06 Paired Samples t-Tests in SPSS – SPSS for Beginners
Summary
TLDRThis 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
📊 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.
🔍 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.
Mindmap
Keywords
💡SPSS
💡within-subjects design
💡paired samples t-test
💡descriptive statistics
💡correlation coefficient
💡inferential statistics
💡t-value
💡degrees of freedom
💡p-value
💡confidence interval
💡effect size
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.
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