Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 9-1 (p. 284) Distributions of the t statistic for different values of degrees of freedom are compared to a normal z-score distribution. Like the normal distribution, t distributions are bell-shaped and symmetrical and have a mean of zero. However, t distributions have more variability, indicated by the flatter and more spread-out shape. The larger the value of df is, the more closely the t distribution approximates a normal distribution.

Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Table 9-1 (p. 285) A portion of the t-distribution table. The numbers in the table are the values of t that separate the tail from the main body of the distribution. Proportions for one or two tails are listed at the top of the table, and df values for t are listed in the first column.

Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 9-2 (p. 286) The t distribution with df = 3. Note that 5% of the distribution is located in the tail beyond t = Also, 5% is in the tail beyond t = – Thus, a total proportion of 10% (0.10) is in the two tails beyond t = ±2.353.

Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 9-3 (p. 287) The basic experimental situation for using the t statistic or the z-score is presented. It is assumed that the parameter µ is known for the population before treatment. The purpose of the experiment is to determine whether or not the treatment has an effect. We ask, Is the population mean after treatment the same as or different from the mean before treatment? A sample is selected from the treated population to help answer this question.

Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 9-4 (p. 289) Apparatus used in Example 9.1

Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 9-5 (p. 289) The critical region in the t distribution for  =.05 and df = 15.

Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 9-6 (p. 291) A sketch of a sample distribution with M = 39 and s = 6. The data do not appear to support a hypothesis that the sample was obtained from a population with µ = 30.

Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 9-7a (p. 293) Deviations from µ = 30 for the scores from Example 9.1. The colored lines show the deviations from the mean for the original scores, including the treatment effect.

Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 9-7b (p. 293) The colored lines show the deviations from the mean for the adjusted scores, after the treatment effect is removed.

Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Table 9-2 (p. 294) Calculation of SS, the sum of squared deviations, for the data in Figure 9.7. The three columns on the left show the calculations for the original scores, including the treatment effect. The three columns on the right show the calculations for the adjusted cores after the treatment effect has been removed.

Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Table 9-3 (p. 295 Criteria for interpreting the value of r 2 as proposed by Cohen (1988).

Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 9-8 (p. 298) The critical region in the t distribution for  =.05, df = 15, one-tailed test.