Data Analysis

Statistical data analysis from descriptive to inferential, covers the univariate and multivariate analysis of the data, exploratory analysis, and visualization of the data

How to Do a T-Test in R

by

Master essential R functions for statistical testing. Learn how to perform correlation, covariance, and t-test in R (One-Sample, Independent, Paired) in R. Perfect for data analysts, students, and job test preparation with practical code examples.

How can one compute correlation and covariances in R?

Computing correlations and covariances is a fundamental task in R, and the language provides several straightforward and powerful ways to do it. One can compute the correlation by using cor() function and cov() function to compute the covariance.

What are the different methods for computing correlation in R?

The cor() function allows you to choose the calculation method. The most common are:

  • "pearson": Standard correlation coefficient for linear relationships. Assumes data is normally distributed. It is the default method for computing Pearson’s Correlation Coefficient.
  • "spearman": Spearman’s rank correlation. A non-parametric method based on ranks, good for monotonic (consistently increasing or decreasing, but not necessarily linear) relationships.
  • "kendall": Kendall’s rank correlation. Another non-parametric method, often used for small data sets or when many tied ranks exist.

Explain how t-test is performed in R?

In R, the t.test() function produces a variety of t-tests. The t-test is the most common test in statistics and is used to determine whether the means of two groups are equal to each other.

The primary function for all t-tests in R is t.test(). Its usage changes slightly depending on the type of test you want to perform (one-sample, independent two-sample, or paired).

One-Sample T-Test

To determine if the mean of a single sample is significantly different from a known or hypothesized population mean. The general syntax of the t-test in R is

t.test(x, mu = hypothesized_mean, alternative = "two.sided")

The description of the argument are:

  • x: A numeric vector of data.
  • mu: The hypothesized true population mean.
  • alternative: The alternative hypothesis. Can be "two.sided", "less", or "greater".

Independent Two-Sample T-Test

To compare the means of two independent groups to see if they are significantly different from each other. The general syntax of the two-sample t-test is

t.test(x, y, alternative = "two.sided", var.equal = FALSE)

The description of the important argument is:

  • x: A numeric vector of data for group 1.
  • y: A numeric vector of data for group 2.
  • var.equal: A crucial argument.
    • var.equal = FALSE: Uses the Welch’s t-test, which does not assume the two groups have equal variances. This is the recommended and safer choice in most real-world situations. It is the default argument value.
    • var.equal = TRUE: Uses the Student’s classic t-test, which does assume equal variances.

The two-sample t-test can be computed by using t.test() function in formula format

t.test(numeric_variable ~ group_variable, data = my_data, ...)

Paired T-Test

To compare the means of the same group at two different times (e.g., before and after a treatment). The data is “paired” because each subject is measured twice. The general syntax for the paired sample t-test is

t.test(x, y, paired = TRUE, alternative = "two.sided")

What are the output objects of t.test() the function, and how can these be extracted?

The t.test() function returns a list object containing all the results. You can store it and extract specific values for reporting.

my_test <- t.test(mtcars$mpg, mu = 15)
How to Do a T-Test in R Language

One can extract specific values from t.test() function.

  • my_test$statistic # t-value
  • my_test$parameter # degrees of freedom (df)
  • my_test$p.value # p-value
  • my_test$estimate # estimated mean (or means)
  • my_test$conf.int # confidence interval

One can print a clean summary of objects

cat("t(", my_test$parameter, ") = ", round(my_test$statistic, 2), ", p = ", format.pval(my_test$p.value, digits=2), sep = "")

Perform Correlation Analysis

Perform Testing of Hypothesis

The glm Function in R

by

Learn about the glm function in R with this comprehensive Q&A guide. Understand logistic regression, Poisson regression, syntax, families, key components, use cases, model diagnostics, and goodness of fit. Includes a practical example for logistic regression using glm() function in R.

What is the glm function in the R language?

The glm (Generalized Linear Models) function in R is a powerful tool for fitting linear models to data where the response variable may have a non-normal distribution. It extends the capabilities of traditional linear regression to handle various types of response variables through the use of link functions and exponential family distributions.

Since the distribution of the response depends on the stimulus variables through a single linear function only, the same mechanism as was used for linear models can still be used to specify the linear part of a generalized model.

What is Logistic Regression?

Logistic regression is used to predict the binary outcome from the given set of continuous predictor variables.

What is the Poisson Regression?

The Poisson regression is used to predict the outcome variable, which represents counts from the given set of continuous predictor variables.

What is the general syntax of the glm function in R Language?

The general syntax to fit a Generalized Linear Model is glm() function in R is:

glm(formula, family = gaussian, data, weights, subset, na.action, start = NULL,
    etastart, mustart, offset, control = list(...), model = TRUE, method = "glm.fit",
    x = FALSE, y = TRUE, contrasts = NULL, ...)

What are families in R?

The class of Generalized Linear Models handled by facilities supplied in R includes Gaussian, Binomial, Poisson, Inverse Gaussian, and Gamma response distributions, and also quasi-likelihood models where the response distribution is not explicitly specified. In the latter case, the variance function must be specified as a function of the mean, but in other cases, this function is implied by the response distribution.

