Attach is assignment instructions. Also is attach already completed assignment from Intellectus Statistics. I just need help with write up portion per the instructions on the assignment sheet. The 8 steps of the hypothesis testing have to be answered for steps 2,3, and 4. |
Results Upper-Tailed Independent Samples t-Test Introduction An upper-tailed independent samples t-test was conducted to examine whether the mean of smok1 was significantly different between the nicotine patch only and nicotine patch and motivational support categories of group. Nicotine Patch n= Nicotine patch & motivational support n= Mean SD Mean SD Age (years) Baseline Values Depression Anxiety Number cigarettes smokes/day Gender Frequency % Frequency % Female Male Assumptions Normality. Shapiro-Wilk tests were conducted to determine whether smok1 could have been produced by a normal distribution for each category of group (Razali & Wah, 2011). The result of the Shapiro-Wilk test for smok1 in the nicotine patch only category was not significant based on an alpha value of 0.05, W = 0.93, p = .113. This result suggests that a normal distribution cannot be ruled out as the underlying distribution for smok1 in the nicotine patch only category. The result of the Shapiro-Wilk test smok1 in the nicotine patch and motivational support category was not significant based on an alpha value of 0.05, W = 0.94, p = .237. This result suggests that a normal distribution cannot be ruled out as the underlying distribution for smok1 in the nicotine patch and motivational support category. The Shapiro-Wilk test was not significant for either the nicotine patch only or nicotine patch and motivational support categories of group, indicating the normality assumption is met. Homogeneity of Variance. Levene's test was conducted to assess whether the variance of smok1 was equal between the categories of group. The result of Levene's test for smok1 was not significant based on an alpha value of 0.05, F(1, 42) = 1.47, p = .231. This result suggests it is possible that the variance of smok1 is equal for each category of group, indicating the assumption of homogeneity of variance was met. Results The result of the upper-tailed independent samples t-test was not significant based on an alpha value of 0.05, t(42) = 0.25, p = .402, indicating the null hypothesis cannot be rejected. This finding suggests the mean of smok1 in the nicotine patch only category of group was not significantly higher than the mean of smok1 in the nicotine patch and motivational support category. The results are presented in Table 1. A bar plot of the means is presented in Figure 1. Table 1 Upper-Tailed Independent Samples t-Test for smok1 by group nicotine patch only nicotine patch and motivational support Variable M SD M SD t p d smok1 19.82 6.01 19.41 4.83 0.25 .402 0.08 Note. N = 44. Degrees of Freedom for the t-statistic = 42. d represents Cohen's d. Figure 1 The mean of smok1 by levels of group with 95% CI Error Bars Descriptives Introduction Summary statistics were calculated for each interval and ratio variable, and frequencies and percentages were calculated for each nominal variable split by group. Results Frequencies and Percentages The most frequently observed categories of sex within the nicotine patch only category of group were male and female (n = 11, 50%). The most frequently observed category of sex within the nicotine patch and motivational support category of group was female (n = 12, 55%). Frequencies and percentages are presented in Table 2. Table 2 Frequency Table for Nominal Variables group Variable nicotine patch only nicotine patch and motivational support Missing sex male 11 (50%) 10 (45%) 0 (0%) female 11 (50%) 12 (55%) 0 (0%) Missing 0 (0%) 0 (0%) 0 (0%) Total 22 (100%) 22 (100%) 0 (100%) Note. Due to rounding error, percentages may not sum to 100%. Summary Statistics For nicotine patch only, the observations of anx1 had an average of 43.05 (SD = 4.82, SEM = 1.03, Min = 33.00, Max = 50.00, Skewness = -0.54, Kurtosis = -0.32). For nicotine patch and motivational support, the observations of anx1 had an average of 41.27 (SD = 4.72, SEM = 1.01, Min = 34.00, Max = 50.00, Skewness = 0.21, Kurtosis = -0.84). For nicotine patch only, the observations of dep1 had an average of 37.68 (SD = 5.48, SEM = 1.17, Min = 24.00, Max = 47.00, Skewness = -0.45, Kurtosis = 0.26). For nicotine patch and motivational support, the observations of dep1 had an average of 40.18 (SD = 5.46, SEM = 1.16, Min = 30.00, Max = 50.00, Skewness = -0.18, Kurtosis = -0.75). For nicotine patch only, the observations of smok1 had an average of 19.82 (SD = 6.01, SEM = 1.28, Min = 11.00, Max = 29.00, Skewness = 0.09, Kurtosis = -1.27). For nicotine patch and motivational support, the observations of smok1 had an average of 19.41 (SD = 4.83, SEM = 1.03, Min = 12.00, Max = 