Hi, everyone
When I try to make a histogram with error bar, I need the average and standard deviation(SD) calculated for one set of data first, and the error bar is represented by SD.
However, what is the error bar of Rate(e.g. morbidity)? For example, I decide to compare the incidence of a disease in two areas(A city and B city). In A city, out of 1000 individuals collected, 25(2.5%) are attacked by the disease. In B city, out of 1100 individuals collected, 10(1%) are attacked by the disease. Then, chi-squared test is used to compare the morbidities, and the P value is 0.00817. Here is the figure.
How to add error bar to the histogram of morbidity? I'm confused what the error bar of Rate means.
Thank you in advance!
I am not quite sure whether you want the bars to represent the standard deviation or the standard errors. However, if I get your question right, this should not even matter.
I would say, for example, that you calculate the upper and lower limits of the SE bars as follows:
LOWER = [FRACTION- SD/sqrt(n)] * 100
UPPER = [FRACTION + SD/sqrt(n)] * 100
Note that FRACTION, e.g., stands for 0.50 instead of 50%, calculated by dividing the number of disease-attacks by the overall population. You would not have to multiply with 100 in the latter case.
You would calculate the 95% confidence intervals similarly:
LOWER = [FRACTION - 1.96 * SD/sqrt(n)] * 100
UPPER = [FRACTION + 1.96 * SD/sqrt(n)] * 100
Hope this helps.
Hi. Yes, let me try to clear up some of the confusion:
First point: the plot you made is not a histogram, but a bar plot of proportions.
Secondly, (EDITED OUT)
You _can_ calculate a confidence interval for a proportion. If so, make sure you use a method appropriate for proportions. In this case, you probably want to use a "multinomial confidence interval for proportions" so it takes into account both cities simultaneously. There are different methods for this.
Finally, I see that there are two stars on the one bar. What analysis did those come from?
References:
Confidence intervals for proportions
http://rcompanion.org/handbook/H_02.html
Multinomial test example with plot and confidence intervals
http://rcompanion.org/handbook/H_03.html#_Toc459550718
As a short side note on Salvatore's answer:
You can calculate a standard deviation, and the variance, of a proportion. However, its meaning/ interpretation is not that insightful. Here is a researchgate link to the respective question: https://www.researchgate.net/post/Can_standard_deviation_and_standard_error_be_calculated_for_a_binary_variable
also here: https://www.researchgate.net/post/Meaning_of_SD_of_dummy_variables
Dear Salvatore and Hendrik,
Thanks for your helpful suggestions.
1) I'm so sorry that I mistook histogram for bar plot. How foolish I am!
2) The two stars mean that the result is highly significant(P=0.00817). If I am wrong again, please point it out and correct me.
3) I can't have the SD from the data. Hence, SD/sqrt(n) can't be used.
4) Indeed the suggestions given by Salvatoreand Hendrik clear up my confusion.
http://rcompanion.org/handbook/H_02.html
https://www.researchgate.net/post/Can_standard_deviation_and_standard_error_be_calculated_for_a_binary_variable
Hua Gai,
No worries on the "histogram" / "bar plot" terms.
On the stars, you are correct. But I was wondering what kind of analysis you used to determine the p-value... The chi-square test was a test of association including CityA / CityB and Disease/NoDisease ?
Hi, Salvatore
My purpose was to investigate whether the distribution of the patients differed in two cities. My data is tabulated as follows. This link may make my interpretation more clear:http://math.hws.edu/javamath/ryan/ChiSquare.html
Then, using SPSS, the chi-square test was carried out.
- Badges
- Science topic
- Similar topics
- Chemistry
- Biochemistry