- To complete the assignment, students will need to access their course text book and possibly the following databases: PubMed, CINAHL, MEDLINE, Cochrane Library, and other resources in the Jay Sexter Library. These data bases can be accessed through the Touro Online Library http://tun.touro.edu/jay-sexter-library/ (Links to an external site.)
- The
**T-tests**learning activity assignment is worth 50 points and will be graded using the designated rubric. Grading criteria include quality of content, appropriate citations, use of Standard English grammar, and overall organization and readability. - Create your assignment using a Microsoft Word application. The document should be saved in a .doc or .docx format.
- There is no required length but should be specific enough to address all requirements.
- The following sections should be included in the document:
- Question #1

- Question #2

- Question #3

- Attached output files in .sav format

Use the provided data set sample and use SPSS to analyze the data. Use the SPSS Screenshot Guide as a reference when running the tests.

**1.** Using the data file survey.sav follow the instructions in Chapter 17 of the *SPSS Survival Manual* to find out if there is a statistically significant difference in the mean score for males and females on the Total Life Satisfaction Scale (tlifesat). *Present this information in a brief report.*

**. **Using the data file experim.sav apply whichever of the t-test procedures covered in Chapter 17 of the *SPSS Survival Manual* that you think are appropriate to answer the following questions.

(a) Who has the greatest fear of statistics at time 1, males or females?

(b) Was the intervention effective in increasing students’ confidence in their ability to cope with statistics? You will need to use the variables, confidence time1 (conf1) and confidence time2 (conf2). Write your results up in a report.

**3.** Using the experim.sav data file compare the depression scores at time 1 and the depression scores at time 2. Did the intervention result in a significant change in depression scores? *The variables you will need are depress1 and depress2.*

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**17**

**T-tests**

In this chapter two of the t-tests available in IBM SPSS Statistics are discussed:

*independent-samples* t*-test:* Used when you want to compare the mean scores of two *different* groups of people or conditions

*paired-samples* t*-test:* Used when you want to compare the mean scores for the *same* group of people on two different occasions, or when you have matched pairs.

In both cases, you are comparing the values on some continuous variable for *two* groups or on *two* occasions. If you have more than two groups or conditions, you will need to use analysis of variance instead.

For both of the t-tests discussed in this chapter there are a set of assumptions that you will need to check before conducting these analyses. The general assumptions common to both types of t-tests are presented in the introduction to Part Five. Before proceeding with the remainder of this chapter, you should read through the introduction to Part Five of this book.

**INDEPENDENT-SAMPLES T-TEST**

An independent-samples t-test is used when you want to compare the mean score on some *continuous* variable for *two* different groups of participants.

**Details of example**

To illustrate the use of this technique, the **survey.sav** data file is used. This example explores sex differences in self-esteem scores. The two variables used are sex (with males coded as 1, and females coded as 2) and Total self-esteem (tslfest), which is the total score that participants recorded on a 10-item Self-Esteem Scale (see the Appendix for more details on the study, the variables and the questionnaire that was used to collect the data). If you would like to follow along with the steps detailed below, you should start IBM SPSS Statistics and open the **survey.sav** file now.

**Example of research question:** Is there a significant difference in the mean self-esteem scores for males and females?

**What you need:**

one categorical, independent variable (e.g. males/females)

one continuous, dependent variable (e.g. self-esteem scores).

**What it does:** An independent-samples t-test will tell you whether there is a statistically significant difference in the mean scores for the two groups (i.e. whether males and females differ significantly in terms of their self-esteem levels). In statistical terms, you are testing the probability that the two sets of scores (for males and females) came from the same population.

**Assumptions:** The assumptions for this test are covered in the introduction to Part Five. You should read through that section before proceeding.

**Non-parametric alternative:** Mann-Whitney *U* Test (see Chapter 16).

**Procedure for independent-samples t-test**

**1.** From the menu at the top of the screen, click on **Analyze**, then select **Compare means**, then **Independent Samples** T **test**.

