Statistical Data Analysis

All data were analyzed at a predetermined confidence level ( =0.05) using the Statistical Analysis Software System, SAS version 9.1, 2003 (SAS Institute, Cary, NC).

31 3.2.3.1 Analysis of Variance

Analysis of variance, often abbreviated as ANOVA, is a technique that compares the means from several samples and tests whether they are all (within experimental error) the same, or whether one or more of them are significantly different (O‟Mahony 1986). Analysis of variance (ANOVA) was used to determine if differences lie among the eight pre-workout drink formulations and/or among the eight post-workout drink formulations in terms of acceptability of each sensory attribute, and overall liking.

To conduct a valid analysis of variance, the following assumptions must be satisfied:

samples taken under each treatment must be randomly picked from their respective populations, the treatments must be independent of each other, samples of scores under each treatment must come from normally distributed populations of scores, and samples of scores under each treatment must come from populations with the same variance (homoscedasticity) (O‟Mahony 1986). ANOVA provides evidence that a significant difference exists, but does not give an indication of how the treatments are different.

Tukey HSD (honest significant difference) is an adjustment that was used, so that after all comparisons, both simple pairwise and complex, the overall level of significance was 0.05.

Tukey (1953) proposed a multiple-comparison method for pairwise comparisons of k means and for simultaneous estimation of differences between means by confidence intervals with a

specified confidence coefficient (1- ) (Gacula and Singh 1984). If n observations are taken in each of k samples and the analysis-of-variance F test is significant, the critical difference to be exceeded for a pair of means to be significantly different is the so-called honest significant difference (HSD), where

HSD = Q ,k,v(√Mse/n).

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Table 4 represents a one-way analysis of variance model. The DF column is known as the degrees of freedom for respective SS (sums of squares); the MS column has the mean squares. A SS divided by its DF is called the mean square. The MS is an estimate of the variance

contributed by its source to the total. The test statistic for testing the equality of treatments effects is the F ratio, or MStr/MSe. The observed F ratio is compared with percentiles of the F distribution. The null hypothesis of no treatment differences is rejected if the observed F ratio is greater than the tabulated F value at the desired significance level (Gacula and Singh 1984).

Table 4. One-Way Analysis of Variance Model Source of

MANOVA (multivariate analysis of variance) is a post-ANOVA technique that was used to determine if significant differences existed among formulations when all of the sensory attributes were compared simultaneously. Descriptive Discriminant Analysis (DDA) was used to determine which of the attributes contributed to the differences among the eight pre-workout and eight post-workout sports drink formulations.

MANOVA and Discriminant Analysis are the preferred methods for determining differences between samples. The chief value of MANOVA is to determine whether treatments applied to a product cause significant differences, and Descriptive Analysis tells the investigator whether certain variables combined are correlated with classes (Piggott 1986). The results of MANOVA provide a single F-statistic, based on Wilks‟ lambda ( ), which assesses the

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influence of all descriptors simultaneously. A significant MANOVA F-statistic (due to a small Wilks‟ lambda) indicates that the samples differ significantly across dependent variables (Lawless and Heymann 1998).

Techniques of Descriptive Discriminant Analysis (DDA) are closely aligned to the study effects determined by a multivariate analysis of variance (Huberty 1994). In DDA, the basic question of interest pertains to grouping variable effects on the multiple outcome variables or, to group separation or group differences with respect to the outcome variables (Huberty 1994).

3.2.3.3 Logistic Regression

Logistic regression, or logit analysis, uses a regression model to fit a categorical

dependent variable. In its most widely used form, the dependent variable is dichotomous (yes/no) and the independent variables are quantitative or categorical. Logistic regression involves the use odds and odds ratios. The odds are an expression of the likelihood of an event happening

compared to the likelihood of that event not happening. An odds of less than one corresponds to a probability of less than 0.5, and an odds greater than one corresponds to a probability above 0.5. Odds are used instead of probabilities because they are on a more sensible scale for multiplicative comparisons, they are directly related to the parameters in the logit model, and they are less sensitive to changes in the marginal frequencies. The odds ratio, not to be confused with the odds, is the proportional change in the odds per unit change in Xi. Logistic regression analysis was used to predict both product acceptability and purchase intent based on the odds ratio point estimate.

3.2.3.4 McNemar Test

The McNemar test is one way of comparing proportions from two dependent samples (in this case, responses before and after consumers had been informed of the exercise enhancing

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benefits) using binary response variables. The test follows a chi-square distribution with df=1 (Agresti 1996). A 95% confidence interval was calculated using marginal sample proportions (p+1 + p1+), which can be used to estimate the actual differences in the means of purchase decision responses (Beckley and others 2007).

In order to calculate the sample proportions (pij), the equation pij = nij/N

was used, where n_ij is the number of consumers making response i and response j after knowing the “fact” about exercise enhancing benefits, and N represents the total number of responses from consumers. Next, the 95% confidence interval for the difference in proportions was calculated using the equation

(p₊₁ – p₁₊) + z _/2(ASE)

where (p+1 – p1+) represents the difference in proportions between consumers who answer yes after knowing the fact (p₊₁) and those who answered yes before knowing the fact (p₁₊); the term z _/2 equals 1.96 and represents the standard normal percentile having a right-tailed probability of

/2; ASE is the estimated standard error for the proportion difference and was calculated using the equation

ASE = ([p1+(1–p1+)+ p+1(1–p+1)–2(p11p22–p12p21)]/N)^1/2

where p11 indicates the number of consumers who answered yes both before and after knowing the fact, p₂₂ represents the number of consumers who answered no both before and after knowing the fact, p12 indicates the number of consumers who answered yes before and no after knowing the fact, and p₂₁ represents the number of consumers who answered no before and yes after knowing the fact (Beckley and others 2007).

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In this study, the McNemar test was used to determine changes in consumer purchase decision before and after consumers were informed of the exercise enhancing benefits of the sports drinks.

3.3 Results and Discussion