How to Read Data From a T Test Using Spss

Using SPSS for t Tests

This tutorial volition show you how to apply SPSS version 12.0 to perform one-sample t-tests, independent samples t-tests, and paired samples t-tests.

This tutorial assumes that yous accept:

• Downloaded the standard grade data gear up (click on the link and save the data file)
• Started SPSS (click on Start | Programs | SPSS for Windows | SPSS 12.0 for Windows)

One Sample t-Tests

1 sample t-tests can be used to determine if the mean of a sample is unlike from a item value. In this example, nosotros will decide if the hateful number of older siblings that the PSY 216 students have is greater than 1.

Nosotros will follow our customary steps:

1. Write the cipher and alternative hypotheses kickoff:
   H₀: µ_{216 Students} ≤ 1
   H₁: µ_{216 Students} > ane
   Where µ is the hateful number of older siblings that the PSY 216 students have.
2. Determine if this is a one-tailed or a 2-tailed exam. Because the hypothesis involves the phrase "greater than", this must be a one tailed examination.
3. Specify the α level: α = .05
4. Determine the appropriate statistical test. The variable of interest, older, is on a ratio scale, so a z-score examination or a t-test might be appropriate. Because the population standard deviation is non known, the z-test would be inappropriate. We will utilize the t-test instead.
5. Calculate the t value, or permit SPSS do it for you!

   The command for a one sample t tests is plant at Clarify | Compare Means | One-Sample T Test (this is shorthand for clicking on the Clarify bill of fare detail at the meridian of the window, and then clicking on Compare Means from the drop down carte, and Ane-Sample T Test from the popular up carte.):
   
   

   The 1-Sample t Test dialog box will appear:
   
   

   Select the dependent variable(southward) that you want to exam by clicking on information technology in the left manus pane of the One-Sample t Exam dialog box. And so click on the pointer push button to move the variable into the Test Variable(s) pane. In this case, motion the Older variable (number of older siblings) into the Exam Variables box:
   
   

   Click in the Test Value box and enter the value that you will compare to. In this example, we are comparing if the number of older siblings is greater than 1, so we should enter one into the Exam Value box:
   
   

   Click on the OK button to perform the ane-sample t test. The output viewer will appear. There are two parts to the output. The start part gives descriptive statistics for the variables that y'all moved into the Test Variable(s) box on the One-Sample t Test dialog box. In this example, nosotros get descriptive statistics for the Older variable:
   
   

   This output tells united states of america that we have 46 observations (N), the mean number of older siblings is 1.26 and the standard deviation of the number of older siblings is ane.255. The standard fault of the mean (the standard deviation of the sampling distribution of ways) is 0.185 (i.255 / square root of 46 = 0.185).

   The 2d part of the output gives the value of the statistical test:
   
   

   The second column of the output gives us the t-test value: (1.26 - 1) / (1.255 / foursquare root of 46) = 1.410 [if y'all exercise the adding, the values will not match exactly considering of round-off fault). The tertiary column tells united states of america that this t test has 45 degrees of freedom (46 - one = 45). The fourth column tells us the two-tailed significance (the two-tailed p value.) But nosotros didn't desire a two-tailed test; our hypothesis is i tailed and there is no selection to specify a one-tailed test. Because this is a one-tailed test, wait in a table of critical t values to make up one's mind the critical t. The critical t with 45 degrees of freedom, α = .05 and one-tailed is i.679.

6. Determine if we can pass up the null hypothesis or non. The decision rule is: if the 1-tailed disquisitional t value is less than the observed t AND the means are in the correct lodge, then we can reject H₀. In this example, the disquisitional t is ane.679 (from the table of critical t values) and the observed t is 1.410, so we fail to turn down H₀. That is, at that place is insufficient bear witness to conclude that the mean number of older siblings for the PSY 216 classes is larger than 1.

