
use!
# Descriptive statistics
analyze(x = tutorial_data$exam_score, var_name = "Exam Score")
#> [statease] Single numeric vector -> Running Descriptive Statistics
#>
#> -- statease Descriptive Report ----------------------------------
#> Variable : Exam Score
#> N : 90 | Missing: 0
#> -----------------------------------------------------------------
#> Mean : 72.10
#> Median : 74.00
#> Std Dev : 11.94
#> Min : 38.00 | Max: 93.00
#> Q1 : 64.00 | Q3: 80.00
#> IQR : 16.00
#> -----------------------------------------------------------------
#> Interpretation:
#> The distribution is approximately symmetric.
#> Spread shows moderate variability (CV = 16.6%).
#> Shapiro-Wilk test suggests non-normality (W = 0.958, p = 0.0054).
#> -----------------------------------------------------------------# Auto t-test
analyze(
x = males,
y = females,
var_name = "Exam Score by Gender"
)
#> [statease] Two numeric vectors detected -> Running T-Test
#>
#> -- statease T-Test Report ----------------------------------------
#> Test : Independent Samples T-Test
#> Variable : Exam Score by Gender
#> Groups : Group 1: n = 45 | Group 2: n = 45
#> -----------------------------------------------------------------
#> t-statistic : 0.026
#> df : 88.0
#> p-value : 0.9790
#> 95% CI : [-4.964, 5.097]
#> Cohen's d : 0.006 (negligible effect)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Normality (x) : PASSED (Shapiro-Wilk p = 0.050)
#> Normality (y) : PASSED (Shapiro-Wilk p = 0.156)
#> Equal variances : PASSED (F-test p = 0.937)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is not statistically significant (p = 0.979 > alpha 0.05).
#> Group 1 had a higher mean (72.13 vs 72.07).
#> Effect size is negligible (d = 0.006).
#> 95% CI: true difference lies between -4.964 and 5.097.
#> -----------------------------------------------------------------# Auto ANOVA
analyze(formula = exam_score ~ method, data = tutorial_data)
#> [statease] 3+ groups detected -> Running One-Way ANOVA
#>
#> -- statease ANOVA Report -----------------------------------------
#> Outcome : exam_score
#> Group : method (3 levels)
#> -----------------------------------------------------------------
#> Group Means:
#> Hybrid : Mean = 79.90 (n = 30)
#> Online : Mean = 70.77 (n = 30)
#> Traditional : Mean = 65.63 (n = 30)
#> -----------------------------------------------------------------
#> F-statistic : 14.267
#> df : 2, 87
#> p-value : 0.0000
#> Eta squared : 0.2470 (large effect)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Normality (Group: Hybrid): PASSED (Shapiro-Wilk p = 0.226)
#> Normality (Group: Online): PASSED (Shapiro-Wilk p = 0.074)
#> Normality (Group: Traditional): PASSED (Shapiro-Wilk p = 0.340)
#> Equal variances : WARNING (Bartlett's p = 0.042 (unequal variances))
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The overall ANOVA result is statistically significant (p = 0.0000 < alpha 0.05).
#> Group differences explain 24.7% of variance
#> (eta^2 = 0.2470, large effect).
#> WARNING: Bartlett's test suggests unequal variances (p = 0.0421).
#>
#> -- Post-Hoc Tukey HSD --------------------------------------------
#> Online-Hybrid
#> Mean diff = -9.133 | p adj = 0.0031 | [significant]
#> Traditional-Hybrid
#> Mean diff = -14.267 | p adj = 0.0000 | [significant]
#> Traditional-Online
#> Mean diff = -5.133 | p adj = 0.1456 | [not significant]
#> -----------------------------------------------------------------
#> Note: Tukey HSD controls for family-wise error rate.
#> -----------------------------------------------------------------# Auto non-parametric
analyze(
formula = exam_score ~ method,
data = tutorial_data,
nonparam = TRUE
)
#> [statease] 3+ groups + nonparam = TRUE -> Running Kruskal-Wallis Test
#>
#> -- statease Kruskal-Wallis Test Report --------------------------
#> Outcome : exam_score
#> Group : method (3 levels)
#> N : 90
#> -----------------------------------------------------------------
#> Group Medians:
#> Hybrid : Median = 81.00 (n = 30)
#> Online : Median = 73.50 (n = 30)
#> Traditional : Median = 64.00 (n = 30)
#> -----------------------------------------------------------------
#> H statistic : 23.052
#> df : 2
#> p-value : 0.0000
#> Eta squared : 0.2420 (large effect)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Minimum group size : NOTE (smallest group n = 30; consider this when assessing the chi-square approximation)
#> Independence : NOTE (assumed from study design, not testable from data)
#>
#> NOTE: These are contextual notes rather than pass/fail checks.
