SPSS INSTRUCTION CHAPTER 6

Transcription

1 SPSS INSTRUCTION CHAPTER 6 Using SPSS to determine whether means differ provides you with the same values for tcalc that you would obtain through the calculations presented in Section 6.3 of this chapter. SPSS output provides this value as well as the degrees of freedom and relevant descriptive statistics. When using SPSS, however, the decision about whether to accept or reject the null hypothesis rests upon the relationship between p and α rather than the relationship between tcalc and tcrit. SPSS determines the exact probability that the difference between sample means does not exist in the population. Thus, you do not have to use the critical value table. You can compare the probability (p) to you chosen α to determine whether the means differ significantly. When p α, the possibility of making a Type I error remains low enough for you to reject the null hypothesis. For these reasons, although computation of tcalc and comparison of this value to tcrit exist as an effective means of assessing significance, researchers tend to prefer using SPSS to perform t tests. Still, as evident from the descriptions in the following sections, using SPSS to perform t tests requires careful organization of raw data on the data view page, an understanding of the different types of t tests available, and recognition of the key values associated with each. One-Sample T Tests in SPSS SPSS requires minimal user preparation of data for the one-sample t test. A single column on in the data editor should contain a list of data points pertaining to subjects in the sample. To obtain correctly labeled output, you should input the name of the variable on the variable view screen. If necessary, you can also use the relevant variable view screen cells to provide a description of the variable and to adjust the number of visible decimal places for the variable s data points. You can then instruct SPSS to perform the one-sample t test. Within the process of computing the t-value, SPSS computes the sample mean. However, the program has no basis of comparison until you enter the population mean. This portion of the process differentiates the one-sample t test procedure from those used for conducting two sample t tests in SPSS. In all cases, however, you begin by informing SPSS you wishes to compare means. The following steps instruct SPSS to perform a one-sample t test. 1. Choose Compare s from the Analyze pull-down menu. 2. Choose One-Sample T Test from the options provided. A One-sample T test window should appear on the screen.

2 FIGURE 6.6 SPSS ONE-SAMPLE T TEST WINDOW The user performs a one-sample t test by selecting the appropriate variable from those listed in the box above and moving it to the Test Variable(s) Box. Then, he or she should enter the population mean into the Test Value box. 3. Highlight the name of the relevant variable from the list appearing in the upper left corner of the window. Click on the arrow to the right of the list to move the name of the variable to the Test Variable(s) List. 4. Change the test value if necessary. The number in this box refers to the population mean. SPSS assumes that this value equals 0 unless the user indicates otherwise. 5. Click OK. The output that results from this procedure consists of two tables that provide all of the values that emerge during the process of computing the one-sample t value, described in Section 6.3 of this chapter. From the output, you can obtain the mean, standard deviation and standard error of the sample as well as the degrees of freedom and calculated t value. In addition, the output contains a two-tailed significance value. This number represents the probability (p) that rejecting the null hypothesis results in a Type I error. You should compare this value to your chosen alpha value. With alpha identifying the largest chance that the researcher allows for a Type I error to occur, p must lie below α to signify a rejected null hypothesis. So, using the standard α=.05, you can claim that the sample mean and population mean differ significantly if p.05, indicating less than a five percent chance of incorrectly characterizing the difference as significant. Assuming you wish to take no more than a five percent chance of making such mistake, you would accept the null hypothesis when p>.05 Example 6.24 SPSS Output for One Variable T Test An SPSS analysis of the data first presented in Example 6.2 proves that this logic provides the same outcome as that obtained when calculating t and comparing its value to tcrit. The output for this analysis appears as follows.