If we were writing this for publication in an APA journal, we would write it every bit:
A t test failed to reveal a statistically reliable deviation between the mean number of older siblings that the PSY 216 form has (M = ane.26, due south = ane.26) and one, t(45) = 1.410, p < .05, α = .05.

Contained Samples t-Tests
Single Value Groups

When two samples are involved, the samples tin come from different individuals who are not matched (the samples are independent of each other.) Or the sample can come from the aforementioned individuals (the samples are paired with each other) and the samples are not independent of each other. A 3rd alternative is that the samples can come from different individuals who have been matched on a variable of interest; this type of sample volition not exist independent. The grade of the t-test is slightly unlike for the independent samples and dependent samples types of 2 sample tests, and SPSS has separate procedures for performing the 2 types of tests.

The Independent Samples t-examination can be used to run into if two ways are different from each other when the two samples that the means are based on were taken from different individuals who have not been matched. In this case, we will decide if the students in sections one and two of PSY 216 have a different number of older siblings.

Nosotros will follow our customary steps:

1. Write the nix and alternative hypotheses starting time:
   H₀: µ_{Section 1} = µ_{Section 2}
   H_i: µ_{Department i} ≠ µ_{Section ii}
   Where µ is the mean number of older siblings that the PSY 216 students take.
2. Determine if this is a ane-tailed or a two-tailed test. Because the hypothesis involves the phrase "different" and no ordering of the ways is specified, this must be a two tailed test.
3. Specify the α level: α = .05
4. Determine the advisable statistical test. The variable of involvement, older, is on a ratio calibration, so a z-score examination or a t-test might exist appropriate. Considering the population standard divergence is not known, the z-test would be inappropriate. Furthermore, in that location are different students in sections 1 and 2 of PSY 216, and they have non been matched. Considering of these factors, we will utilise the contained samples t-test.
5. Calculate the t value, or let SPSS do it for you!

   The control for the independent samples t tests is found at Clarify | Compare Ways | Contained-Samples T Test (this is shorthand for clicking on the Analyze menu item at the top of the window, and then clicking on Compare Ways from the driblet downward menu, and Independent-Samples T Test from the pop up card.):
   
   

   The Independent-Samples t Examination dialog box volition appear:
   
   

   Select the dependent variable(s) that you want to exam by clicking on it in the left hand pane of the Contained-Samples t Examination dialog box. So click on the upper pointer button to move the variable into the Exam Variable(due south) pane. In this case, movement the Older variable (number of older siblings) into the Test Variables box:
   
   

   Click on the contained variable (the variable that defines the two groups) in the left hand pane of the Independent-Samples t Test dialog box. So click on the lower arrow button to movement the variable in the Grouping Variable box. In this example, move the Section variable into the Group Variable box:
   
   

   You need to tell SPSS how to define the two groups. Click on the Define Groups button. The Define Groups dialog box appears:
   
   

   In the Group 1 text box, blazon in the value that determines the starting time grouping. In this example, the value of the 10 AM section is 10. And then you would type 10 in the Group ane text box. In the Group 2 text box, type the value that determines the second group. In this instance, the value of the 11 AM department is 11. And so you would type xi in the Group 2 text box:
   
   

   Click on the Go on button to close the Ascertain Groups dialog box. Click on the OK button in the Contained-Samples t Examination dialog box to perform the t-test. The output viewer will appear with the results of the t exam. The results have 2 principal parts: descriptive statistics and inferential statistics. First, the descriptive statistics:
   
   

   This gives the descriptive statistics for each of the two groups (every bit defined by the group variable.) In this instance, there are fourteen people in the 10 AM section (North), and they accept, on average, 0.86 older siblings, with a standard divergence of ane.027 older siblings. There are 32 people in the 11 AM section (Due north), and they have, on average, ane.44 older siblings, with a standard difference of 1.318 older siblings. The last cavalcade gives the standard error of the mean for each of the ii groups.