Write about the Key components of glm Function in R

Formula

It specifies the relationship between variables, similar to lm(). For example,

y ~ x1 + x2 + x3  # main effects
y ~ x1*x2         # main effects plus interaction
y ~ .

Family

It defines the error distribution and link function. The Common families are:

  • gaussian(): Normal distribution (default)
  • binomial(): Logistic regression (binary outcomes)
  • poisson(): Poisson regression (count data)
  • Gamma(): Gamma regression
  • inverse.gaussian(): Inverse Gaussian distribution

What are the common use cases of glm() function?

Each family has link functions (e.g., logit for binomial, log for Poisson).

Logistic Regression (Binary Outcomes

model <- glm(outcome ~ predictor1 + predictor2, family = binomial(link = "logit"),
             data = mydata)

Poisson Regression (Count Data)

model <- glm(count ~ treatment + offset(log(exposure)), family = poisson(link = "log"),
             data = count_data)

What statistics can be computed after fitting glm() model?

After fitting a model, one can use:

summary(model)   # Detailed output including coefficients
coef(model)      # Model coefficients
confint(model)   # Confidence intervals
predict(model)   # Predicted values

What are model diagnostics and goodness-of-fit?

The following are built-in glm() model diagnostics and goodness of fit:

anova(model, test = "Chisq")  # Analysis of deviance
residuals(model)              # Various residual types available
plot(model)                   # Diagnostic plots

Give an example of logistic regression fitting using glm() function.

Consider the mtcars data set, where am is the response variable

# Fit model
data(mtcars)
model <- glm(am ~ hp + wt, family = binomial, data = mtcars)

# View results
summary(model)

# Predict probabilities
predict(model, type = "response")

# Plot
par(mfrow = c(2, 2))
plot(model)
glm() Function in R Language

Tips for effective Use of glm() function?

  1. Always check model assumptions and diagnostics
  2. For binomial models, the response can be:
    • A factor (first level = failure, others = success)
    • A numeric vector of 0/1 values
    • A two-column matrix of successes/failures
  3. Use drop1() or add1() for model selection
  4. Consider glm.nb() from the MASS package for overdispersed count data

The glm() function in R is fundamental for many statistical analyses in R, providing flexibility to handle various types of response variables beyond normal distributions.

Try Pedagogy Quizzes

Use of Important Functions in R

by

Looking for the most important functions in R? This blog post answers key questions like creating frequency tables (table()), redirecting output (sink()), transposing data, calculating standard deviation, performing t-tests, ANOVA, and more. Perfect for R beginners and data analysts!

  • Important functions in R
  • R programming cheat sheet
  • Frequency table in R (table())
  • How to use sink() in R
  • Transpose data in R (t())
  • Standard deviation in R (sd())
  • T-test, ANOVA, and Shapiro-Wilk test in R
  • Correlation and covariance in R
  • Scatterplot matrices (pairs())
  • Diagnostic plots in R

This Important functions in R, Q&A-style guide covers essential R functions with clear examples, helping you master data manipulation, statistical tests, and visualization in R. Whether you’re a beginner or an intermediate user, this post will strengthen your R programming skills!

Which function is used to create a frequency table in R?

In R, a frequency table can be created by using table() function.

What is the use of sink() function?

The sink() function in R is used to redirect R output (such as the results of computations, printed messages, or console output) to a file instead of displaying it in the console. This is particularly useful for saving logs, results of analyses, or any other text output generated by R scripts.

Explain what transpose is and how it is performed.

Transpose is used for reshaping the data, which is used for analysis. Transpose is performed by t() function.

What is the length function in R?

The length() function in R gets or sets the length of a vector (list) or other objects. The length() function can be used for all R objects. For an environment, it returns the object number in it. NULL returns 0.

What is the difference between seq(4) and seq_along(4)?

seq(4) means vector from 1 to 4 (c(1,2,3,4)) whereas seq_along(4) means a vector of the length(4) or 1 (c(1)).

Vector $v$ is c(1,2,3,4) and list $x$ is list(5:8). What is the output of v*x[[1]]?

[1] 5 12 21 32s

Important functions in R Language

How do you get the standard deviation for a vector $x$?

sd(x, na.rm=TRUE)

$X$ is the vector c(5,9.2,3,8.51,NA). What is the output of mean(x)?

The output will be NA.

Important function in R Programming

How can one compute correlation and covariance in R?

Correlation is produced by cor() and covariance is produced by cov() function.

How to create scatterplot matrices?

pair() or splom() function are used to create scatterplot matrices.

What is the use of diagnostic plots?

It is used to check the normality, heteroscedasticity, and influential observations.

What is principal() function?

It is defined in the psych package that is used to rotate and extract the principal components.

Define mshapiro.test()?

It is a function which defined in the mvnormtest package. It produces the Shapiro-Wilk test for multivariate normality.

Define barlett.test().

The barlett.test() is used to provide a parametric k-sample test of the equality of variances.

Define anova() function.

The anova() is used to compare the nested models. Read more One-Way ANOVA

Define plotmeans().

It is defined under the gplots package, which includes confidence intervals, and it produces a mean plot for single factors.

Define loglm() function.

The loglm() function is used to create log-linear models.

What is t-tests() in R?

We use it to determine whether the means of two groups are equal or not by using t.test() function.

Statistics and Data Analysis