Israel Arevalo 9/22/22
- Before we start
- T-Tests - What are they and how can we use them?
- Generating our Dataset
- Exploring our Data
- Conducting T-Test
- Interpreting the Results
- Conclusion
This guide was designed as a friendly approach to learn how to conduct statistical analysis within the R environment. R is a powerful open-source tool that allows for great flexibility and customization of when conducting data wrangling (cleaning), analysis, interpretation, and reporting. Did I mention its open-source? This not only means that it is free, but the entire code used to develop this exceptional language is entirely available for you to view (and even suggest changes) online.
Several assumptions about the user will be made within this guide.
- You have installed R and an IDE such as RStudio on your computer
- You have a dataset to work with (preferably in .csv format)
If these assumptions are not met, here are a few guides to reference that will get you up to speed
- Installing RStudio
- Exporting SPSS dataset to .csv
- Exporting STATA dataset to .csv
- Exporting Excel file to .csv
T-Tests are among one of the most popular, albeit basic, statistical analysis out there. In a nutshell, T-Tests provide an insight into mean group differences of two variables. A limitation within the T-Test is that it only allows the comparison of two groups - anything larger than two would require approaches such as an ANOVA (discussed in other guides). This guide is far from a lecture on T-Tests and their use. If you would like to learn more about T-Tests here is a useful guide T-Test Introduction. Below is a short scenario to provide you context for the remainder of the tutorial.
As a brief example of a T-Test, let’s say you have two classroom teachers that are implementing different reading interventions in their classrooms (Intervention A and Intervention B). After a 6-week implementation period, the teachers want to know whether there was a significant difference in the students’ performance between each class. In other words, did the students in Classroom A (who received Intervention A) differ in mean reading performance scores compared to Classroom B (who received Intervention B)? Assuming all students started at the exact same average performance in reading, and only one measure was used to determine student reading performance scores (post-intervention), we can use a T-Test to compare whether there is a significant difference in the mean scores between the students in Classroom A and Classroom B.
Note
The above scenario is fictitious and may not be the best way to approach the investigation of an intervention’s efficacy. This scenario is only to give you context for the code we will discuss below.
Using randomly-generated data, let’s build a fictitious dataset to math the scenario above and that we will use to run our T-Test.
Warning
This step is only required for the instructional nature of this tutorial. You will not need to run this step as you do not need to randomly generate your data.
In the code block below, we will generate an array consisting of test scores from students (rows) who received intervention A and B (columns). Since we are taking quite the creative freedoms here, let’s also assume that all students score at least a 60 or above with the max possible score of 100. Let’s also assume that we had an equal amount of students in each classroom (n = 25).
# A seed allows us to pull in the same randomly generated numbers each time we run this command. If we don't set a seed, we will generate different numbers each time we run this command
set.seed(123)
# This command randomly generates a sample of 25 scores between 60-100 for each intervention group (a, b)
intervention_a <- sample(60:100, size = 25)
intervention_b <- sample(60:100, size = 25)
#making the dataframe (combining the two variables into one array) - we will call it "df"
df = (rbind(intervention_a, intervention_b))
#Transpose Dataframe
df <- t(df)
#Display first 6 rows in our data
head(df) intervention_a intervention_b
[1,] 90 98
[2,] 74 71
[3,] 73 74
[4,] 62 91
[5,] 96 66
[6,] 98 68
Let’s take a look at simple descriptive statisitcs within our data.
Running the base (summary) command allows us to look at information such
as the minimum, maximum, quartiles, median, and means for each variable
within our dataset. You can further customize this command by adding
further adjustments to the command itself. For example, if we want to
run a summary command on just 1 or 2 variables within a dataset
containing many other variables, we can adjust our code to specify which
variables we are interested in by adding a $ symbol after the name of
the dataset and then specifying the name of the variable (i.e.,
summary(df$intervention_a). Below we have run a simple summary
command to explore our generated dataset. Since we only generated two
variables, we do not need to specify which variables we are interested
in.
summary(df) intervention_a intervention_b
Min. :62.00 Min. : 60.00
1st Qu.:69.00 1st Qu.: 68.00
Median :85.00 Median : 80.00
Mean :81.48 Mean : 79.84
3rd Qu.:92.00 3rd Qu.: 91.00
Max. :98.00 Max. :100.00
Based on our summary output, we can see that students that received the reading intervention A have a higher mean average score on their post-intervention reading task when compared to those students that received reading intervention b.
To determine whether this difference is statistically significant, we will proceed in conducing our T-Test.
R allows us to run our analysis with only one line of code. Below is a
code block that demonstrates the code that we used to run our T-Test.
The function that we use to call the T-Test formula is called
t.test. After this function we have an open/close parenthesis. Within
these parenthesis, we place our two groups intervention_a and
intervention_b.
That’s it! We have successfully conducted a simple T-Test using our
variables of interest. In the next section, we will be interpreting the
output that our t.test function generated.
t.test(intervention_a, intervention_b) Welch Two Sample t-test
data: intervention_a and intervention_b
t = 0.45657, df = 47.731, p-value = 0.6501
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-5.583308 8.863308
sample estimates:
mean of x mean of y
81.48 79.84
When we conduct a hypothesis test, we want to establish our Null Hypothesis and our Alternative Hypothesis. When conducting T-Tests, our Null Hypothesis (H0) is often reported as H0 = Mu1 = Mu2 - in other words, the mean of group 1 are equal to the mean of group 2 (in its most simplist form). Alternatively (no pun intended), our alternative hypothesis (H1) states that H1 = Mu1 != Mu2 - in other words, the mean of group 1 is not equal to the mean of group 2.
To test whether we reject or fail to reject our null hypothesis, we take a look at our T-Test results above.
Now, let’s take a look at our T-Test output. We can see that we have a
t-value of 0.457, degrees of freedom of 47.731 and a significant
value (p-value) of 0.65. Based on these results, we would fail to
reject our null hypothesis and conclude that based on our data,
studentss’ scores did not vary by a statistically significant amount
regardless of which reading intervention they received. In other words,
the mean differences between intervention_a and intervention_b did
not vary by a statistically significant amount.
If you followed along, you can see that running a simple T-Test within the R environment is something that can be done quickly once your data is cleaned and organized. R provides the flexibility to manipulate and transform your data in an efficient and reproducible way. If you haven’t already, try copying and pasting these codes into your R environment and play with the variables. Also, consider saving your script/rmarkdown file for later use as this may significantly increase your research workflow.