   The second part of the output gives the inferential statistics:
   
   

   The columns labeled "Levene's Test for Equality of Variances" tell u.s.a. whether an assumption of the t-test has been met. The t-test assumes that the variability of each group is approximately equal. If that supposition isn't met, then a special form of the t-exam should be used. Look at the column labeled "Sig." under the heading "Levene'south Exam for Equality of Variances". In this case, the significance (p value) of Levene's test is .203. If this value is less than or equal to your α level for the exam (unremarkably .05), then you tin reject the zero hypothesis that the variability of the 2 groups is equal, implying that the variances are unequal. If the p value is less than or equal to the α level, then you should use the bottom row of the output (the row labeled "Equal variances not assumed.") If the p value is greater than your α level, then you should use the middle row of the output (the row labeled "Equal variances assumed.") In this example, .203 is larger than α, so we will assume that the variances are equal and we will use the middle row of the output.

   The column labeled "t" gives the observed or summate t value. In this instance, assuming equal variances, the t value is 1.461. (We can ignore the sign of t for a ii tailed t-exam.) The cavalcade labeled "df" gives the degrees of liberty associated with the t test. In this instance, in that location are 44 degrees of freedom.

   The cavalcade labeled "Sig. (2-tailed)" gives the two-tailed p value associated with the test. In this example, the p value is .151. If this had been a one-tailed exam, we would need to look upwardly the critical t in a table.

6. Decide if we can reject H₀: As before, the determination rule is given past: If p ≤ α , then reject H₀. In this instance, .151 is non less than or equal to .05, and so we neglect to reject H₀. That implies that nosotros failed to observe a divergence in the number of older siblings betwixt the ii sections of this form.

If we were writing this for publication in an APA periodical, we would write it every bit:
A t test failed to reveal a statistically reliable difference between the mean number of older siblings that the ten AM section has (M = 0.86, s = 1.027) and that the xi AM department has (M = ane.44, s = ane.318), t(44) = 1.461, p = .151, α = .05.

Independent Samples t-Tests
Cutting Signal Groups

Sometimes y'all want to perform a t-test but the groups are defined by a variable that is not dichotomous (i.e., it has more than than ii values.) For example, you lot may want to meet if the number of older siblings is different for students who have higher GPAs than for students who have lower GPAs. Since there is no single value of GPA that specifies "higher" or "lower", we cannot proceed exactly as we did before. Before proceeding, decide which value you will use to divide the GPAs into the higher and lower groups. The median would be a practiced value, since half of the scores are above the median and half are below. (If you exercise not recollect how to calculate the median see the frequency command in the descriptive statistics tutorial.)

1. Write the nix and alternative hypotheses first:
   H₀: µ_{lower GPA} = µ_{higher GPA}
   H₁: µ_{lower GPA} ≠ µ_{College GPA}
   Where µ is the mean number of older siblings that the PSY 216 students have.
2. Determine if this is a 1-tailed or a ii-tailed test. Because the hypothesis involves the phrase "different" and no ordering of the means is specified, this must be a two tailed test.
3. Specify the α level: α = .05
4. Determine the appropriate statistical test. The variable of involvement, older, is on a ratio calibration, so a z-score test or a t-exam might exist appropriate. Because the population standard deviation is not known, the z-examination would be inappropriate. Furthermore, different students accept higher and lower GPAs, so we take a betwixt-subjects design. Because of these factors, nosotros will employ the independent samples t-test.
5. Calculate the t value, or let SPSS do information technology for you.