#> They describe aspects of the data and test method relevant to
#> interpretation, but are not automatically verifiable by the
#> package.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is statistically significant (p = 0.0000 < alpha 0.05).
#> Effect size is large (eta^2 = 0.2420).
#> Note: Kruskal-Wallis test compares multiple groups using ranked values
#> not differences in medians.
#> Medians are reported for descriptive purposes only.
#>
#> -- Post-Hoc Pairwise Comparisons (Wilcoxon) ---------------------
#> Hybrid vs Online
#> p = 0.0006 [significant]
#> Hybrid vs Traditional
#> p = 0.0000 [significant]
#> Online vs Traditional
#> p = 0.0653 [not significant]
#>
#> Note: Pairwise Wilcoxon tests used for post-hoc comparisons.
#> -----------------------------------------------------------------# Auto regression
analyze(formula = exam_score ~ pre_test, data = tutorial_data)
#> [statease] Numeric predictor detected -> Running Simple Linear Regression
#>
#> -- statease Simple Linear Regression Report ---------------------
#> Outcome : exam_score
#> Predictor : pre_test
#> N : 90
#> -----------------------------------------------------------------
#> Model Equation:
#> exam_score = 72.369 + -0.005 * pre_test
#> -----------------------------------------------------------------
#> Coefficients:
#> Intercept : 72.369
#> Slope : -0.005 (SE = 0.137)
#> t-statistic : -0.035
#> p-value : 0.9720
#> 95% CI : [-0.278, 0.268]
#> -----------------------------------------------------------------
#> Model Fit:
#> R-squared : 0.0000
#> Adj R-squared: -0.0113
#> F-statistic : 0.001 (df = 1, 88) p = 0.9720
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Normality (residuals) : WARNING (Shapiro-Wilk p = 0.006, may not be normal)
#> Homoscedasticity : PASSED (non-constant variance test p = 0.413)
#> Residual independence : WARNING (Durbin-Watson DW = 1.47, p = 0.010, possible autocorrelation)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The predictor pre_test is not statistically significant (p = 0.9720 > alpha 0.05).
#> The slope is negative - as pre_test increases by 1 unit, exam_score decreases by 0.005 units.
#> R-squared = 0.0000: pre_test explains 0.0% of the
#> variance in exam_score (negligible effect).
#> -----------------------------------------------------------------# Auto MANOVA
analyze(
formula = cbind(exam_score, pre_test) ~ method,
data = tutorial_data
)
#> [statease] Multiple outcomes detected -> Running MANOVA
#>
#> -- statease MANOVA Report ----------------------------------------
#> Outcomes : exam_score, pre_test
#> Group : method (3 levels)
#> N : 90
#> -----------------------------------------------------------------
#> Group Means:
#>
#> exam_score:
#> Hybrid : 79.90
#> Online : 70.77
#> Traditional : 65.63
#>
#> pre_test:
#> Hybrid : 56.87
#> Online : 55.37
#> Traditional : 54.77
#> -----------------------------------------------------------------
#> Multivariate Test Results:
#> Pillai's Trace : 0.2565
#> Wilks' Lambda : 0.7435
#> F-statistic : 6.400 (df = 4, 174)
#> p-value : 0.0001
#> Effect size : small (Pillai = 0.2565)
#> -----------------------------------------------------------------
#> Interpretation:
#> The overall MANOVA result is statistically significant (p = 0.0001 < alpha 0.05).
#> Pillai's Trace = 0.2565 indicates a small effect.
#> -----------------------------------------------------------------
#> Follow-Up Univariate ANOVAs:
#>
#> exam_score
#> F = 14.267 (df = 2, 87) p = 0.0000 [significant]
#>
#> pre_test
#> F = 0.403 (df = 2, 87) p = 0.6695 [not significant]
#>
#> Note: Follow-up ANOVAs identify which outcomes
#> differ significantly across groups.
#>
#> WARNING: 'exam_score' may not be normally distributed (Shapiro-Wilk p = 0.0054).
