Unfortunately the statistical analysis supporting that point sounds incorrect to me.
Their evidence consists of:
1. A claim that the mean return on equity of the previous CEO of -0.68 in the "savior" case (white CEO following a minority CEO) is significantly different from a value of 0.11 in the control case (white CEO following a white CEO). This can't be true because the low number of samples implies standard errors of 0.66 and 0.05 for the means. I'm computing a z-score of 1.18, corresponding to a two-sided p-value of 0.24, far above the claimed p<0.01.
2. A claim that the mean return on equity of the previous CEO is correlated with a binary variable describing whether we are in the savior case. While their measured correlation coefficient of -0.13 would indeed be statistically significant if it were measuring a correlation of normally distributed data, the use of a binary variable describing unbalanced classes means that 95% of the variance is concentrated on just 5% of the data (28 samples). Bootstrapping based on the published mean and deviation of each class shows a 0.11 standard deviation of the correlation coefficient, and more importantly a p-value of 0.12 which is once again non-significant.
An interesting feature is that the standard deviation of the return on equity differs a lot between classes. I assume that this is because the returns on equity are far from being normally distributed, and indeed data from another class with just 4 samples shows an abnormally low standard deviation, letting us reject the normal distribution hypothesis with p<0.001. Most returns are very close to zero, so necessarily some are much greater than the standard deviation. A few or even just one large-magnitude return in the 28 "savior" samples would suffice to create a spurious correlation.
I would contact the authors about it, but I would like someone here to confirm if my analysis makes any sense.
Their evidence consists of:
1. A claim that the mean return on equity of the previous CEO of -0.68 in the "savior" case (white CEO following a minority CEO) is significantly different from a value of 0.11 in the control case (white CEO following a white CEO). This can't be true because the low number of samples implies standard errors of 0.66 and 0.05 for the means. I'm computing a z-score of 1.18, corresponding to a two-sided p-value of 0.24, far above the claimed p<0.01.
2. A claim that the mean return on equity of the previous CEO is correlated with a binary variable describing whether we are in the savior case. While their measured correlation coefficient of -0.13 would indeed be statistically significant if it were measuring a correlation of normally distributed data, the use of a binary variable describing unbalanced classes means that 95% of the variance is concentrated on just 5% of the data (28 samples). Bootstrapping based on the published mean and deviation of each class shows a 0.11 standard deviation of the correlation coefficient, and more importantly a p-value of 0.12 which is once again non-significant.
An interesting feature is that the standard deviation of the return on equity differs a lot between classes. I assume that this is because the returns on equity are far from being normally distributed, and indeed data from another class with just 4 samples shows an abnormally low standard deviation, letting us reject the normal distribution hypothesis with p<0.001. Most returns are very close to zero, so necessarily some are much greater than the standard deviation. A few or even just one large-magnitude return in the 28 "savior" samples would suffice to create a spurious correlation.
I would contact the authors about it, but I would like someone here to confirm if my analysis makes any sense.