<p>In the previous issue we dealt with various types of study designs and calculating sample size. Once a study is initiated, data will be collected and this data will later be summarized for analysis. In this section, we will deal with various types of data and representation of data.</p></sec><sec id="sec002"><title>Types of data

A data can be broadly classified into qualitative or quantitative data. Another way is to classify the data into categorical, ordinal or numerical data.

Categorical (nominal) data These are the qualitative data wherein a given observation belongs to one of mutually exclusive category. There is no hierarchy in between different categories. If there are only two categories, then it is called dichotomous or binary data.

e.g. 1 grouping neonates into male or female

e.g. 2 causes of mortality in a neonatal ICU

Categorical data are often represented as no. of observations in each group or as percentage or proportions.

Ordinal data These are semi quantitative data. The multiple groups of observations noted will have a hierarchy in that one group means higher or lower than the other. But the gradation of scale is not a mathematical relation.

e.g. In premature infant pain profile 7 different indicators are assigned points. The total score is the sum of all 7 individual scores. The total score can vary from 0 to 21. Score of 10 indicates more pain than score of 5. But there is no mathematical relationship in between the scores. A score of 10 doesn’t mean pain is twice as much as score of 5. Ordinal data are represented by median and range but can also be represented as percentage.

Numerical data These are quantitative data. The data is recorded as continuous or discrete variable. A continuous data can assume any value while a discrete value is measured as a whole number. Age at onset of neonatal seizure is a continuous data as age can take any value. Number of neonatal seizures is a discrete data as it can only be a whole number. There cannot be 2.5 seizures in a given neonate. It can be either 2 or 3 episodes. However, the distinction between discrete and continuous data is some times blurred in presence of large number of observations.

Numerical data are represented by mean and standard deviation.

Summarizing nominal and ordinal data

These data are summarized by rates, ratios, proportions and percentages.

Let us consider an example: In a study of 100 consecutive preterm neonates enrolled in one year, following data are obtained: male = 55 female = 45 babies, RDS = in 10 babies and 1 baby with RDS died.

Proportion It is the number of observations with one characteristic divided by total number of observations

In proportion, numerator is always a part of denominator.

Percentage: is proportion multiplied by 100 and unit is %

Rate: It is similar to proportion but expressed for a specified time frame and multiplier is used.

Ratio: This differs from above in that numerator is not a part of denominator.

Graphically, nominal data can be displayed as bar chart or pie chart.

Summarizing numerical data

Data summary of a numerical data contains two parts: a measure of central tendency and a measure of degree of dispersion. The central tendency is commonly expressed as mean, median or mode. The dispersion is measured by range and standard deviation.

Let us consider an example of 10 values of mean airway pressure (MAP) in neonates ventilated for RDS.

Baby ID	MAP (in cm of H₂O)

1	10.6
2	11.8
3	10.1
4	9.6
5	11
6	17.4
7	12.2
8	11.6
9	10
10	10.6

Mean: The mean (or more precisely arithmetic mean) is the average value of observations.

In the above example

It should be noted that mean is affected by extremes of values such as 17.4. If we remove this value, then mean would be 10.8 cm of H₂O

Median: It is the middle observation for an odd number of observations and is the average of middle two observations for an even number of observations. Before obtaining this middle observation, all observations are arranged in ascending or descending order.

In the above example, first values are arranged as follows:

Sr. No.	Baby ID	MAP (in cm of H₂O)

1	4	9.6
2	9	10
3	3	10.1
4	1	10.6
5	10	10.6
6	5	11
7	8	11.6
8	2	11.8
9	7	12.2
10	6	17.4

The middle observations are 5^th and 6^th (10.6 and 11) and their average is 10.8 cm of H₂O. Hence median value is 10.8 cm of H₂O. The median is not affected by extreme values.

Mode: It is the most recurring observation in a set of observations. In the above example 10.6 is the mode as it has recurred twice while rest of the values are single. It should be noted that mode can be more than one also.