#> -----------------------------------------------------------------Test the association between two categorical variables when sample sizes are small:
result <- fisher_interpret(
tutorial_data$method,
tutorial_data$passed_label
)
print(result)
#>
#> --- statease Fisher's Exact Test Report ---------------
#> N : 90
#> Table size : 3 x 2
#>
#> Contingency Table (Observed):
#> y
#> x Fail Pass
#> Hybrid 6 24
#> Online 8 22
#> Traditional 10 20
#>
#> Expected Frequencies:
#> y
#> x Fail Pass
#> Hybrid 8 22
#> Online 8 22
#> Traditional 8 22
#>
#> -----------------------------------------------------------------
#> p-value : 0.5541
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Expected cell frequencies : NOTE (all cells >= 5 (Chi-square would also be valid))
#> Sample independence : NOTE (assumed from study design, not testable from data)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is not statistically significant (p = 0.5541 > alpha 0.05).
#> There is insufficient evidence of an association between the two variables.
#>
#> WARNING: The contingency table is larger than 2x2. Fisher's Exact Test may require simulation or approximation methods, which can increase computation time and reduce exactness. Interpret results with caution. If simulate.p.value = TRUE was used, explicitly state this in your report.
#>
#> NOTE: All expected frequencies exceed 5. A Chi-square test would also be appropriate and may be preferred for larger samples. Consider using chisq_interpret().
#> -----------------------------------------------------------------Test whether there is a significant difference in paired proportions between two related measurements:
pre_pass <- sample(c("Yes","No"), 90, replace = TRUE,
prob = c(0.4, 0.6))
post_pass <- sample(c("Yes","No"), 90, replace = TRUE,
prob = c(0.7, 0.3))
result <- mcnemar_interpret(pre_pass, post_pass)
print(result)
#>
#> statease McNemar's Test Report --------------------------------
#> N : 90
#> Table size : 2 x 2
#> Discordant : 56 pairs
#> -----------------------------------------------------------------
#> Contingency Table:
#> y
#> x No Yes
#> No 12 43
#> Yes 13 22
#>
#> -----------------------------------------------------------------
#> p-value : 0.0001
#> Matched OR : 3.308
#> 95% CI : [1.779, 6.151]
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Discordant pairs (b+c) : PASSED (n = 56, adequate)
#> Sample independence : NOTE (assumed from study design, not testable from data)
#>
#> NOTE: Assumption checks are diagnostic tools and may be
#> influenced by sample size and other characteristics of the
#> data. Passing a check does not prove that an assumption is
#> satisfied, and a warning does not automatically invalidate
#> the analysis. Interpret these results alongside your
#> knowledge of the data.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is statistically significant (p = 0.0001 < alpha 0.05).
#> There is evidence of a significant difference in paired proportions between the two measurements.
#> Matched OR = 3.308: More subjects changed from the first category to the second category than vice versa.
#> 95% CI [1.779, 6.151] excludes 1: Evidence of a significant difference in paired proportions between measurements.
#>
#> WARNING: McNemar's Test assumes that observations are paired and independent across pairs. Violation of this assumption may affect the validity of the results.
#>
#> NOTE: McNemar's Test requires paired or matched data. Ensure that each row in your data represents the same subject measured twice or a matched pair.
#> -----------------------------------------------------------------Non-parametric alternative to repeated measures ANOVA:
friedman_data <- data.frame(
score = c(23,45,12,67,34,89,56,43,78,90,11,34),
time = rep(c("T1","T2","T3"), each = 4),
subject = rep(1:4, times = 3)
)
result <- friedman_interpret(score ~ time | subject,
data = friedman_data)
#> Warning in friedman_interpret(score ~ time | subject, data = friedman_data):
#> The Friedman Test may have low statistical power with very small sample sizes.
#> Interpret non-significant results with caution.
print(result)
#>
#> -- statease Friedman Test Report -------------------------------
#> Outcome : score
#> Time/Group : time (3 levels)
#> Subjects : subject (n = 4)
#> -----------------------------------------------------------------
#> Group Medians (descriptive only):
#> T1 : 34.00
#> T2 : 49.50
#> T3 : 56.00
#> -----------------------------------------------------------------
#> Chi-square : 0.500
#> df : 2
#> p-value : 0.7788
#> Kendall's W : 0.0625 (negligible effect)
#> -----------------------------------------------------------------
#> Assumption Checks:
#> Sample size (subjects) : NOTE (n = 4)
#> Independence of blocks : NOTE (assumed from study design, not testable from data)
#>
#> NOTE: These are contextual notes rather than pass/fail checks.
#> They describe aspects of the data and test method relevant to
#> interpretation, but are not automatically verifiable by the
#> package.
#> -----------------------------------------------------------------
#> Interpretation:
#> The result is not statistically significant (p = 0.7788 > alpha 0.05).
#> There is insufficient evidence of a significant difference in ranks across the related groups or repeated measurements.
