Factorial ANOVA using PASW

Factorial ANOVA using PASW

Factorial Analysis of Variance (ANOVA) According to Field (2013) factorial analysis is being show to test the hypothesis whether one’s age influences his or her preference or likeness for particular music. Data on 90 participants (n = 90) grouped by age are analyzed using the statistical technique called Factorial Analysis of Variance (ANOVA). SPSS ver 21 is the statistical software used to performed the analysis. Underlying Assumptions of Statistical Test Factorial ANOVA is a statistical analysis technique or model, the use of which requires that the following assumptions are met: (a) the independent variable is nominal and that it has two or more levels; (b) the sample groups are independent; (c) the level of measurement of the dependent variable must be interval or ratio data, (d) the two or more groups from which the samples are collected are normally distributed; and (e) the groups have equal variance (StatSoft, n.d.; Laurette Education, Inc., n.d.). The data set being analyzed have met all of these assumptions. The level of measurement for the independent variables is norminal with two or more levels; the sample groups (grouped by age) are independent; the level of measurement of the dependent variable is interval or ratio data evident by the data values that range from -100 to 100; and the groups have equal variance. The equality of group variance was verified using the Levene’s Test of Equality which shows a Sig. level of .322, a value that indicates that there is no significant diference in variance given that the p-Value is (p < .05).

Research Question Is there a relationship between age and music preference? Hypotheses Null Hypothesis (H0): There is not a relationship between age and music preference. Alternative Hypothesis (HA): There is a relationship between age and music preference.

Variables Independent Variables (IV): There are two independent variables in this analysis – Age and music preference. Age has two levels – age above 40 and age below 40. In the dataset, participants that are above 40 years old are coded with the value of 1, while participants who are 40 years and younger are coded with the value of 2. Dependent Variables (IV): The dependent variable in this analysis is liking. Liking is a personal music rating scale that range from -100, which means the participant really hates the music, through 0, which means the participant is completely indifferent to the music, to +100, which means the participant loves the music very much (Field, 2013). Results As shown in Table 1, the descriptive statistics from this analysis reveals that young people (age < 40) gave high ratings to Fugazi music compared to their older (age > 40) counterparts. The mean rating given to Fugazi music by younger people is 66.2 with a standard deviation of 19.9, while the mean rating given to Fugazi by older people is -75.8 with a standard deviation of 14.3. The reverse is true for the ratings given by both groups to Garf Brooks music. The mean rating given to Garf Brooks music by younger people is -71.4 with a standard deviation of 23.7, while the mean rating given to Garf Brooks music by older people is 74.2 with a standard deviation of 22.2. Both age groups gave similar ratings to Abba music (older people: mean = 59.9, std = 19.9; younger people: mean = 64.1 , std =16.9). Table 1 Ratings by age group Music Age Group Mean (Average) Std Deviation Fugazi 40+ -75.86 14.37 0-40 66.2 19.9 Abba 40+ 59.93 19.98 0-40 64.13 16.99 Garf Brook 40+ 74.26 22.29 0-40 -71.46 23.17 Note: Std = Standard The answer showned in the error bar chart shown in Figure 1. The error bar chart, young people like Fugazi music and older people like Garf Brooks music. according to chart,both young and old people like Abba. Figure 1 Error Bar Chart

Note: CI = Confidence Interval

There are three factors being considered in interpreting the output of this analysis: the main effect of music on the ratings; the main effect of age on the ratings; and the interaction effect of music and age on the ratings. These factors are supported by the degree of freedom (df) and the F-ratios in Table 2 – Tests of Between-Subjects Effects table. Table 2 Test of Between-Subjects Effects

Source Type III Sum of Squares df Mean Square F Sig Corrected Model Intercept 39265.933 5 78530.987 202.639 .000 34339.800 1 34339.600 88.609 .000 Music Age 81864.067 2 40932.033 105.620 .000 .711 1 .711 .002 .966 Music + Age Error 310790.156 2 155395.078 400.977 .000 32553.467 84 387.541 Note: df = Degree of freedom, F = F-ratios, Sig = Significance level Table 2 shows that the relationship between type of music and preference is statistically significant ( F(2, 84) = 105.62, p < .05) which is less than the set Alpha (p = .05). It is safe to conclude that the main effect of music on the ratings is significant. Given an F-ratio of 105 and a degree of freedom (df) of 2, this output can be written as F(2, 84) = 105.62, p < .05. Age is not shown to have a statistically signficiant relationship to music preference (p=.966) which indicates that this null hypothesis should not be rejected. The interaction of music and age however is statistically significant (p

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