Mean and Median Significance

When the mean and the median are significantly different, it usually means that the mean is being driven by outliers. The first thing to do would be to make a histogram of your data. It is not going to be normal. You probably have two distributions, one that has more data points, a tight distribution (small sigma) and is centered around "no significant change" and another distribution that has a very large sigma.

I think this would make sense given what you are studying. Most announcements are snoozers and are ignored by investors. A few are big and cause a significant change in how investors see the company.

Thanks engineer, appreciate that

Hi Engineer,

I have another query:

- I have separated my sample into different types of announcements and calculated the market reactions for each.
There are two particular samples; one sample provokes a positive and significant market reaction, the other positive but not significant.

However, when I then test the significance between the two samples I find the different to be not significant. Why you this be? And how would you interpret something like this?

Many thanks, again

I'm not sure I understand what you are telling me. It sounds like you have two distributions that are significantly different. What does "when I then test the significance between the two samples I find the different to be not significant" mean? Some questions:

- Are the two distributions normal or close to normal? What are the means and standard deviations?
- What is your working hypothesis (in words, not in statistical terms)?
- How big is your sample size for each distribution?

Hi Engineer,

Apologies for unclear exp.

Hopefully this time- I have two sets of data, which are cumulative abnormal returns (CARs) for each sample. I then have taken the mean of each of these and tested them using t-stat and p-value. One sample (call it 'A') has a mean which is significantly different from zero; B is not significantly different from zero. (The medians of each, using a z-stat are not significant.) A is a sample of 138 CARS; B is 220.

I then take the 138 and 220 CARs and, in MS Excel, run "t-test: two sample assuming unequal variance". This produces a two tailed p-value of 0.178, therefore not significant.

I hope this is understandable- does this make sense?

Thanks,

Kind of. Do you have the mean and standard deviation for each group?

Hi,

I don't

I have a number of companies that I am examining how their stock price reacts to certain announcements. I have a range of stock prices for each company for a number of days pre-and post-announcement, centring on the announcement.

For each company, I take the mean of all of the stock prices on all pre-and post-announcement days (inc the day of the announcement).

For announcement type A I have 138 companies; 220 for companies for announcement type B. Now taking only announcement type A, I find the mean is positive and significant. For announcement type B, I find stock price reaction is not significant. Therefore, I can say that there is a stock market reaction to announcement type A, but not for type B.

I then want to test if the difference between announcement type A and type B are significantly different. I do this using the excel tool.

The results indicate that the difference is no significant.

Does this make clear the approach I am taking?

Apologies I'm not hitting the nail on the head!

I think I see your problem. Here is how I would analyze this data.

- For each company, take the difference between the pre and post stock price. You might need to average a few days before and a few days after to get better data. Next, divide each number by the original price to get the percentage move. Absolute move is not the correct metric for stock prices. Do not combine information across multiple companies.
- Create a histogram with these data points and study that plot. It might tell you something that you can't see with means and standard deviations.
- For each of your two data sets, compute a mean and standard deviation. Are the distributions normal or approximately so?
- If the distributions look approximately normal, you can do a student t-test to see if they are significantly different. If not, you can use more advanced tests.

Brilliant, thanks again for your help.

Cheers,