#>
#> NOTE: Medians are reported for descriptive purposes only.
#> The Friedman Test assesses whether rank distributions
#> differ across groups and does not directly test for
#> differences in medians.
#>
#> Post-hoc tests not run (overall result not significant).
#>
#> NOTE: Normality assumption appears reasonable. If the assumptions of repeated measures ANOVA are met, consider using repeated measures ANOVA for greater statistical power.
#> -----------------------------------------------------------------Before running a test, check its assumptions automatically:
result <- check_assumptions(
"ttest",
x = males,
y = females
)
print(result)
#>
#> -- statease Assumption Check Report -------------------------------
#> Test : ttest
#> ---------------------------------------------------------------------
#>
#> [PASSED] Normality (x)
#> Shapiro-Wilk test: statistic = 0.950, p = 0.0502. Normality assumption appears satisfied.
#>
#> [PASSED] Sample size guidance (x)
#> n = 45. Sample size appears reasonable.
#>
#> [PASSED] Normality (y)
#> Shapiro-Wilk test: statistic = 0.963, p = 0.1561. Normality assumption appears satisfied.
#>
#> [PASSED] Sample size guidance (y)
#> n = 45. Sample size appears reasonable.
#>
#> [PASSED] Homogeneity of variance
#> Levene's Test: p = 0.8482. Variances appear approximately equal.
#>
#> ---------------------------------------------------------------------
#> NOTE: Assumption checks are based on statistical tests and
#> heuristics. They provide guidance but should not be
#> interpreted as definitive proof that assumptions are met
#> or violated.
#>
#> NOTE: Failure to reject an assumption test does not prove
#> that the assumption has been satisfied.
#>
#> NOTE: Visual inspection of residual plots is always
#> recommended alongside formal assumption tests.
#> ---------------------------------------------------------------------Determine the sample size needed to detect an effect:
result <- power_interpret(
"ttest.two",
effect_size = 0.5
)
print(result)
#>
#> -- statease Power Analysis Report
#> Test : Independent Samples T-Test
#> Mode : Calculate required sample size
#> -----------------------------------------------------------------
#> Effect size : 0.500 (medium)
#> Alpha : 0.05
#> Desired power: 0.80 (80%)
#> Required n : 64
#> Total N : 128 (2 groups x 64)
#> -----------------------------------------------------------------
#> Interpretation:
#> To detect a medium effect (effect size = 0.50) with 80% power at alpha = 0.05, you need at least 64 participants per group (128 total for 2 groups).
#>
#> NOTE: Power analysis results are estimates based on assumptions about effect size, alpha, and power. Actual results may differ depending on the true effect size in the population.
#> NOTE: Effect sizes should ideally be based on previous research, pilot studies, or theoretically justified values, not chosen arbitrarily to reduce required sample size.
#> NOTE: A power of 0.80 is a conventional minimum. In high stakes research such as clinical trials, a higher power of 0.90 or 0.95 is often recommended.
#> NOTE: Power analysis assumes that the chosen statistical test and its assumptions are appropriate for the data.
#> -----------------------------------------------------------------For users who prefer a point-and-click interface, statease includes a built-in Shiny app:
This launches an interactive web application where you can upload your data, select variables, and run any statease function without writing code.
| Test | Function | analyze() support |
|---|---|---|
| Descriptive stats | describe() |
✔ |
| Independent t-test | ttest_interpret() |
✔ |
| One-sample t-test | ttest_interpret() |
✔ |
| Paired t-test | ttest_interpret() |
✔ |
| One-way ANOVA | anova_interpret() |
✔ |
| Two-way ANOVA | anova2_interpret() |
✔ |
| MANOVA | manova_interpret() |
✔ |
| Chi-square | chisq_interpret() |
✔ |
| Correlation | cor_interpret() |
✔ |
| Simple regression | reg_interpret() |
✔ |
| Multiple regression | mlr_interpret() |
✔ |
| Logistic regression | logistic_interpret() |
✔ |
| Mann-Whitney U | mannwhitney_interpret() |
✔ |
| Wilcoxon Signed Rank | wilcoxon_interpret() |
✔ |
| Kruskal-Wallis | kruskal_interpret() |
✔ |
| Fisher’s Exact | fisher_interpret() |
✔ |
| McNemar’s Test | mcnemar_interpret() |
✔ |
| Friedman Test | friedman_interpret() |
✔ |
| Check Assumptions | check_assumptions() |
✔ |
| Power Analysis | power_interpret() |
✔ |
| P-value interpretation | interpret_p() |
- |