3 One-Sample Statistics f ish Std. Error N Std. Dev iation One-Sample Test Test Value = % Confidence Interval of the Difference T Df Sig. (2-tailed) Difference Lower Upper Fish TABLE 6.8 AND TABLE 6.9 SPSS OUTPUT FOR ONE-SAMPLE T TEST Table 6.8 displays descriptive statistics from the sample. Table 6.9 contains the values related to the actual comparison between the sample mean and the population mean. The researcher pays particular attention to the significance value (p), which indicates whether to accept or reject the null hypothesis. As expected, many of the values in Table 6.8 and Table 6.9 also appear in the computations based upon Equation 6.1. The numerator of this equation consists of the difference between the sample mean of 3.9, located in Table 6.8 and the population mean of 8.4, labeled as the test value in Table 6.9. The mean difference of -4.6, shown in Table 6.9, verifies accurate calculations in the numerator of the equation. One can find the standard error, which constitutes the denominator of Equation 6.1, in Table 6.8 as well. Most obviously, though, the t value and the degrees of freedom value in Table 6.9 match those obtained through the calculations in Section 6.3 of this chapter. The researcher can use the degrees of freedom value to locate the critical t value associated with his or her chosen alpha and then follow the procedure of comparing tcalc to tcrit. However, the presence of the p value, labeled as Sig (2-tailed) in Table 6.9 simplifies this process. The value of.006 indicates that one who states that a significant difference exists between the sample mean and the population mean has a 0.6% chance of being incorrect. This probability lies well under the standard alpha value of.05 and, thus, one using this alpha value would reject the null hypothesis. In fact, this p value would even satisfy researchers who wish to take much less than a 5 percent chance of making a Type I error. One can claim with 99.4% certainty that the two values differ significantly. Paired-Samples T Tests in SPSS

4 The straightforward approach of listing all data points in a single column, used to enter data into SPSS for the one-sample t test, becomes a bit more complicated with the inclusion of a second sample. For the paired sample t test, the arrangement of data in SPSS data editor must not only specify which subjects belong to which category, but must also communicate the pairings of subjects. You can provide this information by using two columns, each representing one category of subjects, like the appearance of the raw data in Example 6.5. Reading across each row, then, paired scores lie next to each other. Example 6.25 SPSS Data View Screen for Paired-samples T Tests Table 6.10 shows the SPSS data view screen as it should appear in preparation for conducting a paired-samples t test using the data regarding the number of fish caught by the same individuals fishing in freshwater and in saltwater. TABLE 6.10 SPSS PAIRED SAMPLE T TEST DATA ARRANGEMENT Placing data points from the two samples side by side in the SPSS data view screen indicates the intended parings of scores. The user inserts column headings, which describe the conditions for each sample, in the variable view screen. In this example, each row corresponds to one subject s scores in two different conditions. However, rows can also correspond to scores from logically-connected subjects, as presented in Example 6.9. SPSS uses the two values in each row to calculate the difference scores that form the basis of the formula for the paired-samples t statistic. Instructing SPSS to compare the means for the two paired sample groups and to provide the user with the resulting p value involves the following steps. 1. Choose Compare s from the Analyze pull-down menu. 2. Choose Paired-Samples T Test from the options provided. A Paired Sample T Test WINDOW should appear on the screen.

5 FIGURE 6.7 SPSS PAIRED-SAMPLES T TEST WINDOW The user performs a paired-samples t test by selecting the appropriate category names from those listed in the box above. The names of these categories transfer to the Paired Variables box simultaneously. 3. Highlight the names of BOTH of the relevant categories from the list appearing in the upper left corner of the window. Click on the arrow to the right of the list to move the name of the variable to the Paired Variables list. 4. Click OK. The additional sample in this context, as opposed to the one-sample t test, results in an additional table in the output. Along with the familiar statistics table and test table, the output contains a correlations table. The values in this table describe the pattern of changes between scores in the two samples. The correlation value in this table indicates the predictability with which one set of values increases as the other increases, designated by a positive value, or with which one set of values decreases as the other increases, designated by a negative value. Chapter 8 of this book provides a full explanation of correlation coefficients as well as a description of the situations in which researchers might find them useful. For the paired-subjects t test, the researcher should pay the most attention to the values contained within and produced by Equation 6.3. If you simply need to determine whether to accept or reject the null hypothesis, you can concentrate on the significance value (p), located to the far left of the paired-samples t test table. As in the other cases, a p value smaller than your chosen α indicates a significant difference and, thus, a rejected null hypothesis. A closer examination of output, however, provides evidence of the procedure used to obtain t calc. Example 6.26 SPSS Output for Paired-Subjects T Test For instance, one can easily identify descriptive statistics for the two categories of subjects as well as values for the degrees of freedom and t calc in output from the paired-samples t test comparing mean daily catches for subjects who fish in freshwater and in saltwater. Paired-samples Statistics

