06 Paired Samples t-Tests in SPSS – SPSS for Beginners

Summary

This video from the RStats Institute at Missouri State University is the sixth in a series on SPSS for beginners, focusing on the paired samples t-test. It explains how to compare two related means, such as before-and-after measurements, using a within-subjects design. The video demonstrates the process in SPSS, including setting up the test, interpreting the output, and understanding the significance of the t-value and p-value. It also clarifies the concept of confidence intervals and the importance of accurate measurement despite the example's limitations.

Takeaways

• 📚 The video is part of a series on SPSS for Beginners by the RStats Institute at Missouri State University, focusing on comparing two means from the same sample in a within-subjects design.
• 🔍 The method demonstrated is the paired samples t-test, used to compare two related means, such as before and after measurements on the same group of subjects.
• 📈 The example provided involves a flawed comparison between height in inches and weight in pounds, illustrating the importance of using comparable measurement scales.
• 📊 To perform a paired samples t-test in SPSS, one must select the appropriate variables and follow the steps under Analyze -> Compare Means -> Paired Samples t-Test.
• 📝 The output of the test includes descriptive statistics, correlation coefficient, and inferential statistics, with the latter being the focus for determining statistical significance.
• 🔢 The t-value, degrees of freedom, and p-value are critical in the inferential statistics table to assess whether the means are significantly different.
• 🚫 A significant result is indicated by a t-value greater than the critical value from the t-distribution table, a p-value less than .05, and a confidence interval that does not cross zero.
• 🔄 The negative t-value signifies that the second group's mean is higher than the first, but the sign does not affect the interpretation of the results.
• 📉 The confidence interval provides a range where the mean difference is likely to fall 95% of the time, offering a more certain but less precise measure than the mean difference itself.
• 🔄 Reversing the order of variables in the t-test does not change the output significantly, except for the direction of the confidence interval and the sign of the t-value.
• 📝 For a proper application of the paired samples t-test, it is recommended to watch additional videos from the RStats Institute for a deeper understanding of statistical theory, test setup, result interpretation, and APA style reporting.

Q & A

What is the focus of the sixth video in the SPSS for Beginners series from the RStats Institute?

The focus of the sixth video is to demonstrate how to compare two means from two measurements of the same sample using a paired samples t-test in SPSS, which is also known as a within-subjects design or a repeated measures design.

What is a paired samples t-test used for in SPSS?

A paired samples t-test in SPSS is used to compare two related means, such as in a before-and-after design, where the same sample is measured twice under different conditions.

How is the data set in the video example structured for the paired samples t-test?

The data set in the video example has a single sample measured twice, which could be a before-and-after scenario or two different measurements of the same group, such as height and weight.

What is the fundamental flaw in comparing height and weight as demonstrated in the video?

The fundamental flaw in the example is that height is measured in inches and weight in pounds, which means two completely different measurement scales are being compared.

What is the correct approach to measure the effect of a calorie-restricted diet on weight?

The correct approach would be to measure the weight before starting the diet and then again six weeks later to see if there has been weight loss.

What are the steps to perform a paired samples t-test in SPSS according to the video?

The steps are to go to Analyze -> Compare Means -> Paired Samples t-Test, select the variables to compare, and then click OK to run the test.

What does the first table in the SPSS output of a paired samples t-test show?

The first table contains descriptive statistics for each variable, including the mean, sample size, standard deviation, and standard error of the mean.

Why is the correlation coefficient displayed in the output, even though it's not needed immediately?

The correlation coefficient is displayed because it will be used later when calculating the effect size, which provides additional insight into the strength of the relationship between the two variables.

How can you determine if the means from the paired samples t-test are statistically significantly different?

You can determine if the means are statistically significantly different by checking if the t-value is greater than the critical value from the Student's t Table, if the p-value is less than .05, or if the 95% confidence interval does not cross zero.

What does the negative t-value in the example indicate?

The negative t-value indicates that the second group (in this case, weight) had a higher mean than the first group (height). The sign of the t-value does not affect the interpretation of the results.

What is the purpose of a confidence interval in the context of a paired samples t-test?

A confidence interval provides a range in which the mean difference is likely to fall 95% of the time, indicating the level of certainty around the mean difference while accounting for potential variability in the data.

Outlines

00:00

📊 Paired Samples t-Test in SPSS

This segment of the video script from the RStats Institute introduces the concept of a within-subjects or paired samples design, where two related means are compared using a paired samples t-test in SPSS. The video uses a dataset from a previous video, focusing on a single sample measured twice, such as a before-and-after scenario. The example given involves comparing height and weight, despite the mismatch in measurement units, to demonstrate the test procedure. The script guides viewers through the steps in SPSS, from selecting the variables to interpreting the output, including descriptive statistics, correlation coefficient, and inferential statistics. The significance of the t-value, degrees of freedom, and p-value is explained, along with how to interpret the results in terms of statistical significance.