29.00, Skewness = 0.13, Kurtosis = -0.75). For nicotine patch only, the observations of age had an average of 26.55 (SD = 7.97, SEM = 1.70, Min = 19.00, Max = 46.00, Skewness = 1.45, Kurtosis = 0.99). For nicotine patch and motivational support, the observations of age had an average of 27.27 (SD = 8.99, SEM = 1.92, Min = 19.00, Max = 45.00, Skewness = 1.19, Kurtosis = -0.11). When the skewness is greater than 2 in absolute value, the variable is considered to be asymmetrical about its mean. When the kurtosis is greater than or equal to 3, then the variable's distribution is markedly different than a normal distribution in its tendency to produce outliers (Westfall & Henning, 2013). The summary statistics can be found in Table 3. Table 3 Summary Statistics Table for Interval and Ratio Variables by group Variable M SD n SEM Min Max Skewness Kurtosis anx1 nicotine patch only 43.05 4.82 22 1.03 33.00 50.00 -0.54 -0.32 nicotine patch and motivational support 41.27 4.72 22 1.01 34.00 50.00 0.21 -0.84 dep1 nicotine patch only 37.68 5.48 22 1.17 24.00 47.00 -0.45 0.26 nicotine patch and motivational support 40.18 5.46 22 1.16 30.00 50.00 -0.18 -0.75 smok1 nicotine patch only 19.82 6.01 22 1.28 11.00 29.00 0.09 -1.27 nicotine patch and motivational support 19.41 4.83 22 1.03 12.00 29.00 0.13 -0.75 age nicotine patch only 26.55 7.97 22 1.70 19.00 46.00 1.45 0.99 nicotine patch and motivational support 27.27 8.99 22 1.92 19.00 45.00 1.19 -0.11 Note. '-' indicates the statistic is undefined due to constant data or an insufficient sample size. Upper-Tailed Paired Samples t-Test Introduction An upper-tailed paired samples t-test was conducted to examine whether the mean difference of smok1 and smok2 was significantly different from zero. Assumptions Normality. A Shapiro-Wilk test was conducted to determine whether the differences in smok1 and smok2 could have been produced by a normal distribution (Razali & Wah, 2011). The results of the Shapiro-Wilk test were not significant based on an alpha value of 0.05, W = 0.98, p = .490. This result suggests the possibility that the differences in smok1 and smok2 were produced by a normal distribution cannot be ruled out, indicating the normality assumption is met. Homogeneity of Variance. Levene's test was conducted to assess whether the variances of smok1 and smok2 were significantly different. The result of Levene's test was not significant based on an alpha value of 0.05, F(1, 86) = 0.02, p = .886. This result suggests it is possible that smok1 and smok2 were produced by distributions with equal variances, indicating the assumption of homogeneity of variance was met. Results The result of the upper-tailed paired samples t-test was significant based on an alpha value of 0.05, t(43) = 6.53, p < .001,="" indicating="" the="" null="" hypothesis="" can="" be="" rejected.="" this="" finding="" suggests="" the="" difference="" in="" the="" mean="" of="" smok1="" and="" the="" mean="" of="" smok2="" was="" significantly="" greater="" than="" zero.="" the="" mean="" of="" smok1="" was="" significantly="" higher="" than="" the="" mean="" of="" smok2.="" the="" results="" are="" presented="" in="" table="" 4.="" a="" bar="" plot="" of="" the="" means="" is="" presented="" in="" figure="" 2.="" table="" 4="" upper-tailed="" paired="" samples="" t-test="" for="" the="" difference="" between="" smok1="" and="" smok2="" smok1="" smok2="" ="" ="" ="" m="" sd="" m="" sd="" t="" p="" d="" 19.61="" 5.39="" 14.25="" 5.17="" 6.53="">< .001 0.98 note. n = 44. degrees of freedom for the t-statistic = 43. d represents cohen's d. figure 2 the means of smok1 and smok2 with 95% ci error bars anova introduction an analysis of variance (anova) was conducted to determine whether there were significant differences in smok2 by dep1_lev3. assumptions normality. the assumption of normality was assessed by plotting the quantiles of the model residuals against the quantiles of a chi-square distribution, also called a q-q scatterplot (decarlo, 1997). for the assumption of normality to be met, the quantiles of the residuals must not strongly deviate from the theoretical quantiles. strong deviations could indicate that the parameter estimates are unreliable. figure 3 presents a q-q scatterplot of model residuals. figure 3 q-q scatterplot for normality of the residuals for the regression model. homoscedasticity. homoscedasticity was evaluated by plotting the residuals against the predicted values (bates et al., 2014; field, 2017; osborne & walters, 2002). the assumption of homoscedasticity is met if the points appear randomly distributed with a mean of zero and no apparent curvature. figure 4 presents a scatterplot of predicted values and model residuals. figure 4 residuals scatterplot testing homoscedasticity outliers. to identify influential points, studentized residuals were calculated and the absolute values were plotted against the observation numbers (field, 2017; pituch & stevens, 2015). studentized residuals are calculated by dividing the model residuals by the estimated residual standard deviation. an observation with a studentized residual greater than 3.29 in absolute value, the 0.999 quantile of a t distribution with 43 degrees of freedom, was considered to have significant influence on the results of the model. figure .001="" 0.98="" note.