   The control for the independent samples t tests is constitute at Analyze | Compare Means | Contained-Samples T Test (this is shorthand for clicking on the Analyze menu item at the height of the window, and then clicking on Compare Ways from the drop down menu, and Independent-Samples T Test from the pop up menu.):
   
   

   The Independent-Samples t Examination dialog box volition appear:
   
   

   Select the dependent variable(s) that yous want to test by clicking on it in the left hand pane of the Independent-Samples t Test dialog box. So click on the upper arrow button to move the variable into the Test Variable(southward) pane. In this example, motility the Older variable (number of older siblings) into the Test Variables box:
   
   

   Click on the independent variable (the variable that defines the two groups) in the left hand pane of the Independent-Samples t Test dialog box. Then click on the lower pointer push to move the variable in the Grouping Variable box. (If in that location already is a variable in the Group Variable box, click on it if it is non already highlighted, and and then click on the lower arrow which should be pointing to the left.) In this example, motility the GPA variable into the Grouping Variable box:
   
   

   You demand to tell SPSS how to define the two groups. Click on the Ascertain Groups push. The Define Groups dialog box appears:
   
   

   Click in the circle to the left of "Cutting Bespeak:". Then type the value that splits the variable into two groups. Group 1 is defined every bit all scores that are greater than or equal to the cut point. Group 2 is defined as all scores that are less than the cut point. In this example, use 3.007 (the median of the GPA variable) every bit the cut point value:
   
   

   Click on the Continue button to shut the Ascertain Groups dialog box. Click on the OK button in the Independent-Samples t Examination dialog box to perform the t-test. The output viewer will appear with the results of the t test. The results take two main parts: descriptive statistics and inferential statistics. First, the descriptive statistics:
   
   

   This gives the descriptive statistics for each of the 2 groups (every bit defined past the group variable.) In this example, there are 23 people with a GPA greater than or equal to 3.01 (Northward), and they take, on average, 1.04 older siblings, with a standard departure of 1.186 older siblings. At that place are 23 people with a GPA less than 3.01 (Due north), and they have, on average, 1.48 older siblings, with a standard deviation of 1.310 older siblings. The last column gives the standard error of the mean for each of the two groups.

   The second part of the output gives the inferential statistics:
   
   

   Equally earlier, the columns labeled "Levene'south Test for Equality of Variances" tell us whether an supposition of the t-examination has been met. Await at the column labeled "Sig." under the heading "Levene'south Test for Equality of Variances". In this example, the significance (p value) of Levene'south test is .383. If this value is less than or equal to your α level for this test, and then you tin reject the null hypothesis that the variabilities of the two groups are equal, implying that the variances are unequal. In this example, .383 is larger than our α level of .05, and so we will assume that the variances are equal and we volition use the middle row of the output.

   The column labeled "t" gives the observed or calculated t value. In this example, assuming equal variances, the t value is 1.180. (We can ignore the sign of t when using a two-tailed t-test.) The column labeled "df" gives the degrees of freedom associated with the t test. In this case, there are 44 degrees of freedom.

   The column labeled "Sig. (ii-tailed)" gives the 2-tailed p value associated with the examination. In this example, the p value is .244. If this had been a ane-tailed test, we would need to await up the disquisitional t in a table.

6. Make up one's mind if nosotros can turn down H₀: As before, the conclusion dominion is given by: If p ≤ α , then reject H₀. In this example, .244 is greater than .05, and so we fail to reject H₀. That implies that in that location is not sufficient evidence to conclude that people with higher or lower GPAs take different number of older siblings.

If we were writing this for publication in an APA journal, we would write information technology as:
An equal variances t exam failed to reveal a statistically reliable departure between the hateful number of older siblings for people with higher (M = ane.04, south = 1.186) and lower GPAs (K = 1.48, s = 1.310), t(44) = 1.18, p = .244, α = .05.

Paired Samples t-Tests

When 2 samples are involved and the values for each sample are collected from the same individuals (that is, each individual gives usa two values, ane for each of the two groups), or the samples come from matched pairs of individuals and so a paired-samples t-test may exist an appropriate statistic to use.

The paired samples t-test can exist used to make up one's mind if two means are different from each other when the 2 samples that the means are based on were taken from the matched individuals or the same individuals. In this example, we will determine if the students take different numbers of younger and older siblings.

