Reply to the chi square goodness of fit test is used in situation

1. Reply to
The chi-square goodness of fit test is used in situations where a
researcher wants to know whether the observed frequency of an
experiment is similar or different from the expected frequencies
(Gravetter et al., 2021). For example, if it is expected that a
child would prefer all colors equally, then observing a
significant preference for one particular color would be a
significant difference. This would yield a high chi-square
statistic and could be used to measure effect size. All
observations used for a chi-square test must be independent
observations, meaning that there must be only one observation
per participant.
The chi-square test for independence would be used in
situations where a researcher wants to know the relationship
between two variables, using the frequency of the observations
rather than numerical data (Gravetter et al., 2021). For example,
a researcher may want to see whether the variable of age group
and preference of color are correlated. The expectation would
be that age would have no impact on color preference, but the
observed frequency of color selection might show a difference
in relation to age group. This would be the difference in
proportion between the expected frequency and observed
frequencies. Both chi-square tests compare the difference
between observed frequencies and expected frequencies, and the
proportion of that difference and the expected frequency
(Gravetter et al., 2021). Each cell in a variable matrix must be
computed, and the sum of all of the proportions are added
together to compute the chi-square statistic (Gravetter et al.,
2021).