Range: It is the difference between the largest and smallest observations. It is usually represented by mentioning both extreme values rather than mentioning the difference. In the above example range is (9.6-17.4) and not 7.8 cm of H₂O.

Percentiles: Here, all observations are ranked (arranged in ascending order) and divided into 100 equal parts each part being one percentile. Then, we can describe 25^th, 50^th and 75^th percentiles. 50^th percentile is median value and 25^th – 75^th centile is called interquartile range.

The median and inter quartile range are represented graphically by box and whisker plot. The box represents the inter quartile range and whisker represents the range or 5^th – 95^th centile or 3^rd – 97^th centile. A box and whisker plot looks like this: Box and Whisker plot

eg: In their study, Upadhyay et al⁵ used box and whisker plot to represent duration of cry in neonates exposed to pain due to sampling. The box shows the inter quartile range and whisker shows range excluding outliers.

Standard deviation: It is defined as “root mean square deviation”. This is an important statistical data that measures degree of dispersion.

It can be calculated using computer. However for purpose of understanding, steps of calculation are explained here. It is calculated for the above example.

Step 1: Calculate deviation of each value from mean

Step 2: Square this value (this will remove the negative sign)

Step 3: Take mean of this squared value. This mean is called variance. Here, by definition, number of observations (n) should be used in denominator. But n – 1 (called degree of freedom) is taken as denominator as this will give more accurate estimate of true population standard deviation.

It should be noted that variance is square of standard deviation.

Step 4: Lastly take out square root of variance. This value is the standard deviation. In the above example, SD = “5.01 = 2.24 cm of H₂O.

Baby ID	MAP	Deviation (in cm of H₂O)
1	10.6	−0.8	0.64
2	11.8	0.4	0.16
3	10.1	−1.3	1.69
4	9.6	−1.8	3.24
5	11	−0.4	0.16
6	17.4	6	36
7	12.2	0.8	0.64
8	11.6	0.2	0.04
9	10	−1.4	1.96
10	10.6	−0.8	0.64
Mean = 11.4

Coefficient of variation: It is defined by the expression

This represents the relative size of standard deviation to mean. This is expressed as percentage in contrast to standard deviation which retains same unit as the original data. This has an advantage. By adjusting for scales, the dispersion of two variables can easily compared by CV than by SD.

Normal distribution

This is an important concept in statistics. When any biological parameter is measured and plotted, it shows a wide variation with a tendency of values to cluster around a central value. The extreme a given value is from this central value, less frequent is its occurrence in the population. This distribution is called Gaussian or normal distribution. The other types of distributions include binomial and Poisson distribution and will not be discussed. Fig 1The normal distribution curve

Characteristics of normal distribution

The curve of normal distribution is symmetric bell shaped one.

The normal distribution has two essential parameters - mean and standard deviation. The value of these two will determine how much narrow or wide the curve is.

68.3% of the area under the curve lies within mean + 1SD.

95.4% of the area under the curve lies within mean + 2SD.

99.7% of the area under the curve lies within mean + 3SD.

For example the normal CSF protein value in ELBW neonates is reported as 150 + 56 mg/dl.⁶ This means in 68.3% of normal ELBW neonates CSF protein will be between 94 – 206 mg/dl. 13.5% of ELBW neonates will have CSF protein in range of 207-262mg%. Values beyond 3SD are rare in normal population. CSF protein > 318mg% is beyond 3SD and more likely to be abnormal.

The normal distribution with mean of 0 and standard deviation of 1 is called standard normal distribution or Z distribution. Tables are available for area under curve for this Z distribution. This area under the curve is important as it gives the percentage of population beyond a given value. However, there is no need for and not possible to have tables for area under curve for all mean and standard deviations. Any given value can be transformed into Z score and with this transformed value table for standard normal curve can be used.

Numerical Representation of Data