1. Write the null and alternative hypotheses:
   H₀: µ_older = µ_younger
   H₁: µ_older ≠ µ_younger
   Where µ is the mean number of siblings that the PSY 216 students accept.
2. Make up one's mind if this is a one-tailed or a two-tailed examination. Because the hypothesis involves the phrase "different" and no ordering of the means is specified, this must be a two tailed test.
3. Specify the α level: α = .05
4. Determine the advisable statistical test. The variables of involvement, older and younger, are on a ratio scale, so a z-score test or a t-test might be advisable. Considering the population standard deviation is not known, the z-test would be inappropriate. Furthermore, the same students are reporting the number of older and younger siblings, nosotros have a within-subjects design. Considering of these factors, we will employ the paired samples t-test.
5. Let SPSS summate the value of t for you.

   The command for the paired samples t tests is constitute at Analyze | Compare Means | Paired-Samples T Test (this is shorthand for clicking on the Clarify menu item at the summit of the window, and so clicking on Compare Means from the drop down menu, and Paired-Samples T Test from the pop up menu.):
   
   

   The Paired-Samples t Test dialog box will appear:
   
   

   You must select a pair of variables that stand for the two conditions. Click on one of the variables in the left hand pane of the Paired-Samples t Test dialog box. So click on the other variable in the left hand pane. Click on the arrow push to move the variables into the Paired Variables pane. In this example, select Older and Younger variables (number of older and younger siblings) and so click on the arrow push to motion the pair into the Paired Variables box:
   
   

   Click on the OK push in the Paired-Samples t Examination dialog box to perform the t-test. The output viewer volition appear with the results of the t test. The results have 3 main parts: descriptive statistics, the correlation between the pair of variables, and inferential statistics. First, the descriptive statistics:
   
   

   This gives the descriptive statistics for each of the ii groups (equally defined by the pair of variables.) In this example, at that place are 45 people who responded to the Older siblings question (N), and they have, on average, 1.24 older siblings, with a standard deviation of ane.26 older siblings. These aforementioned 45 people also responded to the Younger siblings question (Northward), and they take, on average, 1.13 younger siblings, with a standard deviation of 1.xx younger siblings. The final column gives the standard mistake of the mean for each of the two variables.

   The 2nd part of the output gives the correlation betwixt the pair of variables:
   
   

   This once again shows that there are 45 pairs of observations (N). The correlation between the two variables is given in the tertiary cavalcade. In this instance r = -.292. The last column requite the p value for the correlation coefficient. As e'er, if the p value is less than or equal to the alpha level, and so you can reject the null hypothesis that the population correlation coefficient (ρ) is equal to 0. In this case, p = .052, so we fail to reject the zip hypothesis. That is, there is insufficient testify to conclude that the population correlation (ρ) is different from 0.

   The 3rd part of the output gives the inferential statistics:
   
   

   The column labeled "Hateful" is the departure of the two means (1.24 - i.xiii = 0.11 in this example (the difference is due to round off error).) The next cavalcade is the standard divergence of the difference between the two variables (one.98 in this example.)

   The column labeled "t" gives the observed or calculated t value. In this case, the t value is 0.377 (you can ignore the sign.) The cavalcade labeled "df" gives the degrees of freedom associated with the t examination. In this example, there are 44 degrees of freedom. The column labeled "Sig. (2-tailed)" gives the two-tailed p value associated with the exam. In this example, the p value is .708. If this had been a i-tailed test, nosotros would need to look up the critical value of t in a table.

6. Decide if we can reject H₀: As before, the conclusion dominion is given by: If p ≤ α, then reject H₀. In this example, .708 is not less than or equal to .05, so we neglect to decline H₀. That implies that there is insufficient show to conclude that the number of older and younger siblings is different.

If nosotros were writing this for publication in an APA journal, we would write it as:
A paired samples t test failed to reveal a statistically reliable difference between the hateful number of older (M = 1.24, s = 1.26) and younger (M = 1.13, s = one.20) siblings that the students accept, t(44) = 0.377, p = .708, α = .05.

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Source: https://academic.udayton.edu/gregelvers/psy216/spss/ttests.htm

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