My research objectives(proposed) and the statistical analysis I have planned are as follows :
1.To examine if there are any significant differences in connectedness to nature, subjective well-being environmental identity and pro-environmental behavior between casual urban bird-watchers and non bird- watchers.
statistical analysis : T-test or Welch's t-test
2.To examine the nature and strength of relationship between
a. Connectedness to nature and subjective well-being
b. Connectedness to nature and environmental identity.
c. Connectedness to nature and pro-environmental behavior.
d. Environmental identity and subjective well-being.
e. Environmental identity and pro-environmental behavior
Note: If statistically significant differences are found between the two groups, then, the nature and strength of relationship between the variables under research objective “2” (a. to e.) will be examined separately for the urban bird-watchers and non bird-watchers. But if the differences between the two groups stand out as insignificant, then they shall be treated as a single pool of research participants.
Statistical Analysis : Pearson product moment correlation, because the variables - connectedness to nature, environmental identity,pro-environmental behavior, subjective well-being are all going to provide me with test scores, so they are interval variables. But, yes, the two groups - urban bird-watchers and non-watchers are categorical variables. But I am checking the nature and strength of relationship between interval variables (connectedness to nature and subjective well-being , for example). So can I use Pearson correlation , provided the data is found to be linear and normally distributed?
3.Connectedness to nature and environmental identity as predictors of subjective well-being and pro-environmental behavior.
this again will be examined either for the 2 groups separately or as one sample depending upon the result of the t-test
Statistical analysis - Multivariate multiple correlation
Am I being right in my decision?
Pearsons product Moment correlation coefficient and Chi- square test can do in testing the significance unless the sample size is low t-test may not be convenient here
My guess is that the Wilcoxon rank-sum test would be adequate for testing differences between the two groups. The number of intervals in your scales is important and I assume that you have around 5. For 1) I would run this test for each variable, adjusting for the four comparisons by setting the critical p-value to 0.0125 (if you are happy with a family-wise Type I error rate of 0.05). For 2) the product-moment correlation would be adequate, as already suggested, but again an adjustment for the multiple comparisons is recommended. For 3), you might try two nonparametric linear models, one for each response variable. It is necessary to justify why you have chosen the particular relationships that you are testing, or reviewers may suspect that you have just tested all possible relationships and only reported some.
One aspect of Pearson's correlation coefficient is that it assumes a linear relationship (in fact it assumes that the variables are normal). It is advisable to plot the data in histograms and scatter diagrams. If the histograms do not seem normal and/or the points do not form a straight line, a nonparametric correlation coefficient such a Kendall's Tau or Spearman's Correlation Coefficient may be more appropriate. Even so, Kendal and Spearman assumes the relationship is monotonic. If Y increases as X increases up to a point and then decreases if X increases further, either correlation coefficient may indicate that there is "no correlation".
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