Independent t-test

An independent-samples t-test is suitable to compare the mean score of two different groups of subjects (Howitt and Cramer, 2008; Pallant, 2007).

Statistical significance, in this case, suggests that the two samples are different to a level which is unlikely to have happened by chance.

Independent samples t-test was used to analyse Q2 in order to identify any significant differences between respondents who have previous experiences with Austria and those who have not.

5.5.2.5.4. ANOVA

5.5.2.5.4.1. One-Way Analysis of Variance, with Post Hoc Comparisons

The one-way analysis of variance (ANOVA) also called unrelated/uncorrelated analysis of variance, is extension of the independent t-test and is used when the researcher is interested in whether the means from several (>2) independent groups differ (Ho, 2006; Howitt and Cramer, 2008). This test is known as the one-way ANOVA since there is just one independent variable; however, it is possible to extend the number of independent variables on the two-way ANOVA. The one-way analysis of variance test assumes that each of the sets of scores comes from different individuals. It is not essential to have equal numbers of scores for each set of scores (Howitt and Cramer, 2008). Essentially ANOVA compares the variation in the group means with the variation within the groups using the variance or F-ratio – “The more variation there is between the group means compared to the variation within the groups the more likely it is that the analysis will be statistically significant” (Howitt and Cramer, 2008: 314), or in other words, it will mean that the independent variable is having an effect on the scores (Field, 2005).

5.5.2.5.4.2. Two-way ANOVA

Two-way ANOVA allows the researcher to look at the individual and joint effect of two independent variables on one dependent variable (Howitt and Cramer, 2008). The advantage of using a two-way design is that the “main effect” for each independent variable can be tested and also the likelyhood of an “interaction effect” could be explored. An interaction effect exists when the effect of one independent variable on a dependent variable is affected by the level of influence of another independent variable (Ho, 2006; Pallant, 2005).

5.5.2.5.4.3. Mixed between-within subjects ANOVA There are some situations in which the combination of one-way and two-way ANOVA seems appropriate to analyse particular phenomenon (Field, 2005;

Howitt and Cramer, 2008). In this case, there are two independent variables:

one is a between subjects variable (for example, gender) and the other is a within-subjects variable (for example, time t1 and t2) and one dependent variable. This type of ANOVA is particularly appropriate for studies that investigate change over a period of time. So it will be used when a single group of participants are studied at different time points (Howitt and Cramer, 2008). SPSS allows such combination of between-subjects and within-subjects variables in one analysis (Pallant, 2005).

5.5.2.5.4.4. Post Hoc Comparison

The interpretation of the analysis of variance can be difficult when more than two groups are used (Field, 2005) because even if the overall analysis of variance is statistically significant, it is difficult to know which of the three or more groups is significantly different from the other groups (Howitt and Cramer, 2008). To obtain multiple comparisons between the different independent groups a Post Hoc comparison test needs to be performed.

“Post hoc tests consist of pairwise comparisons that are designed to compare all different combinations of the treatment groups. It is rather like taking every pair of groups and then performing a t-test on each pair of groups” (Field, 2005: 412).

As it is well known test statistics are used to show whether there is an effect in the population of interest (to a certain degree of confidence) caused by one or another factor. There are two possibilities in the real world: there is, in reality, an effect in the population, or there is, in reality, no effect in the population. Obviously, it is important that we are as accurate as possible, which is why Fisher originally said that we should be very conservative and only believe that a result is genuine when we are 95% confident that it is – or when there is only a 5% chance that the results could occur by chance.

However, even if we are 95% confident there is still a small chance that we get it wrong.