**2.** Move the dependent (continuous) variable (e.g. total self-esteem: tslfest) into the **Test variable** box.

**3.** Move the independent (categorical) variable (e.g. sex) into the section labelled **Grouping variable**.

**4.** Click on **Define groups** and type in the numbers used in the data set to code each group. In the current data file, 1 = males, 2 = females; therefore, in the **Group 1** box, type 1, and in the **Group 2** box, type 2. If you cannot remember the codes used, right click on the variable name and then choose **Variable Information** from the pop-up box that appears. This will list the codes and labels.

**5.** Click on **Continue** and then **OK** (or on **Paste** to save to **Syntax Editor**).

The syntax generated from this procedure is:

T-TEST GROUPS=sex(1 2)

/MISSING=ANALYSIS

/VARIABLES=tslfest

/CRITERIA=CI(.95).

The output generated from this procedure is shown below.

**Group Statistics**

sex sex | N | Mean | Std. Deviation | Std. Error Mean | |

tslfest Total Self esteem | 1 MALES | 184 | 34.02 | 4.911 | .362 |

2 FEMALES | 252 | 33.17 | 5.705 | .359 |

**Independent Samples Test**

Levene’s Test for Equality of Variances | t-test for Equality of Means | 95% Confidence Interval of the Difference | ||||||||

F | Sig. | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | Lower | Upper | ||

tslfest Total Self esteem | Equal variances assumed | 3.506 | .062 | 1.622 | 434 | .105 | .847 | .522 | -.179 | 1.873 |

Equal variances not assumed | 1.661 | 422.3 | .098 | .847 | .510 | -.156 | 1.850 |

**Interpretation of output from independent-samples t-test**

Step 1: Check the information about the groups

In the **Group Statistics** table, IBM SPSS Statistics gives you the mean and standard deviation for each of your groups (in this case, male/female). It also gives you the number of people in each group (*N*). Always check these values first. Are the *N* values for males and females correct? Or are there a lot of missing data? If so, find out why. Perhaps you have entered the wrong code for males and females (0 and 1, rather than 1 and 2). Check with your codebook.

Step 2: Check assumptions

The first section of the **Independent Samples Test** table gives you the results of Levene’s Test for Equality of Variances. This tests whether the variance (variation) of scores for the two groups (males and females) is the same. The outcome of this test determines which of the* t* values that IBM SPSS Statistics provides is the correct one for you to use.

If your Sig. value for Levene’s test is larger than .05 (e.g. .07, .10) you should use the first row in the table, which refers to **Equal variances assumed**.

If the significance level of Levene’s test is *p* = .05 or less (e.g. .01, .001), this means that the variances for the two groups (males/females) are *not* the same. Therefore, your data violate the assumption of equal variance. Don’t panic—IBM SPSS Statistics is very kind and provides you with an alternative t value which compensates for the fact that your variances are not the same. You should use the information in the *second* row of the t-test table, which refers to **Equal variances not assumed**.

In the example given in the output above, the significance level for Levene’s test is .06. This is larger than the cut-off of .05. This means that the assumption of equal variances has not been violated; therefore, when you report your t value, you will use the one provided in the first row of the table.

Step 3: Assess differences between the groups

To find out whether there is a significant difference between your two groups, refer to the column labelled **Sig. (2-tailed)**, which appears under the section labelled t**-test for Equality of Means**. Two values are given, one for equal variance, the other for unequal variance. Choose whichever your Levene’s test result says you should use (see Step 2 above).

If the value in the **Sig. (2-tailed)** column is *equal to or less* than .05 (e.g. .03, .01, .001), there is a significant difference in the mean scores on your dependent variable for each of the two groups.

If the value is *above .*05 (e.g. .06, .10), there is no significant difference between the two groups.

In the example presented in the output above, the **Sig. (2-tailed)** value is .105. As this value is *above* the required cut-off of .05, you conclude that there is *not* a statistically significant difference in the mean self-esteem scores for males and females. The **Mean Difference** between the two groups is also shown in this table, along with the **95% Confidence Interval of the Difference** showing the **Lower** value and the **Upper** value.

