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If you are going to be doing leisure or social science research, these are the major data analysis techniques to use:
– Chi-square test. This test, signified by the symbol X2, is used to show the relationship between two nominal variables, which are variables that describe something, such as one’s gender or age. This test is designed to show if the relationship is significant or not, and if so, the null hypothesis of no difference will be rejected. The test is done by examining the counts or percentages in the cells of a table and comparing the actual counts with the expected count which would occur if there was no difference according to the null hypothesis, such as if there was an equal number of people of two different racial groups in a study of participation in two different leisure activities. One would expect the same number of members of different racial groups in each activity if there is no difference, but if one activity is more popular with one group and the other activity is more popular with the other group, then there would be a difference. The Chi-Square test involves summing up the differences between the counts or percentages and the expected counts or percentage, so that the larger the total, the bigger the Chi-square value would be. In other words, this value results from summing up the squared values of the differences.
– T-Test. This test involves comparing two means to determine if the differences between them are significant, based on rejecting the null hypothesis of no difference and accepting the alternative hypothesis that there is a difference. For example, the test might look at the average income of people participating in different recreational activities, such as golf versus bowling, to see if there is a difference between them, which might be expected, since golf is a fairly expensive sport while bowling is a relatively inexpensive sport. The test can be either used as a paired samples test or an independent samples test. In the paired samples test, the means of two variables, such as two different activities for everyone in the whole sample are compared, such as the amount of time spent on the Internet and the amount of time watching TV. By contrast, in the independent samples test, the means of two subgroups in the sample are compared in relation to a single variable to see if there are any differences between them, such as the amount of time teenagers and their parents spend on the Internet.
– One-way analysis of variance or an ANOVA test. This test is used to compare more than two means in a single test, such as comparing the means for males and females in participating in a number of activities, such as eating out, spending time on the Internet, watching TV, going shopping, participating in an active sport, or going to spectator sports. The test examines whether the mean for each variable in the test is different from the overall mean, which is the alternative hypothesis, or is the same as the overall mean, which is the null hypothesis. The test not only considers the differences between the mean for the overall population and for the different subgroups, but it considers the differences which occur between the means, which is called the “variance.” This variance is determined by summing the differences between the individual means and the overall mean to get the results which are interpreted in this way. The higher the variance between groups, the more likely there is a significant difference between the groups, whereas the higher the variance within groups, the less likely there is a significant difference between the groups. The F score represents the analysis of these two difference measures of variance to show the ratio between the two types of variance – the between groups variance and the within groups variance. Also, one needs to take into consideration the number of groups and the size of the samples, which determine the degrees of freedom for that particular test. The result of these calculations produces an F score, and the lower the F score, the more likely there is a significant difference between the means of the groups.
– Factorial analysis of variance. This is another ANOVA test, which is based on analyzing the means of more than a single variable, such as examining the relationship between participating in an activity and the gender and age of the participants. In effect, this test involves cross-tabulating the means of different groups to determine if they are significant by comparing both the means of the groups and the degree of spread between the groups. Thus, in this test too, the degrees of freedom are taken into consideration along with the sum of the squares to produce a mean square and then an F score. Again, the lower the score, the greater the likelihood of a significant difference between the group means.
– Correlation coefficient (usually designated by “r”). This coefficient ranges from 0 when there is no correlation to +1 if the correlation between two variables is perfect and positive or -1 if the correlation between the variables in perfect and negative. The numbers between 0 and +1 or -1 indicate the degree of positive or negative correlation between the variables. The size of r is determined by calculating the mean for each variable and examining how far each point of data is on the x and y axis from the mean in a positive or negative connection. Then, one multiplies the two differences, and takes into consideration the size of the sample to determine how significant r is at a predetermined level of significance (usually the 95%or 5% level).
– Linear regression. This approach is used when there is a sufficiently consistent correlation between two variables, so that a researcher can predict one variable by knowing the other. (Veal, p. 358). To this end, a researcher creates a model of this relationship by developing an equation that states what this relationship is. This equation is generally stated as y = a + bx., in which “a” is a constant, and “b” refers to the slope of the line that best indicates the fit or correlation between the two variables being measured.
– Non-linear regression. This refers to a situation that occurs when two variables are not related in a linear way, so that a single straight line can’t be used to express their relationship. Such a non-linear regression might occur if there is a curved relationship, such as when there is a gradual growth of interest in an activity, followed by a spurt of enthusiasm, and then a plateau of interest. Another example might be a bimodal distribution or cyclical relationship, such as when there is a pattern of interest in an activity twice a year or an up and down growth of interest, such as if there is a spike of interest following the introduction of a new program several times a year, followed by a decline of interest until a new program is introduced again.
write by Fergus