05 One-Sample t-Tests in SPSS – SPSS for Beginners

Summary

This video from the RStats Institute at Missouri State University teaches how to perform a one-sample t-test in SPSS. The tutorial focuses on comparing a sample mean, such as height, to a known population mean, like the national average. It guides viewers through the process of setting up the test, interpreting the output including t-value, p-value, and confidence intervals, and concludes that the sample mean is not significantly different from the population mean. The video also highlights the importance of statistical significance and provides tips for further learning.

Takeaways

• 📚 The video is part of a SPSS for Beginners series by RStats Institute at Missouri State University.
• 📈 The tutorial focuses on how to perform a one sample t-test to compare a sample mean to a known population mean.
• 🔍 The example used is to determine if participants' height is different from the national average of 65 inches.
• 📝 The process involves using SPSS to calculate the sample mean and then compare it to the hypothesized population mean.
• 💻 The steps in SPSS include going to Analyze -> Compare Means -> One Sample t-Test and inputting the variable and test value.
• 📊 The output includes descriptive statistics like mean, standard deviation, and standard error of the mean.
• 📉 Inferential statistics are used to determine if the sample mean is significantly different from the known mean, indicated by the t-score, degrees of freedom, and p-value.
• 🔑 A p-value less than .05 is typically considered statistically significant, indicating the sample mean is different from the population mean.
• 📘 There are three methods to assess significance: comparing the t-value to a critical value from a t-table, examining the p-value, and checking if the confidence interval includes zero.
• 📌 In the example, the t-value, p-value, and confidence interval all suggest that the sample mean is not significantly different from the national average height.
• 🔍 The video concludes with the sample height not being different from the national average, demonstrating the practical application of a one sample t-test in SPSS.

Q & A

What is the main focus of the fifth video in the SPSS for Beginners series?

The main focus of the fifth video is to demonstrate how to perform a one sample t-test in SPSS to determine if two means are different.

What are the three types of T tests mentioned to be covered in the next three videos?

The specific types of T tests are not mentioned in the transcript, but it is stated that three kinds of T tests will be discussed using the same dataset created in the first video.

Why might someone be interested in comparing the height of a group to the national average?

One might be interested in such a comparison to determine if certain factors, such as a specific disorder, diet, or geographical location, have an effect on the height of individuals compared to the average American or a typical healthy person.

What is the purpose of the one sample t-test in the context of this video?

The purpose of the one sample t-test is to calculate the mean from a sample and compare it to a known population mean, in this case, to see if the sample's height is significantly different from the national average height.

How does one perform a one sample t-test in SPSS according to the video?

To perform a one sample t-test in SPSS, one should go to Analyze -> Compare Means -> One Sample t-Test, move the variable of interest into the Test Variables box, and set the hypothesized population mean in the Test Value box before clicking OK.

What are the two tables presented in the output window after conducting a one sample t-test?

The two tables in the output window are the descriptive statistics table, which includes mean, standard deviation, and standard error of the mean, and the inferential statistics table, which contains the t-score, degrees of freedom, and p-value.

What does the t-score represent in the context of a t-test?

The t-score represents the test statistic that indicates how far the sample mean is from the hypothesized population mean in terms of standard errors.

What is the typical cutoff for statistical significance in research?

The typical cutoff for statistical significance in research is a p-value of less than .05, indicating that the result is unlikely to have occurred by chance.

How does the confidence interval relate to the hypothesis test in a one sample t-test?

In a one sample t-test, if the 95% confidence interval includes zero, it suggests that the mean difference is not significantly different from zero, indicating that the sample mean is not significantly different from the population mean.

What does the video suggest about the height of the sample compared to the national average?

The video suggests that the sample's mean height of 65.8 inches is not significantly different from the national average of 65 inches based on the t-value, p-value, and confidence interval.

What additional resources are mentioned for learning more about one sample t-tests?

The video mentions other videos from the RStats Institute that will teach more about statistical theory, setting up the test, interpreting the results, and writing up findings in APA style.

Outlines

00:00

📊 Introduction to One Sample t-Test in SPSS

This paragraph introduces the fifth video in the SPSS for Beginners series by RStats Institute at Missouri State University. The video's focus is on demonstrating how to use a one sample t-test in SPSS to determine if two means are different. The presenter uses the example of comparing the height of a sample group to a known national average height. The process involves calculating the sample mean, comparing it to a hypothesized population mean, and using the one sample t-test for analysis. The video promises to cover the steps to perform the test, interpret the results, and understand the significance of the findings in the context of statistical analysis.

05:02

🔍 Conducting and Interpreting One Sample t-Test Results

The second paragraph details the steps to conduct a one sample t-test in SPSS. The presenter guides the viewers through the process of setting up the test by moving the variable 'Height' into the Test Variables box and setting a hypothesized population mean. Using the example of a known average height of 65 inches, the presenter explains how to interpret the output, which includes descriptive statistics and inferential statistics. The paragraph emphasizes the importance of looking at the t-score, degrees of freedom, and the p-value to determine if the sample mean is significantly different from the hypothesized mean. It also explains alternative methods of determining significance, such as comparing the t-value to a critical value from a Student's t-Table, using the p-value threshold of .05, and examining the 95% confidence interval. The example concludes with the finding that the sample mean is not significantly different from the national average, illustrating the practical application of the one sample t-test in SPSS.

Keywords

💡SPSS

SPSS, which stands for Statistical Package for the Social Sciences, is a software used for statistical analysis in various disciplines. In the video, SPSS is the primary tool used to demonstrate how to perform statistical tests, specifically the one sample t-test, to compare means.

💡Means

In statistics, the mean is the average value of a set of numbers. The video script discusses calculating means using SPSS and comparing them to determine if they are significantly different, which is central to the theme of the video.