05:06

🔍 Understanding Confidence Intervals and t-Value Significance

The second paragraph delves deeper into the interpretation of the paired samples t-test results, emphasizing the concept of confidence intervals as a range where the mean difference is likely to fall 95% of the time. It contrasts the precision of the mean difference with the broader certainty of the confidence interval, highlighting the impact of good measurements and low variability on accuracy. The paragraph also addresses the t-value's negativity, explaining its implication that the second group has a higher mean than the first, and clarifies that the sign of the t-value is not crucial for interpretation but rather indicates the order of group entry. The script concludes with a practical demonstration of how changing the order of variables in the t-test affects the output, and it encourages viewers to explore additional resources from the RStats Institute for a comprehensive understanding of statistical theory, test setup, result interpretation, and APA style reporting.

Keywords

💡SPSS

SPSS stands for Statistical Package for the Social Sciences. It is a widely used software for statistical analysis in various fields, including social sciences, health sciences, and market research. In the context of the video, SPSS is the tool used to demonstrate how to compare two means from two measurements of the same sample, which is a fundamental aspect of statistical analysis.

💡within-subjects design

A within-subjects design, also known as a repeated measures design, involves measuring the same subjects under different conditions. This design is used to control for individual differences and is exemplified in the video by measuring a group of people before and after a treatment to observe changes. The video script uses this design to illustrate how to perform a paired samples t-test in SPSS.

💡paired samples t-test

The paired samples t-test is a statistical test used to compare the means of two related groups. It is particularly useful when the same sample is measured twice, such as in a before-and-after scenario. The video script explains how to conduct this test in SPSS, highlighting its application in comparing two related means.

💡descriptive statistics

Descriptive statistics summarize and describe the features of a data set. They include measures like mean, standard deviation, and sample size. In the video, descriptive statistics are presented in the output of the paired samples t-test to provide an overview of the data for each variable being compared.

💡correlation coefficient

The correlation coefficient is a statistical measure that expresses the extent to which two variables are linearly related. Although not the main focus of the video, the script mentions that the correlation coefficient is part of the SPSS output and will be used later for calculating the effect size, indicating the relationship between the two variables being compared.

💡inferential statistics

Inferential statistics are used to make inferences about a population based on a sample. The video script refers to inferential statistics when discussing the results of the paired samples t-test, which includes the t-value, degrees of freedom, and p-value, to determine if the means of the two samples are statistically significantly different.

💡t-value

The t-value is a calculated statistic used in hypothesis testing, specifically in t-tests. In the context of the video, the t-value is used to determine if there is a statistically significant difference between the means of two related samples. The script explains how to interpret the t-value in relation to a critical value from the Student's t-distribution table.

💡degrees of freedom

Degrees of freedom in statistics refer to the number of values in the data set that are free to vary when calculating an estimate. The video script mentions degrees of freedom in the context of the paired samples t-test, as it is part of the formula used to determine the critical value for the t-test.

💡p-value

The p-value is the probability that the observed difference between two groups could be due to chance. In the video, a p-value of .000 is mentioned, indicating a very low probability that the observed difference is not statistically significant. The script explains that a p-value less than .05 is typically considered significant.

💡confidence interval

A confidence interval provides a range of values within which the true population parameter is likely to fall with a certain level of confidence, typically 95%. The video script explains the concept of a confidence interval in relation to the mean difference between the two samples, illustrating how it reflects the precision and certainty of the estimate.

💡effect size

Effect size is a measure of the strength or magnitude of the relationship between variables in a study. Although not explicitly defined in the script, the correlation coefficient mentioned is used in calculating the effect size, which helps to understand the practical significance of the results beyond statistical significance.

Highlights

Introduction to the sixth video in the SPSS for Beginners series by the RStats Institute at Missouri State University.

Explanation of within-subjects design, repeated measures design, and paired samples design.

Demonstration of how to use a paired samples t-test to compare two related means in SPSS.

Use of a dataset created in the first video to illustrate the paired samples t-test.

Description of a before-and-after design in research projects, such as measuring a group before and after a treatment.

Example of comparing height and weight measurements in the dataset, despite different measurement scales.

Clarification of the importance of using scale variables for the paired-samples t-test in SPSS.

Guidance on navigating the SPSS interface to perform a paired samples t-test.

Presentation of descriptive statistics, including mean, sample size, standard deviation, and standard error of the mean.

Discussion of the correlation coefficient and its relevance to calculating effect size later.

Analysis of inferential statistics, focusing on the t-value, degrees of freedom, and p-value.