Two mistakes could threaten the results: Type I and a Type II error. A Type I could happen when the researcher believes that there is a genuine effect in the population of interest when in fact there is not. The opposite is a Type II error, which could happen when the researcher believes that there is no effect in the population when, in fact, there is (Field, 2005; Pallant, 2007).The Type I error rate and the statistical power of a test are linked. Therefore, there is always a trade-off: if a test is conservative (the probability of a Type I error is small) than it is likely to lack statistical power (the probability of a Type II error is high). Thus, it is important that multiple comparison procedures control the Type I error rate, but without a substantial loss in power. The selection of comparison procedure is affected mainly by the exact research situation and the right balance between keeping strict control over the Type I error and allowing greater statistical power. However, some general guidelines can be drawn. When the sample sizes are equal and there is a confidence that the population variances are similar then REGWO or Tukey can be used as both have good power and tight control over the Type I error rate. Bonferroni is perceived as a conservative choice, but if guaranteed control over the type I error rate is desired, then this is the most appropriate technique. If sample sizes have some differences then Gabriel’s procedure is recommendable because of the greater power it has. If, however, there is a substantial discrepancy between the sample sizes, Hochberg’s GT2 is cited as the best choice. If any doubts about the equality of population variances exist, then the Games-Howell procedure seems to be the most appropriate as it appears to offer the best performance (Field, 2005). The Scheffe test does not require equal number of cases in the groups and is also more conservative, which means that the differences are less likely to be significant (Pallant, 2005).

5.5.2.5.5. MANOVA

Multivariate analysis of variance (MANOVA) is an extension of ANOVA and applicable when more than one dependent variable is analysed (Howitt and Cramer, 2008). These dependent variables, however, should show some degree of correlation or conceptual rationale for using them simultaneously.

MANOVA calculates the group means and shows if the differences between them on the combination of dependent variables are likely to have happened entirely by chance. To do this, MANOVA combines the original dependent variables to produce a new dependent variable and shows whether there is a significant difference between the groups on this newly calculated dependent variable and also calculates the univariate results for each of the dependent variables independently (Howitt and Cramer, 2008). The advantage of using MANOVA instead of a series of ANOVAs separately for each dependent variable is the fact that MANOVA “controls” the risk of a Type 1 error (Howitt and Cramer, 2008; Pallant, 2005; Field, 2005).

MANOVA can be used in one-way, two-way and higher-order factorial designs (with multiple independent variables). However, if MANOVA is statistically significant then it is appropriate to test the significance of the individual dependent variables using ANOVAs (Howitt and Cramer, 2008).

For one-way MANOVA one categorical, independent variable and two or more continuous, dependent variables are required. For two-way MANOVA, on the other hand, two categorical independent variable and two or more continuous, dependent variables are needed (Howitt and Cramer, 2008;

Pallant, 2005).

The potential influence of socio-demographic characteristics (Q1, Q27, Q 28, Q29 and Q30), motivation (Q6) and information sources (Q12) on Linz’s “a priori” and “on-situ” cognitive and affective components was analysed using one-way MANOVA.

MANOVA was used to test whether there are significant differences among the groups of the first-time visitors, second-time visitors and frequent visitors (three independent variables) to Linz in terms of their perceptions (eight

factor analysed dependent variables) of Linz before arrival (Q3, Q9 and Q10) and after arrival (Q20 and 21) with ten factor analysed dependent variables.

Multivariate MANOVA was also applied to assess familiarity group differences across the pre-travel and “on-situ” image components of Linz. In order to conduct this test a familiarity index was calculated by combining Q3 and Q12 data and by establishing four different familiarity groups – “low familiarity”, “moderate familiarity”, “high familiarity” and “extremely high familiarity”, which represented the independent variables.

The significance of the relationship between date of arrival (Q4) and Linz’s

“on-situ” image was also analysed by using multivariate MANOVA. In addition, destination activity index was calculated as a composite of amount of events (attended/ marked down to be attended, Q17) and sights (visited/marked down to be visited, Q23). Three “destination activity” groups emerged “low activity consumption” group, “moderate activity” group and

“high activity” group, which was then included as independent variables in multivariate MANOVA to assess destination activity group differences across the on-situ image components of Linz.

Another index was calculated as a combination of Q25 (respondents’

intention to recommend Linz as a tourist destination) and Q26 (respondents’

intention to return to Linz) and called “Destination loyalty” index. From the combination of these two dummy variables three categories were established: “low loyalty” group, “medium loyalty” group and “high loyalty”

group, which served as independent variables a multivariate MANOVA analysis on the relationship between Linz’s “on-situ” image components and the loyalty index.