Hi, could somebody with an advanced understanding of statistics please point me in the right direction?
I have a question relating to the interpretation of confidence intervals generated from data demonstrating a logarithmic distribution on excel. As a disclaimer, this is 'getting into the weeds' territory, but for a variety of reasons it is important to identify the upper and lower bounds of our estimates.
I am using a reagant tests ('BART') to estimate the population of bacteria present in a given sample of water. The tests will generate an estimate of the number of bacteria present in the sample in units of cfu/ml, based on the number of days before a reaction occurs.
I'm not certain of this, but it seems that the estimates generated using this method have a logarithmic distribution. It it appears to be skewed to the right ('Skew' function yields '2' in Excel), and this is consistent given that the nature of microbial growth is exponential. For example  a reaction after 1 day may indicate that 500,00 cfu/ml are present, but a reaction on day three indicates that only 35,000 bacteria are present.
I'd like to give an average of the number of bacteria present, and I realize a confidence interval would be necessary. While four samples are not a robust sample size, some results replicate quite well with only one outlier (for example: 9,000, 9,000, 9,000, 35,000 cfu/ml).
Would the confidence interval generated using this approach (logarithmic) be more accurate? And if so, how do I calculate the 'real' confidence interval using the log distribution? I have done this so far by summing the logarithm of the average and confidence interval, and then raising 10 to this power (undoing the log). once I have this value, I subtracted the calculated average.
The 'Exact Test' and Chi Squared both seem like potential alternatives, but do not seem to apply to this type of data (non categorical).Any help or examples of a viable approach would be greatly appreciated. A screen shot of my excel sheet is attached with one control group highlighted. The standard deviation, Coefficient of variation, average, and confidence interval are calculated in blue for the raw data, and in green for the logarithmic data.
Thank you.
I have a question relating to the interpretation of confidence intervals generated from data demonstrating a logarithmic distribution on excel. As a disclaimer, this is 'getting into the weeds' territory, but for a variety of reasons it is important to identify the upper and lower bounds of our estimates.
I am using a reagant tests ('BART') to estimate the population of bacteria present in a given sample of water. The tests will generate an estimate of the number of bacteria present in the sample in units of cfu/ml, based on the number of days before a reaction occurs.
I'm not certain of this, but it seems that the estimates generated using this method have a logarithmic distribution. It it appears to be skewed to the right ('Skew' function yields '2' in Excel), and this is consistent given that the nature of microbial growth is exponential. For example  a reaction after 1 day may indicate that 500,00 cfu/ml are present, but a reaction on day three indicates that only 35,000 bacteria are present.
I'd like to give an average of the number of bacteria present, and I realize a confidence interval would be necessary. While four samples are not a robust sample size, some results replicate quite well with only one outlier (for example: 9,000, 9,000, 9,000, 35,000 cfu/ml).
Would the confidence interval generated using this approach (logarithmic) be more accurate? And if so, how do I calculate the 'real' confidence interval using the log distribution? I have done this so far by summing the logarithm of the average and confidence interval, and then raising 10 to this power (undoing the log). once I have this value, I subtracted the calculated average.
The 'Exact Test' and Chi Squared both seem like potential alternatives, but do not seem to apply to this type of data (non categorical).Any help or examples of a viable approach would be greatly appreciated. A screen shot of my excel sheet is attached with one control group highlighted. The standard deviation, Coefficient of variation, average, and confidence interval are calculated in blue for the raw data, and in green for the logarithmic data.
Thank you.
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