The Arching Rainbows

The arching rainbows are perhaps the most frequently seen types seen in the archipelago. There are 7 members of this group as follows:

For the members of this group, the primary trait is the same, and other various features are similar. Each of these rainbow types has itʻs own page on this website. On this page, the sign data for the group as a whole is shown in the table below. There are 18 signs/omens that appeared within the sources that were analyzed. Each of these signs are important because, the breadth of contexts in which these types of rainbows were shown by the various authors can be understood. Examining the data, it can be seen that the signs concerning a presence appeared most often (78). The data of all the sign groups is interesting, however, an interesting question perhaps, from the mathematical perspective, is the total (78) of the signs concerning a presence greater than the total of each of the other sign groups? How would these totals be measured against each other? The thing that is needed is method to perform this measurement. Mathematics has an appropriate method, namely the Chi-square goodness-of-fit test.[1] This test was used as a way to understand the totals of the sign groups in relation to each other. If the totals of the groups were the same, then it would be expected that the frequency of appearence of the signs of each group would be the same. See the appendix tab for links to sites explaining the Chi-square goodness-of-fit test in greater detail.

The signs of the arching rainbows

Translation Key

Since the total of all the sign groups is 171, if all the appearances of these types of rainbows were equally distributed across the sign groups, the expected data would be 171/5 or about 34 for each group. The null hypothesis is that there is no difference in the totals for all the groups.The result of the Chi-square goodness-of-fit test is that the null hypothesis is rejected and therefore one or more of the groups is significantly different than the others from a mathematical perspective.[2] Which group(s)? Perhaps it is the group of signs concerning a presence. The Chi-square goodness-of-fit is western mathematical test, and it provides a methond for understanding the data of these sign groups. However, there is a need to also closely examine all the signs for each type of rainbow, each are important. However the sign that appears most often for a particular type of rainbow is very interesting. The preponderance of appearances perhaps indicates the preponderance of thought concerning the most important sign of a particular rainbow type.

[1] Frederick J. Gravetter and Larry B Wallnau. 2013. Essentials of Statistics for the Behavioral Sciences. 8. Wadsworth Cenegage Learning. ʻaoʻao 518. E nānā ʻia ka Pākuʻina 1 no kekahi hoʻākāka ʻana e pili ana i kēia hōʻike makemakika.

[2] ʻO ka hopena o ka hōʻike haʻihelu hoʻoili: χ2 (4, n = 171) = 89.67, p < 0.001. No laila, hōʻole ʻia ke kuhiakau kūpapa.