Interpretation of the t-value and p-value to determine if the means are statistically significantly different.

Explanation of the 95% confidence interval and its role in understanding the precision and accuracy of the mean difference.

Clarification on the meaning of a negative t-value and its interpretation.

Demonstration of how to reverse the order of variables in SPSS for a second paired samples t-test.

Illustration of how the sign of the t-value does not affect the interpretation of the results.

Emphasis on the importance of looking at actual means when interpreting findings from a paired samples t-test.

Recommendation to watch additional RStats Institute videos for further understanding of statistical theory and APA style writing.

Transcripts

This is the sixth video in SPSS for Beginners from the RStats Institute

at Missouri State University. In this video I'm going to show you how to

compare two means from two measurements of the same sample. This is called a

within-subjects design, a repeated measures design, or a paired samples

design. When we compare two related means with SPSS, we use a paired samples t-test.

So as before, we will use the data set that we created in the first video.

For this research project we have a single sample that we have measured

twice. You will often see this as a before-and-after design. You measure a

group of people, then you give them a treatment, and then you measure them

again a second time. If their scores on the post-test are higher than on the

pretest, you know that the treatment had in effect. Another time that we will have

paired measures is when we have two measurements of the same group. In our

data set, we measure the same people for both their height and their weight. Each

person has a pair of measures. Of course, there is a fundamental flaw in

this example, because height is measured in inches, and weight is measured in

pounds, so, I'm comparing two completely different measurement scales. A much

better example would be to have a before weight, and then put people on a calorie

restricted diet, and then six weeks later measure them again to see if they have

lost weight; however, in order to show you how to conduct this type of test in SPSS,

I'm going to go with this rather silly example, because these are the only two

scale variables that I have. We are going to use the

paired-samples t-test, which means we need to scale variables. So go to Analyze ->

-> Compare Means -> Paired Samples t-Test. Move over the variables that you want to

compare. We want to compare height to weight: our two scale level variables. And

when you're ready, click OK. The first table contains descriptive statistics

for each variable. It has the mean, a sample size, the standard deviation, and

the standard error of the mean for each variable. Below that, in the second

table, we see the correlation coefficient between the two variables. We do not

really need this output right now, but you will use the correlation coefficient

later, when we calculate the effect size. This third table has our inferential

statistics. This is what we want to look at right now. On the far right, we see

the t-value, the degrees of freedom, and the p-value that corresponds to a t-

score of 17.4 with 9 degrees of freedom. So as before, we want to know are

these means statistically significantly different? And we can answer that

question in three ways: first, is the t- value greater than a critical value that

we look up on Student's t Table? With 9 degrees of freedom, I looked up that

critical value; it was 2.262. This t-value of 17.4 is MUCH

larger than 2.262. I will tell you more about that negative

sign here in a minute. Second, is the p value less than .05? Our

p-value is .000, which is WAY less than .05.

Third, does the 95% confidence interval cross zero? It does not. Both the

upper and lower values are negative, so they are on the same side of zero.

Therefore, we conclude that these means ARE statistically significantly

different. But as I told you, that is really not particularly surprising,

because we are comparing inches and pounds. So let me say something more

about that confidence interval. What is that? A confidence interval is a range

in which the mean difference is likely to fall 95% of the time. You see, the mean

difference of -67.2 is very precise, but it is also very likely

to be wrong. If we drew another sample and tested it, most likely, the mean

difference would be slightly different than -67.2. On the

other hand, if I repeated this study 100 times, 95% of the time, the mean

difference would be between -75.9 and -58.4. So, the

mean is precise, but wrong. The confidence interval is much more certain, but also

less precise. However, with good measurements and low variability, we can

get both the mean and the confidence intervals as accurate as possible. I also

want to point out something about that t- value.

Notice that the t is negative. All that means is that the second group had a

higher mean than the first group. You interpret a positive t-value exactly the

same way as you interpret a negative t- value. Let me show you. Go to Analyze ->

-> Compare Means -> Paired Samples t-test. See that we have a space to do a second

t-test? Let's move over the height and weight variables, but this time in the

opposite order. Click OK. When we examine the output,

we see two t-tests. Notice that all of the output is exactly the same, except in

places where it is just reversed, such as with this confidence interval. In one

case, the t-value is negative, in the other case, it is positive. So, basically

you do not need to focus on whether the sign is positive or negative, because the

sign simply tells us which group was entered first or second. You SHOULD look

at the actual means when you interpret these findings. And that is how we do a

paired samples t-test in SPSS. When you are ready to do your paired samples

t-test for real, check out these other videos from RStats Institute, that

will teach you more about statistical theory, setting up the test, interpreting

the results, and writing up your findings in APA style.