="" n="44." degrees="" of="" freedom="" for="" the="" t-statistic="43." d="" represents="" cohen's="" d.="" figure="" 2="" the="" means="" of="" smok1="" and="" smok2="" with="" 95%="" ci="" error="" bars="" anova="" introduction="" an="" analysis="" of="" variance="" (anova)="" was="" conducted="" to="" determine="" whether="" there="" were="" significant="" differences="" in="" smok2="" by="" dep1_lev3.="" assumptions="" normality.="" the="" assumption="" of="" normality="" was="" assessed="" by="" plotting="" the="" quantiles="" of="" the="" model="" residuals="" against="" the="" quantiles="" of="" a="" chi-square="" distribution,="" also="" called="" a="" q-q="" scatterplot="" (decarlo,="" 1997).="" for="" the="" assumption="" of="" normality="" to="" be="" met,="" the="" quantiles="" of="" the="" residuals="" must="" not="" strongly="" deviate="" from="" the="" theoretical="" quantiles.="" strong="" deviations="" could="" indicate="" that="" the="" parameter="" estimates="" are="" unreliable.="" figure="" 3="" presents="" a="" q-q="" scatterplot="" of="" model="" residuals.="" figure="" 3="" q-q="" scatterplot="" for="" normality="" of="" the="" residuals="" for="" the="" regression="" model.="" homoscedasticity.="" homoscedasticity="" was="" evaluated="" by="" plotting="" the="" residuals="" against="" the="" predicted="" values="" (bates="" et="" al.,="" 2014;="" field,="" 2017;="" osborne="" &="" walters,="" 2002).="" the="" assumption="" of="" homoscedasticity="" is="" met="" if="" the="" points="" appear="" randomly="" distributed="" with="" a="" mean="" of="" zero="" and="" no="" apparent="" curvature.="" figure="" 4="" presents="" a="" scatterplot="" of="" predicted="" values="" and="" model="" residuals.="" figure="" 4="" residuals="" scatterplot="" testing="" homoscedasticity="" outliers.="" to="" identify="" influential="" points,="" studentized="" residuals="" were="" calculated="" and="" the="" absolute="" values="" were="" plotted="" against="" the="" observation="" numbers="" (field,="" 2017;="" pituch="" &="" stevens,="" 2015).="" studentized="" residuals="" are="" calculated="" by="" dividing="" the="" model="" residuals="" by="" the="" estimated="" residual="" standard="" deviation.="" an="" observation="" with="" a="" studentized="" residual="" greater="" than="" 3.29="" in="" absolute="" value,="" the="" 0.999="" quantile="" of="" a="" t="" distribution="" with="" 43="" degrees="" of="" freedom,="" was="" considered="" to="" have="" significant="" influence="" on="" the="" results="" of="" the="" model.=""> .001 0.98 note. n = 44. degrees of freedom for the t-statistic = 43. d represents cohen's d. figure 2 the means of smok1 and smok2 with 95% ci error bars anova introduction an analysis of variance (anova) was conducted to determine whether there were significant differences in smok2 by dep1_lev3. assumptions normality. the assumption of normality was assessed by plotting the quantiles of the model residuals against the quantiles of a chi-square distribution, also called a q-q scatterplot (decarlo, 1997). for the assumption of normality to be met, the quantiles of the residuals must not strongly deviate from the theoretical quantiles. strong deviations could indicate that the parameter estimates are unreliable. figure 3 presents a q-q scatterplot of model residuals. figure 3 q-q scatterplot for normality of the residuals for the regression model. homoscedasticity. homoscedasticity was evaluated by plotting the residuals against the predicted values (bates et al., 2014; field, 2017; osborne & walters, 2002). the assumption of homoscedasticity is met if the points appear randomly distributed with a mean of zero and no apparent curvature. figure 4 presents a scatterplot of predicted values and model residuals. figure 4 residuals scatterplot testing homoscedasticity outliers. to identify influential points, studentized residuals were calculated and the absolute values were plotted against the observation numbers (field, 2017; pituch & stevens, 2015). studentized residuals are calculated by dividing the model residuals by the estimated residual standard deviation. an observation with a studentized residual greater than 3.29 in absolute value, the 0.999 quantile of a t distribution with 43 degrees of freedom, was considered to have significant influence on the results of the model. figure>