6 N Std. Deviation Std. Error Pair 1 freshwater Saltwater Paired-samples Correlations N Correlation Sig. Pair 1 freshwater & saltwater Pair 1 freshwater saltwater Std. Deviation Paired-samples Test Paired Differences Std. Error 95% Confidence Interval of the Difference Upper Lower T Sig. (2- Df tailed) Std. Error Mea Std. Deviation n TABLE 6.11, TABLE 6.12, AND TABLE 6.13 SPSS OUTPUT FOR PAIRED-SAMPLES T TEST Table 6.11 displays descriptive statistics from the samples. Table 6.13, contains the values related to the actual comparison between the sample means. The researcher pays particular attention to the significance value (p), which indicates whether to accept or reject the null hypothesis. The values in Table 6.11 describe each data set individually and the correlation coefficient in Table 6.12 indicate that as the number of fish caught in freshwater increases, the number of fish caught in saltwater decreases rather predictably. Table 6.6 values such as the mean difference score of -.60, the standard error of 3.67, the four degrees of freedom, and the t calc of -.16 come as no surprise given the computations from Example 6.7. The two-tailed significance value (p), however, provides new information, indicating the exact probability of making a Type I error should you reject the null hypothesis. When using the formulas from Section and making the subsequent comparison between t crit and t calc, one can only discern whether the possibility of incorrectly claiming that a significant difference exists lies within or outside of the acceptable range, dictated by the chosen value of alpha. The p value of.878 greatly exceeds the standard α of.05. Even those willing consider alpha values greater than.05 in hopes of increasing his or her chances of rejecting the null hypothesis could not reasonably do so with a p value of.878. Doing so would mean that you are only 12.2% certain that any difference existing between the two groups of subjects in your sample also exists in the population.

7 Independent-Samples T Tests in SPSS Unlike, paired-samples t tests, independent-samples t tests do not involve associations between particular subjects within the two samples compared. This lack of constraints would seem to make SPSS data entry for independent-samples tests simple in comparison to than entry for the paired-samples test. However, you must put more effort into organizing independent-samples data than into organizing paired-samples data in the SPSS data editor. Because SPSS automatically associates data points across a row with to single subject or with linked subjects, you cannot enter data from each subject group for an independent-samples test into separate columns. Rather, you must list all raw data in a single column and creates a second column of dummy variables to identify each subject s group placement within the independent variable categories. A coding scheme designates a separate value to represent each group. Example 6.27 SPSS Data View Screen for Independent-samples T Tests The data view screen for the independent-samples t test shown in Section s examples would appear as follows. In this example, those who fished in freshwater receive a code of 1 and those who fished in saltwater receive a code of 2. TABLE 6.14 SPSS INDEPENDENT SAMPLE T TEST DATA ARRANGEMENT All dependent-variable data points from the two samples appear in the column labled fish. The designations of 1 and 2 in the column labeled location distinguish between the two samples identified by the independent variable. The user should enter these codes and their meanings into the values cell on the variable view screen. The coding technique shown in Example 6.27 also allows you to select two groups from a non-dichotomous variable for comparison. If, for example, the independent variable distinguishes between more than two types of fishing locations, you could identify each with a dummy value and then, during the course of conducting the t test, specify which two groups to include in the analysis.

8 User instructions to SPSS for performing the independent-samples t test in SPSS begin the same way as they do for the single sample and paired-samples tests. In all cases, you first indicate that you wish to compare means. The remainder of the process for the independent-samples test, however, involves more steps than do the steps for the other types of t tests. Directions for the entire procedure for conducting independent-samples t tests in SPSS follow. 1. Choose Compare s from the Analyze pull-down menu. 2. Choose Independent-Samples T Test from the options provided. An Independent Sample T test window should appear on the screen. FIGURE 6.8 SPSS INDEPENDENT-SAMPLES T TEST WINDOW The user performs an independent-samples t test by selecting the names of the independent variable, which becomes the grouping variable, and the dependent variable, which becomes the test variable from those listed in the box above. The Define Groups button allows the user to specify the two groups of the independent variable that he or she wishes to compare. 3. Highlight the name of the dependent variable from the list appearing in the upper left corner of the window. Click on the arrow to the left of the Test Variable(s) box. The name of the variable should move to this box. 4. Identify the independent variable groups to compare. a. Highlight the name of the independent variable from the list appearing in the upper left corner of the window. Click on the arrow to the left of the Grouping Variable box. The name of the variable should move to this box. b. Click on the Define Groups button. A Define Groups window should appear on the screen. This window provides the user with two options for identifying the groups for comparison. -The User Specified Values option allows you to input the dummy variables for the groups that you wish to compare. For a data set that includes only two

