t-test in R Programming - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a t-test used for in statistics?

A t-test is used to compare the means of two groups to see if they are significantly different from each other.

beginner

What are the two main types of t-tests?

The two main types are: 1) Independent (two-sample) t-test, which compares means from two different groups, and 2) Paired t-test, which compares means from the same group at different times or conditions.

beginner

In R, which function is used to perform a t-test?

The function t.test() is used to perform a t-test in R.

beginner

What does the p-value from a t-test tell you?

The p-value tells you the probability that the observed difference between groups happened by chance. A small p-value (usually less than 0.05) means the difference is statistically significant.

beginner

How do you specify a paired t-test in R using t.test()?

You set the argument paired = TRUE inside t.test() to perform a paired t-test.

Which R function is used to perform a t-test?

A lm()

B t.test()

C summary()

D mean()

The t.test() function is specifically designed to perform t-tests in R.

What does a p-value less than 0.05 usually mean in a t-test?

A The difference between groups is statistically significant

B The sample size is too small

C The test was performed incorrectly

D The difference between groups is likely due to chance

A p-value less than 0.05 usually means the difference is statistically significant, not likely due to chance.

Which argument in t.test() makes it a paired t-test?

A type = 'paired'

B paired = FALSE

C paired = TRUE

D method = 'paired'

Setting paired = TRUE tells R to perform a paired t-test.

An independent t-test compares:

A Means from the same group at two times

B Variances of two groups

C Median values of two groups

D Means from two different groups

An independent t-test compares means from two different groups.

Which assumption is important for a t-test?

A Data should be normally distributed

B Data must be categorical

C Groups must have the same number of observations

D Data must be binary

A key assumption for t-tests is that the data in each group should be approximately normally distributed.

Explain what a t-test is and when you would use it.

Think about checking if two groups are really different or just by chance.

Describe how to perform a paired t-test in R and what it means.

Consider situations like measuring before and after treatment on the same people.

Practice

1.

What does a t-test primarily compare in two groups?

easy

A. The difference between their medians

B. The difference between their averages

C. The total number of observations

D. The variance of each group

Solution

1. Step 1: Understand the purpose of a t-test

   A t-test is used to compare the means (averages) of two groups to see if they are different.

2. Step 2: Identify what is compared

   The test focuses on the average values, not medians, counts, or variances.

3. Final Answer:

   The difference between their averages -> Option B

4. Quick Check:

   t-test compares means = A [OK]

Hint: Remember: t-test checks averages, not medians or counts [OK]

Common Mistakes:

• Confusing mean with median
• Thinking it compares counts
• Assuming it compares variances

2.

Which of the following is the correct way to run a t-test in R comparing two numeric vectors x and y?

easy

A. t_test(x, y)

B. ttest(x, y)

C. t.test(x, y)

D. test.t(x, y)

Solution

1. Step 1: Recall the correct function name in R

   The built-in function for t-test in R is t.test().

2. Step 2: Check the syntax for comparing two vectors

   Using t.test(x, y) compares the two numeric vectors correctly.

3. Final Answer:

   t.test(x, y) -> Option C

4. Quick Check:

   Correct function is t.test() = A [OK]

Hint: Use exact function name t.test() with dot [OK]

Common Mistakes:

• Misspelling the function name
• Using underscores instead of dots
• Confusing function with other test names

3.

What will be the output of this R code snippet?

group1 <- c(5, 7, 8, 6, 9)
group2 <- c(10, 12, 11, 13, 14)
test <- t.test(group1, group2)
round(test$p.value, 3)

medium

A. 0.001

B. 0.05

C. 0.5

D. 1.0

Solution

1. Step 1: Understand the data groups

   Group1 has smaller values around 5-9, Group2 has larger values around 10-14, so means differ.

2. Step 2: Interpret the p-value from t.test()

   Since the groups differ clearly, the p-value will be very small, close to 0.001 after rounding.

3. Final Answer:

   0.001 -> Option A

4. Quick Check:

   Distinct groups give low p-value = B [OK]

Hint: Big difference in groups means very small p-value [OK]

Common Mistakes:

• Assuming p-value is large for different groups
• Confusing p-value with test statistic
• Ignoring rounding in output

4.

Identify the error in this R code for a t-test:

data1 <- c(4, 5, 6)
data2 <- c(7, 8, 9)
test <- t.test(data1 + data2)

medium

A. t.test() cannot compare numeric vectors

B. Missing parentheses in t.test()

C. Vectors data1 and data2 must be data frames

D. Using '+' instead of ',' to separate vectors

Solution

1. Step 1: Check the function call syntax

   The t.test() function expects two separate vectors as arguments separated by a comma.

2. Step 2: Identify the mistake in argument passing

   The code uses '+' to add vectors instead of separating them with a comma, which is incorrect.

3. Final Answer:

   Using '+' instead of ',' to separate vectors -> Option D

4. Quick Check:

   Arguments must be comma-separated = D [OK]

Hint: Separate vectors with comma, not plus sign [OK]

Common Mistakes:

• Adding vectors instead of passing separately
• Confusing function arguments syntax
• Thinking t.test needs data frames

5.

You have two groups of exam scores: before and after a training program. Which t-test is best to check if the training improved scores?

hard

A. Paired t-test using t.test(before, after, paired=TRUE)

B. Two-sample t-test using t.test(before, after)

C. One-sample t-test using t.test(after)

D. Variance test using var.test(before, after)

Solution

1. Step 1: Understand the data relationship

   Scores are from the same students before and after training, so data are paired.

2. Step 2: Choose the correct t-test type

   A paired t-test compares matched pairs to see if scores changed after training.

3. Final Answer:

   Paired t-test using t.test(before, after, paired=TRUE) -> Option A

4. Quick Check:

   Paired data needs paired=TRUE = C [OK]

Hint: Use paired=TRUE for before-after same subjects [OK]

Common Mistakes:

• Using two-sample test for paired data
• Using one-sample test incorrectly
• Confusing variance test with t-test