💡One Sample t-test

A one sample t-test is a statistical test used to compare the mean of a sample to a known or hypothesized population mean. The video provides a step-by-step guide on how to perform this test in SPSS, which is a key concept in the script.

💡Variable

In the context of statistics and data analysis, a variable is a characteristic that can vary across observations. The script specifically mentions 'Height' as the variable of interest for the one sample t-test.

💡Hypothesized Population Mean

The hypothesized population mean is a value that is assumed for the mean of the entire population before any data is collected. In the script, it is set as 65 inches, which the sample mean is compared against.

💡Descriptive Statistics

Descriptive statistics summarize and describe the features of a data set. The script mentions the output of descriptive statistics in SPSS, such as mean, standard deviation, and standard error of the mean.

💡Inferential Statistics

Inferential statistics are used to make inferences about a population based on a sample. The script discusses inferential statistics in the context of the one sample t-test and its output, including the t-score and p-value.

💡t-Score

The t-score is a value calculated in a t-test that indicates the number of standard errors a sample mean is from the hypothesized mean. The script explains how to interpret the t-score in determining statistical significance.

💡Degrees of Freedom

In statistics, degrees of freedom are the number of values in the data set that are free to vary. The script mentions that the degrees of freedom for a t-test is n - 1, where n is the sample size.

💡p-Value

The p-value is a measure of the probability that the observed sample mean (or a more extreme value) would occur if the null hypothesis were true. The script explains that a p-value less than .05 is typically considered statistically significant.

💡Confidence Interval

A confidence interval is a range of values that is likely to contain the population parameter of interest. The script uses the 95% confidence interval to determine if the sample mean is significantly different from the hypothesized mean.

Highlights

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

Explanation of how to perform a one sample t-test in SPSS to compare sample means to a known mean.

Demonstration of selecting the 'Height' variable for analysis in SPSS.

Importance of comparing sample data to a national average or other relevant benchmarks.

Guidance on using the 'Analyze -> Compare Means -> One Sample t-Test' path in SPSS.

Instructions on moving the 'Height' variable into the Test Variables box in SPSS.

Setting the hypothesized population mean in the Test Value field.

Use of a hypothetical average height of 65 inches as a comparison value.

Description of the output window and the two tables it contains.

Explanation of descriptive statistics including mean, standard deviation, and standard error of the mean.

Details on inferential statistics and the significance of the t-score, degrees of freedom, and p-value.

Three methods to determine statistical significance: t-value comparison, p-value, and confidence interval.

How to find the critical value from the Student's t-Table based on degrees of freedom.

Interpretation of the t-value, p-value, and confidence interval to conclude if the sample mean is different from the known mean.

Example conclusion that the sample mean of 65.8 is not different from the national average of 65.

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

Transcripts

Welcome to the fifth video in SPSS for Beginners from RStats Institute at

Missouri State University. Earlier, we learned how to calculate means using

SPSS, so now I'm going to show you how we test whether two means are different

(or not) using a procedure called the one sample t-test. T tests are easy to do

in SPSS. In the next three videos, we will learn about three kinds of T tests. Each

of them will use the data set that we created in the first video. I'm

interested in the variable Height. Specifically, I want to know if my

participants are taller or shorter than the national average.

Perhaps we sampled these people from a certain country and we want to know how

they compare to the average American. Or perhaps they have a certain disorder and

I want to know how they compare to the typical average healthy person. Or

perhaps these are children who grew up eating a certain diet and I want to know

if that diet affected their height compared to an average child. So what I

have is one group of people whom I have measured one time. I want SPSS to

calculate the mean from my sample and then compare that sample mean to another

known mean. And to do this, I'm going to use a one sample t-test.

Go to Analyze -> Compare Means -> One Sample t-Test. A window pops up just like we

have seen before. We will move our variable Height into the Test Variables

box. We can do that with the arrow or just by dragging it over. And then we

need to set our hypothesized population mean in this box - labeled Test Value.

So imagine that we went to the scientific literature and we read that other people,

similar to this sample, have an average height of 65 inches tall.

I want SPSS to calculate this sample mean and then compare it to the known

value of 65. So, click OK. The output window will pop up and you will see two

tables. The first table contains our descriptive statistics, just like we've

calculated before. We see the mean, standard deviation, and something called

the standard error of the mean. The second table contains our inferential

statistics, and this is where we find out if the mean of our sample is

significantly different from 65, or not. We have the t-score right here, the

degrees of freedom (which is n - 1) the number of scores minus 1, and finally

the p-value that corresponds to this t-score at this degrees of freedom. In the

box "Sig. (2-tailed)." There are three ways that we can determine if one mean

is statistically significantly different from another mean. The first is by

looking at the t-value. We would go to a table called "Students t-Table" and look

up a Critical Value. If the T value is larger than the

critical value from that table, then the means are different. A second way is to

look at the p-value. Typically, scientists and researchers use p < .05 as

the cutoff for statistical significance, where any values .05 or

less are said to be "statistically significant." A third way of determining

significance is to look at the confidence interval. We are testing a

hypothesis that the mean difference was 0. So if the 95% confidence interval

includes 0, then the means are NOT different. So, I looked up the critical

value on Students t-Table and I found that for a test with 9 degrees of

freedom, the critical value is 2.262. This t value is smaller than

2.262. I can see that the p-value is .318, which

is larger than .05. And finally, I can see that the lower

confidence interval is negative but the upper value is positive, so this

confidence interval crosses zero. These three findings all tell us the

same thing: the mean of our sample 65.8 is NOT different than

the national average of 65. Our sample was pretty much the same height as our

comparison group. And that is how you do a one sample t-test in SPSS. When you are

ready to do a real one sample t-test, 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.