**Calculating the effect size for independent-samples t-test**

In the introduction to Part Five of this book, the issue of effect size was discussed. Effect size statistics provide an indication of the magnitude of the differences between your groups (not just whether the difference could have occurred by chance). There are several different effect size statistics, the most commonly used being eta squared and Cohen’s *d.* Eta squared can range from 0 to 1 and represents the proportion of variance in the dependent variable that is explained by the independent (group) variable. Cohen’s *d*, on the other hand, presents the difference between groups in terms of standard deviation units. Be careful not to get the different effect size statistics confused when interpreting the strength of the association.

IBM SPSS Statistics does not provide effect size statistics for t-tests in the output. There are, however, websites that allow you to calculate an effect size statistic using information provided in the output. If you do decide to use Cohen’s *d* (often required for medical journals) please note that the criteria for interpreting the strength are different from those for eta squared in the current example. For Cohen’s *d* .2 = small effect, .5 = medium effect, and .8 = large effect (Cohen 1988).

Eta squared can be calculated by hand using the information provided in the output.

The formula for eta squared is as follows:

Using the appropriate values from the example above:

The guidelines (proposed by Cohen 1988, pp. 284–287) for interpreting this value are: .01 = small effect, .06 = moderate effect, and .14 = large effect. For our current example, you can see that the effect size of .006 is very small. Expressed as a percentage (multiply your eta squared value by 100), only .6 per cent of the variance in self-esteem is explained by sex.

**Presenting the results from independent-samples t-test**

If you have conducted a t-test on only one variable you could present the results in a paragraph as follows:

An independent-samples t-test was conducted to compare the self-esteem scores for males and females. There was no significant difference in scores for males (*M *= 34.02, *SD* = 4.91) and females (*M* = 33.17, *SD* = 5.71; *t*(434) = 1.62, *p* = .11, two-tailed). The magnitude of the differences in the means (mean difference = .85, 95% CI [–.18, 1.87]) was very small (eta squared = .006).

If you have conducted a series of t-tests you might want to present the results in a table. I have provided an example below, formatted in APA style (American Psychological Association 2019). For other examples, see Chapter 5 in Nicol and Pexman (2010b).

**Presenting the results from a series of t-tests in a table**

To provide the extra material for the table I conducted the t-test procedure detailed earlier in this chapter for both the Mastery and Optimism Scales (see output below). Both these measures recorded a significant result from Levene’s Test for Equality of Variances. When presenting the results I therefore had to report the information provided in the second row of the Independent Samples Test (Equal Variances Not Assumed).

The output generated from this procedure is shown below.

**Independent Samples Test**

Levene’s Test for Equality of Variances | t-test for Equality of Means | 95% Confidence Interval of the Difference | ||||||||

F | Sig. | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | Lower | Upper | ||

tmast Total Mastery | Equal variances assumed | 5.096 | .024 | 2.423 | 434 | .016 | .927 | .383 | .175 | 1.679 |

Equal variances not assumed | 2.483 | 425.338 | .013 | .927 | .373 | .193 | 1.660 | |||

toptim Total Optimism | Equal variances assumed | 4.491 | .035 | -.428 | 433 | .669 | -.184 | .430 | -1.030 | .661 |

Equal variances not assumed | -.440 | 424.751 | .660 | -.184 | .419 | -1.008 | .639 |

The results of the analysis could be presented as follows:

**PAIRED-SAMPLES T-TEST**

A paired-samples t-test (also referred to as ‘repeated measures’) is used when you have only one group of people (or companies, machines etc.) and you collect data from them on two different occasions or under two different conditions. Pre-test and post-test experimental designs are examples of the type of situation where this technique is appropriate. You assess each person on some continuous measure at Time 1 and then again at Time 2 after exposing them to some experimental manipulation or intervention. This approach is also used when you have matched pairs of participants (i.e. each person is matched with another on specific criteria, such as age, sex). One of the pair is exposed to Intervention 1 and the other is exposed to Intervention 2. Scores on a continuous measure are then compared for each pair.

Paired-samples t-tests can also be used when you measure the same person in terms of their response to two different questions (e.g. asking them to rate the importance in terms of life satisfaction of two dimensions of life: health, financial security). In this case, both dimensions should be rated on the same scale (e.g. from 1 = not at all important to 10 = very important).

**Details of example**

To illustrate the use of the paired-samples t-test, I use the data from the file labelled **experim.sav** (included on the website accompanying this book). This is a manufactured data file—created and manipulated to illustrate different statistical techniques. Full details of the study design, the measures used and so on are provided in the Appendix.

