- Description

**This Weeks’ Statistical Technique for Review – Analysis of Variance (ANOVA)**** **

There are different types of ANOVA, but the focus of this statistical technique is on examining differences between two or more groups. The one-way ANOVA is conducted when differences are examined for a study that has one independent variable and one dependent variable. The **two-way ANOVA **is conducted when differences are examined in a study that has two independent variables and one dependent variable. The **multivariate analysis of variance **(MAN OVA) is conducted when a study has more than one independent and dependent variables. **Repeated measures analysis of variance **is used to analyze data from studies where the same variable(s) are repeatedly measured over time in a group or groups of subjects. The intent is to determine the change that occurs over time in the dependent variable(s) with the exposure to the independent variable(s). More details on the types of ANOVA can be found in your research and statistical texts (Burns & Grove, 2005; Munro, 2001).

#### Introduction** **

Stevens et al. (2005) conducted a study to investigate the differences between two groups of youth, those who had a negative affect reported and those who did not, on their smoking behaviors, attitudes, and self- efficacy. This study was conducted to “shed light on differences in adolescent smoking maintenance and cessation” based on their affect. “721 [N = 721] smoking youth participated in a cognitive-behavioral smoking cessation program. Reasons for smoking were categorized, and youth were placed into one of two groups based on presence or absence of negative affect. One-way ANOVA determined if differences existed on Fagerstrom Nicotine Tolerance Dependence (FNTD) scores” (Stevens et al., 2005, p. 589).

#### Relevant Study Results** **

“For future intentions, one-way repeated measures ANOVA reveled a significant main effect pre to post- program on number of days intended to smoke in the next 30 (F(I,449) = 7.98,p = 0.005) and age intended quit (F(I,320) == 7.51, P == 0.006). Those reporting negative affect intended to smoke more days in the next 30 days and reported a higher intended age of quit than those not reporting negative affect as a reason for use (Table 2)” (Stevens et al., 2005, p. 593).

“One-way analysis of variance revealed no significant differences on pre-program FTND scores between the two groups (F (I, 715) = 3.128,p = 0.077 [or 0.08 as in Table 2]. The group not reporting negative affect had a slightly higher dependent score (mean = 3.53; SD = 2.65) than the group self-reporting negative affect (mean = 3.18; SD = 2.46) (Table 2). According to the FTND scale, however, these scores indicate that neither group is very dependent on nicotine” (Stevens et al., 2005, p.593).

“There were significant pre- to post-program main effects for the following attitude items: ‘Smoking makes me look older’ (F (1,51?) = 17.02, P < 0.001); ‘Smoking helps me make and keep friends’ (F (1, 51?) = 11.05,p= 0.001); and ‘Smoking helps me be accepted’ (F (I,SI8) = 9.86,p = 0.002), with both groups agreeing more with these statements from pre- to post-programs (Table 2)… Significant main effects (F(1,500) = 3.86,p =.05) and significant group by time interaction (F(I,500) = 6.08, P = 0.014) for overall self-efficacy were demonstrated, with the negative affect group decreasing and the non-negative affect group increasing in self-efficacy from pre- to post-program (Table 2). Additionally, significant main effects for the following self-efficacy items were noted pre- to post program: ‘I believe I can quit if I try’ (F(I, 499) = 9.13, P = 0.003); and ‘I have the skills necessary to quit’ (F (I, 498) = 12.10, P = 0.001), with both groups increasing in agreement with these items. Significant group by time interaction was found from pre- to post-program on the items: ‘Quitting would be easy’ (F(I, 499) = 6.10, P = 0.014), with the group reporting negative affect as a reason for smoking decreasing in agreement with this item, and the group not reporting negative affect agreeing more; and on item: ‘I can quit using anytime I want’ (F(I, 500) = 7.70, P = 0.006), with the group reporting negative affect as a reason for smoking agreeing less with this item and the group not reporting negative affect agreeing more. There was no significance for the following self-efficacy item: ‘I can resist peer pressure to use’ (Table 2)” (Stevens et al., 2005, pp. 593-4).

#### Case Study Homework Questions** **

- On average, did the participants in Group 1 or Group 2 report more cigarettes smoked daily? Provide a rational for your

- According to Table 2, which of the following statements about the differences between Group 1 and Group 2 on the attitude “Smoking is very enjoyable” is true? Provide a rational for your answer.
- Sampling error probably did not create the difference between the
- Sampling errors probably did create the difference between the

- What type of ANOVA was conducted to examine the main effect pre- to post-program on number of days intended to smoke in the next 30 (
*F*(1,449) = 7.98, p = (0.005)? What is the focus of this type of ANOVA?

- Should the null hypothesis be rejected for “I believe I can quit smoking if I try”? Provide a rational for your answer

- What were the results (means,
*SDs*, and*p*value) for the age intended to quit smoking? Provide your interpretation of what these results

- In Table 2, how many of the comparisons between Groups 1 and 2 were not statistically significant? Provide a rational for your answer.

- Was the difference between Group 1 and Group 2 on overall efficacy scores statistically significant? At what level of alpha could one reject the null hypothesis for this result?

- Which of the seven attitudes was (were) statistically significant at the strongest level? Provide a rational for your answer.

- The result for “Smoking makes me look older” was
*F*(1, 517) = 17.02,*p*< 0.001. Using this result, identify how many groups were examined in this analysis and the number of participants. Provide a rational for your answer.

**Source**: Stevens, S. L., Colwell, B., Smith, D. w., Robinson, J., & McMillan, C. (2005). An exploration of self- reported negative affect by adolescents as a reason for smoking: Implications for tobacco prevention and intervention programs. *Preventive Medicine, *41(2), 589-96.