For plotting and analysing fluorescence intensities of control and treated samples on a flow cytometry histogram, different MFIs (Median, Geometric mean and Arithmetic mean) have been used by researchers . Which one should be used when comparing MFIs for detecting phenomena like ROS, RNS, Mitochondrial membrane potential and autophagy in cancer, diabetic and Glaucoma cell model.Why Median FIs is recommended by many researchers.
Dear Abhinav Prasad
I think that the best answer can be found in the following essay that provides nine differences between arithmetic mean Vs. the geometric mean.
https://www.wallstreetmojo.com › geometric-mean-vs-arithmetic-mean
Best regards
Depends, first find out mechanism and span of data (i.e. linear span or logarithmic span) than you can yourself understand which mean would be a better representation, with basics and a little "intuition" of statistics.
Suppose, hair growth at various stages are are relerated and retarded by processes that are almost gaussian-distributed. like simple probability law, these normal distribution random effects are multiplicative on long run, and hair/cilia/appendage length for biological specimen follows lognormal distribution. since there are too large hairs that can deviate the mean significantly even if present in small amount, you should choose geometric mean. if too small hairs are also present in small numbers that can deviate the geometric mean as well, you may use median, Target is to find a representative mean that is robust.
now find out what are the factors that deviate electronic properties of mitochondria from average value or what is the correlation between size, chemical composition of potential irritant and phagocytosis tendency of leukocytes . Is the variation linear or logarithmic or exponential in scale? are there insignificant number of outliers that can drastically alter the chosen mean? You have to choose arithmetic, geometric, harmonic mean/median/mode from these considerations.
Geometric mean
Defined only by a set of numbers in which all terms are positive. It is also often used in cases where data are values that are supposed to multiply together, or those data of an exponential nature, such as exponential growth of population groups, or to calculate the adjusted interest rate over several years. The geometric mean is one of the three Pythagorean averages, in addition to the arithmetic mean and the harmonic mean.
Arithmetic mean
It is also called the arithmetic mean, and it is the most used measure. It is a value that mediates a group of numbers, which is calculated by adding those numbers and dividing the result by their number, and by its value, it can judge the rest of the group's values. As for its uses, it is so many that it is used in different life applications, such as: calculating the average spending during the month, and calculating the average time taken to do something
Harmonic mean
It is one of the measures of central tendency, which is the reciprocal of the mean of the inversions of these values. It is preferred to use it over the rest of the averages in the case of finding the velocity and change rates. It cannot be used if one of these values is equal to zero. Methods for calculating the harmonic mean: -1- Calculating the harmonic mean From ungrouped data H = n /? (1 / X) where n represents the number of variables X represents the value of the variable.
The geometric mean of a set of numbers is less than or equal to its mean, but it is greater than or equal to its harmonic mean
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