Module 4

• Mean:
  • Sum of all observations/no of observations
• Median:
  • It is the value which occupies the middle position when the data is
    arranged in ascending or descending order
  • Not all individual data is considered
  • We are just concerned with value in middle position.
• Mode:
  • It is most frequently occurring value in the distribution
  • It is not concerned with all individuals.

Extreme value/outlying value in the distribution /outlier:

• Means a value, which is either much larger or much smaller than the rest of the values in the distribution.
• For example: 110, ……140, 160, 165, 155, 170, …195. 110 and 195 are outlier.
• If there is extreme value means will be affected as we have to include it while calculation
• Whenever, extreme value or outlier is present in distribution, mean is the measure of central tendency
• Extreme value will pull the value towards itself
  • If small: lower down the mean in the data
  • If large: increase the mean in the data
• Q statistics or Q test is used to know if a value is outlier. It is used for identification and rejection of an outlier. Then we can either include or exclude in the analysis.
• If extreme/outlier is NOT present, we get normal distribution curve.
• As per presence of outlier:
  • Present: Asymmetrical or skewed distribution
  • Absent: Normal or symmetrical distribution.

1. Range: It is the difference between the maximum and the minimum values.
2. SD: formula needs to be seen
   • It is also called root mean square deviation (RMS Deviation)
   • SD α 1/n i.e. SD is inversely proportional to the size of the sample or total number of observations. The SD increases, as the number of observations decreases (from formula)
   • Each of 10 babies born on a day had birth weight of 2.8 kg. What is the SD in the birth weight?
     • The answer is zero. Here the mean = 2.8, range =0, SD=0, variance = SD 2 = 0
     • In this situation, the value of variation is zero i.e. any measure of deviation will be zero.
3. Variance: It is SD^2
4. Standard error
5. Coefficient of variation

It is practiced at two different stages

1. At selecting subjects/recruitment called random selection. For example, class of 50 people, I need to recruit 10 persons for my study
   • First approach: people in front row: non random selection as each member is not given chance on back benchers had no chance
   • Second method: lottery method: random selection as each member had chance of being included
2. At the time dividing study to two group called random group allocation: out of 10 people I need to divide into 2 groups
   • Non-random group: People sitting to left drug A and to right to drug B
   • Randomization: computer generated list for drug A and drug B

Important note: I may have done random selection, but randomization means in second stage at the time of group allocation.

1. Single blinding: Study subjects are not aware of group allocation
2. Double blinding: Study subjects and investigator are not aware what is group A and what is group B. This is most common form of blinding.
3. Triple Blinding: Study subjects, investigator and data analyst are not
   aware of groups A and B. Entire study is coded and once study is over,
   it will be decoded. This is the best form of blinding.