For the example below, I explore the impact of an intervention designed to increase students’ confidence in their ability to survive a compulsory statistics course. Students were asked to complete a Fear of Statistics Test (FOST) both before (Time 1) and after (Time 2) the intervention. The two variables from the data file that I use are fost1 (scores on the Fear of Statistics Test at Time 1) and fost2 (scores on the Fear of Statistics Test at Time 2). If you wish to follow along with the following steps, you should start IBM SPSS Statistics and open the file labelled **experim.sav**.

**Examples of research questions:** Is there a significant change in participants’ Fear of Statistics Test scores following participation in an intervention designed to increase students’ confidence in their ability to successfully complete a statistics course? Does the intervention have an impact on participants’ Fear of Statistics Test scores?

**What you need:** One set of participants (or matched pairs). Each person (or pair) must provide both sets of scores. Two variables:

one categorical, independent variable (in this case it is time, with two different levels: Time 1, Time 2)

one continuous, dependent variable (e.g. Fear of Statistics Test scores) measured on two different occasions or under different conditions.

**What it does:** A paired-samples t-test will tell you whether there is a statistically significant difference in the mean scores for Time 1 and Time 2.

**Assumptions:** The basic assumptions for t-tests are covered in the introduction to Part Five. You should read through that section before proceeding.

**Additional assumption:** The difference between the two scores obtained for each subject should be normally distributed. With sample sizes of 30+, violation of this assumption is unlikely to cause any serious problems.

**Non-parametric alternative:** Wilcoxon Signed Rank Test (see Chapter 16).

**Procedure for paired-samples t-test**

**1.** From the menu at the top of the screen, click on **Analyze**, then select **Compare Means**, then **Paired Samples** T **test**.

**2.** Click on the two variables that you are interested in comparing for each subject (e.g. fear of stats time1 fost1, fear of stats time2 fost2) and move them into the box labelled **Paired Variables** by clicking on the arrow button. Click on **OK** (or on **Paste** to save to **Syntax Editor**).

The syntax for this is:

T-TEST PAIRS=fost1 WITH fost2 (PAIRED)

/CRITERIA=CI(.9500)

/MISSING=ANALYSIS.

The output generated from this procedure is shown below.

**Paired Samples Statistics**

Mean | N | Std. Deviation | Std. Error Mean | ||

Pair 1 | fost1 fear of stats time1 | 40.17 | 30 | 5.160 | .942 |

fost2 fear of stats time2 | 37.50 | 30 | 5.151 | .940 |

**Paired Samples Correlations**

N | Correlation | Sig. | ||

Pair 1 | fost1 fear of stats time1 & fost2 fear of stats time2 | 30 | .862 | .000 |

**Paired Samples Test**

Paired Differences | |||||||||

95% Confidence Interval of the Difference | |||||||||

Mean | Std. Deviation | Std. Error Mean | Lower | Upper | t | df | Sig. (2-tailed) | ||

Pair 1 | fost1 fear of stats time1 – fost2 fear of stats time2 | 2.667 | 2.708 | .494 | 1.655 | 3.678 | 5.394 | 29 | .000 |

**Interpretation of output from paired-samples t-test**

Step 1: Determine overall significance

In the table labelled **Paired Samples Test** you need to look in the final column, labelled **Sig. (2-tailed)**—this is your probability (*p*) value. If this value is less than .05 (e.g. .04, .01, .001), you can conclude that there is a significant difference between your two scores. In the example given above, the probability value is .000. This has been rounded down to three decimal places—it means that the actual probability value was less than .0005. This value is substantially smaller than our specified alpha value of .05. Therefore, we can conclude that there is a significant difference in the Fear of Statistics Test scores at Time 1 and at Time 2. Take note of the* t* value (in this case, 5.39) and the degrees of freedom (*df =* 29), as you will need these when you report your results. You should also note that the **Mean** difference in the two scores was 2.67, with a 95 per cent confidence interval stretching from a **Lower** bound of 1.66 to an **Upper** bound of 3.68.

