Week 4 - Case Study ANOVA

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Week 4 - Case Study

ANOVA

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

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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).

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Case Study Homework Questions

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

2. 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.

a. Sampling error probably did not create the difference between the means. b. Sampling errors probably did create the difference between the means.

3. 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?

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

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

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

7. 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?

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

9. 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.