9 groups, you would identify one of the dummy variable codes as Group 1 and the other as Group 2. When more than two categories exist, however, you should enter the dummy variable codes that represent the categories you wish to compare. One who wishes to compare the mean numbers of points scored by college basketball players during their Freshman years and Senior years, for example, would enter the values of 1 and 4. -The Cut Point option allows one to create two independent variable categories from continuous data by specifying a value that separates the subjects into two groups. You can, thus, instruct SPSS to compare the subjects with independent variable scores less than this cut point to those with scores equal to or greater than this cut point. c. Click Continue to return to the An Independent Sample T test window. 5. Click OK. Independent-samples t test output that contains two tables. The Group Statistics table presents descriptive statistics for the two samples. The Independent-samples Test table presents the values used to assess significance. In particular, the tcalc and relevant significance (p) value appear portion of the second table that refers to the t test for equality of means. In fact, this portion of the table contains two values for t and p. Often these values are equal or almost equal. Any difference between them reflects a slight modification to the calculations used when the two categories have unequal variances. You should refer to the value on the top row when the category variances do not differ significantly and you should use the value on the bottom row when a significant difference exists. Luckily, SPSS provides you with a way to compare the categories variances in the form of Levene s Test for Equality of Variance. You can find a significance value for Levene s test to the left of the t test information in the Independent-samples Test table. Be sure that you do not mistake this significance value for the p value that you must use to make a decision about your t test outcome. A Levene s significance value that exceeds the α that you have chosen indicates equality of variances and a Levene s significance value lower than α indicates a significant difference between the categories variances. Once you have determined whether you should focus on the top or bottom row of the right side of the table, you can compare the appropriate p value to α. A p<α suggests a significant difference between category means, meaning that you should reject the null hypothesis. You can accept the null hypothesis when p> α. Example SPSS Output for Independent Variables T Test The following output, produced by an SPSS independent variables t test analysis using the data first presented in Example 6.11, clearly displays all values of interest.

10 Group Statistics number of fish caught in one day fishing location N Std. Deviation Std. Error Freshwater Saltwater Independent-samples Test number of fish caught in one day Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances F Sig. T df t test for Equality of s Sig. (2- tailed) Difference Std. Error Difference 95% Confidence Interval of the Difference Upper Lower TABLE 6.15 AND TABLE 6.16 SPSS OUTPUT FOR INDEPENDENT-SAMPLES T TEST Descriptive statistics from the samples appear in Table Table 6.16, contains the values related to the actual comparison between the sample means. In this table, the researcher pays particular attention to the two-tailed significance value (p), which indicates whether to accept or reject the null hypothesis. Unless, for some reason, the samples contain data with vastly different ranges, the researcher should assume equal variances and, thus, consider only values in the top row of Table Among the values included in the Groups Statistics table one can find the mean for each of the groups involved in the comparison. The difference between these means, -.60, along with the standard error, 2.74, which appear in the Independent-samples Test table, constitute numerator and denominator of the tcalc formula. The researcher does not need to perform any computations, however, as the table also contains the calculated t value. Most importantly, however, the researcher should take notice of the two-tailed significance value. The p value of.832, which lies well above any reasonable alpha value, indicates that no significant difference exists between means of the two samples. This value indicates that the difference between sample means correctly characterizes the population only 16.7 percent of the time. Thus, the researcher, unwilling to take an 83.2 percent chance of making a Type I error by incorrectly claiming that those who fish in freshwater and those who fish in saltwater have different daily catches, would accept the null hypothesis. Presenting SPSS Results You can use the same general technique of presenting results from a t test performed in SPSS as you use to present results of a chi-square test performed in SPSS. (See the Chapter

11 5 Companion Website for a brief explanation of how to do so). The most important pieces of information to include are the calculated statistical value, in this case, t, and the p value. You should also note whether the p value has led you to accept or reject your null hypothesis.