We want to know whether male or female nurses at a local hospital are more likely to gain promotions within the first 2 years of employment within a confidence level of 95 % (α
.05). In other words are the promotions independent of gender? Is there a statistically significant relationship between gender and promotions (
) or are these differences simply due to chance (
)? The data are provided below.
The data shows that there are 237 nurses at this hospital, 117 of whom are female while 120 are male. At first review of the data it appears that male nurses have received more promotions (37) than female nurses (46). The null hypothesis is that the two variables are independent, that the likelihood of getting promoted is the same for males and females.
Table of observed and expected values
As with all
testing we need the observed and expected values. Expected values are calculated based on the row and column totals from the table. With two variables the expected value for each cell of the table can be calculated using the following formula:
(Row Total
Column Total)/Total N count for overall table
There is no Excel function that will do these calculations automatically but you can input them as formula for each cell. By using CHISQ.TEST in Excel we generate a p-value of 0.171 (B10), but we must refer to the number of degrees of freedom to be totally correct. There is no Excel function that will automatically calculate this so you can input the formula
In this table, there were two rows and two columns. Therefore, the number of degrees of freedom is one. We can now state that the p-value was calculated with one degree of freedom as 0.17 (B10); this value exceeds our pcritical of 0.05. Our results are not statistically significant; we cannot reject the null hypothesis. The relationship between gender and promotions is not significant, and so we can assume is these results are simply due to chance. For reporting we may also want to report the actual
test statistic. Unfortunately Excel does not provide this to the user in any simple way. Once again you need to input a formula:
To formally report our results, we would say “no statistically significant relationship was found between gender and promotions,
(1)
1.88, p
0.17”.