Step 2: Compare mean values

Having established that there is a significant difference, the next step is to find out which set of scores is higher (Time 1 or Time 2). To do this, inspect the first printout table, labelled **Paired Samples Statistics**. This box gives you the **Mean** scores for each of the two sets of scores. In our case, the mean fear of statistics score at Time 1 was 40.17 and the mean score at Time 2 was 37.50. Therefore, we can conclude that there was a significant decrease in Fear of Statistics Test scores from Time 1 (prior to the intervention) to Time 2 (after the intervention).

*Caution:* Although we obtained a significant difference in the scores before and after the intervention, we cannot say that the intervention caused the drop in Fear of Statistics Test scores. Research is never that simple, unfortunately! There are many other factors that may have also influenced the decrease in fear scores. Just the passage of time (without any intervention) could have contributed. Any number of other events may also have occurred during this period that influenced students’ attitudes to statistics. Perhaps the participants were exposed to previous statistics students who told them how great the instructor was and how easy it was to pass the course. Perhaps they were all given an illegal copy of the statistics exam (with all answers included!). There are many other possible confounding or contaminating factors. Wherever possible, the researcher should try to anticipate these confounding factors and either control for them or incorporate them into the research design. In the present case, the use of a control group that was not exposed to an intervention but was similar to the participants in all other ways would have improved the study. This would have helped to rule out the effects of time, other events and so on that may have influenced the results of the current study.

**Calculating the effect size for paired-samples t-test**

Although the results presented above tell us that the difference we obtained in the two sets of scores was unlikely to occur by chance, it does not tell us much about the magnitude of the intervention’s effect. One way to discover this is to calculate an effect size statistic (see the introduction to Part Five for more on this topic).

IBM SPSS Statistics does not provide effect size statistics for t-tests in the output. There are, however, websites that will allow you to calculate an effect size statistic using information provided in the output. If you do decide to use Cohen’s *d* (often required for medical journals) please note that the criteria for interpreting the strength are different from those for eta squared in the current example. For Cohen’s *d .*2 = small effect, .5 = medium effect and .8 = large effect (Cohen 1988).

The procedure for calculating and interpreting eta squared (one of the most commonly used effect size statistics) by hand is presented below.

Eta squared can be obtained using the following formula:

The guidelines (proposed by Cohen 1988, pp. 284–287) for interpreting this value are: .01 = small effect, .06 = moderate effect, .14 = large effect. Given our eta squared value of .50 we can conclude that there was a large effect, with a substantial difference in the Fear of Statistics Test scores obtained before and after the intervention.

**Presenting the results from paired-samples t-test**

The key details that need to be presented are the name of the test, the purpose of the test, the *t-*value, the degrees of freedom (*df*), the probability value and the means and standard deviations for each of the groups or administrations. Most journals now require an effect size statistic (e.g. eta squared) to be reported as well. If you conduct a t-test on only one variable you could present the results in a paragraph as shown below.

A paired-samples t-test was conducted to evaluate the impact of the intervention on students’ scores on the Fear of Statistics Test (FOST). There was a statistically significant decrease in FOST scores from Time 1 (*M* = 40.17, *SD* = 5.16) to Time 2 (*M *= 37.5, *SD* = 5.15), *t*(29) = 5.39, *p* < .001 (two-tailed). The mean decrease in FOST scores was 2.67, with a 95% confidence interval ranging from 1.66 to 3.68. The eta squared statistic (.50) indicated a large effect size.

If you conduct several t-tests using the same dependent variable, it would be more appropriate to present the results in a table (see the example provided for the independent t-test earlier in this chapter).

**ADDITIONAL EXERCISES**

**Business**

Data file: **staffsurvey.sav**. See Appendix for details of the data file.

1. Follow the procedures in the section on independent-samples t-tests to compare the mean staff satisfaction scores (*totsatis*) for permanent and casual staff (*employstatus*). Is there a significant difference in mean satisfaction scores?

**Health**

Data file: **sleep.sav**. See Appendix for details of the data file.

1. Follow the procedures in the section on independent-samples t-tests to compare the mean sleepiness ratings (Sleepiness and Associated Sensations Scale total score: *totSAS*) for males and females (*gender*). Is there a significant difference in mean sleepiness scores?