SmartstatXL offers various types of Student's T-tests, including One-Sample T-test, Independent T-test, and Paired T-test. The Student's T-test is a statistical method used to determine if there is a significant difference between the averages of two groups. In this tutorial, we will discuss how to perform this analysis using SmartstatXL.
For the Independent T-test, which compares two mutually exclusive samples, we have two options, depending on how our dataset is arranged. If the data to be compared are in separate variable columns, we can select the Two-Sample Independent T-test (Between Variables). However, if the data to be compared are in the same column or variable, and the differentiators (categories, groups, or clusters) are in another column or variable, we can opt for the Two-Sample Independent T-test (Between Groups).
Before we proceed further, it's crucial to understand that the choice of Student's T-test type is highly dependent on the structure and characteristics of our data. Therefore, a good understanding of the data and the objectives of our analysis is essential. In this tutorial, we will discuss how to choose the appropriate type of Student's T-test based on our data and how to execute it using SmartstatXL.
One-Sample T-test
Steps for One-Sample T-test:
- Activate the worksheet (Sheet) that will be analyzed.
- Place the cursor on the dataset (for creating a dataset, see Data Preparation guide).
- If the active cell is not on the Dataset, SmartstatXL will automatically attempt to identify the Dataset.
- Activate the SmartstatXL Tab
- Click the T-Student Test Menu.
- SmartstatXL will display a dialog box to confirm whether the Dataset is correct (usually, the cell address for the Dataset is automatically selected correctly).
- If correct, click Next Button
- A subsequent dialog box will appear:
- In this example case, suppose we want to test whether the Bulk Density (BD) for the soil is the same as the general range for Andisols, which is 0.8 g/cm3, or different.
- Under the Type of Student's T-Test option, choose: One-Sample T-Test (with a standard value)
- In the Variable to be Tested box, choose BD (g/cm3)
- In the Text Box Test/Standard Value: Type 0.8
- Next, click the OK Button
One-Sample T-Test Analysis Results
The one-sample T-test is used to compare the average bulk density (BD) of a sample with a specific standard value, which is 0.8 g/cm3.
- The null hypothesis (H0) proposed is that the average BD is equal to 0.8 g/cm3,
- The alternative hypothesis (H1) states that the average BD is not equal to 0.8 g/cm3.
Based on the test results, the calculated t-value is -11.253. This value is far lower than the t-table value at the 5% significance level (2.040). In addition, the p-value obtained is 0.000, which is lower than 0.05. This indicates that the results are statistically significant.
The average BD in this sample is 0.450 g/cm3, which is much lower than the standard value of 0.8 g/cm3. Therefore, based on the t-test results, we have sufficient evidence to state that the average BD of the soil significantly differs from the standard value. Hence, we reject the null hypothesis (H0) and accept the alternative hypothesis (H1).
However, it should be noted that even though the results are statistically significant, the difference may also be practically significant depending on the context and purpose of the research. For example, if this research is conducted to determine the soil's suitability for agriculture, this difference may have important implications for soil productivity.
Independent Two-Sample T-Test (Between Levels/Groups)
Steps for Analysis of Independent Two-Sample T-Test (Between Levels/Groups)
- Activate the worksheet (Sheet) to be analyzed.
- Place the cursor on the dataset (for creating a dataset, see Data Preparation).
- If the active cell is not on the dataset, SmartstatXL will automatically try to determine the dataset.
- Activate the SmartstatXL Tab
- Click Menu T-Test.
- SmartstatXL will display a dialog box to confirm whether the dataset is correct or not.
- If correct, Click Next Button.
- A dialog box will appear as follows:
- In this example case, we want to examine whether the “Percentage of Sand” in the two soil types (Andesitic and Basaltic) differ or not. We will compare data in the same column, and the differentiator (Group/Category) is in another column, namely the “Type” variable. For this case, the T-test type is an independent two-sample T-test.
- Select the “Variable to be tested”: Sand
Data layout for comparison: Between Levels
Factor: Type
Comparison: can select all comparisons or between levels
Hypothesis: choose H0: μ1 ≠ μ2 - Press the Advanced Options button to specify the Levene’s test for homogeneity.
- After you have determined the Response Variable to be tested, press the OK button.
Independent Two-Sample T-Test Analysis Results
This analysis uses an independent T-test to compare the average sand content (SAND) between two types of soil, namely Andesitic and Basaltic.
- The null hypothesis (H0) in this analysis is that there is no difference in the average sand content between Andesitic and Basaltic soil (μ1 - μ2 = 0),
- The alternative hypothesis (H1) is that there is a difference in the average sand content between the two soil types (μ1 - μ2 ≠ 0).
Before conducting the T-test, the Levene's Test is performed to check the homogeneity of variances between the two groups. The Levene's Test shows a p-value of 0.187, which is greater than 0.05, so we can assume that the variances of both groups are homogeneous.
The t-value obtained from the T-test is 1.475, which is lower than the t-table value at the 5% significance level (2.042). Moreover, the p-value (0.151) is greater than 0.05, indicating that the results are not statistically significant.
Based on these findings, we do not have sufficient evidence to reject the null hypothesis (H0). This means that, based on the data we have, there is no significant difference in the average sand content between Andesitic and Basaltic soil.
Two-Sample Independent T-Test (Between Variables)
Consider the sample data arranged as follows:
The variables to be compared are located in two distinct columns.
Steps for Analysis in Two-Sample Independent T-Test (Between Variables)
- The procedure is the same as the previous Two-Sample Independent T-Test.
- In the Data Layout for Comparison option, select Between Variables
- Next, choose the variables to compare.
- Finally, click OK
Results of Two-Sample Independent T-Test (Between Variables)
The results are identical to the analysis conducted in the previous method.
Two-Sample Paired T-Test
The data layout for a paired t-test can be arranged in two layouts:
- The variables to be compared are located in different columns (Dataset on the left).
- The variables to be compared are located in the same column (Dataset on the right).
Steps for Analysis in Two-Sample Paired T-Test
Variables to be Compared are Located in Different Columns
- Here is an example case for the Paired T-Test: "A researcher wants to test the effect of a particular stimulus on blood pressure. They apply the stimulus to 15 patients. The research findings can be seen in the table below."
- For the Paired T-Test, the variables to be compared should be placed in separate columns, as per the layout of the above table.
- Proceed with the analysis as before, and in the t-test dialog box, follow the steps as seen in the image below:
- For the Type of Student's t-Test option, select Paired Sample t-Test
- In the Variables to Test box, select both variables to be tested (X1 and X2)
- Finally, click OK
Results of Two-Sample Paired T-Test
This analysis uses a paired T-Test to compare blood pressure before and after the administration of the stimulus.
- The null hypothesis (H0) in this analysis posits that there is no average difference in blood pressure before and after the stimulus (μd = 0).
- The alternative hypothesis (H1) suggests that there is an average difference in blood pressure before and after the stimulus (μd ≠ 0).
The t-score generated from the T-Test is -1.250, which is lower than the critical t-value at the 5% significance level (2.145). Moreover, the p-value (0.232) is greater than 0.05, indicating that the results are not statistically significant.
Based on these results, we do not have sufficient evidence to reject the null hypothesis (H0). This means that, based on the data at hand, there is no significant difference in average blood pressure before and after the stimulus.
