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Welcome to this 14th session of ergonomics for beginners industrial design perspective.
Now, today, the last class of module number 3, that is human physical dimension concerns.
That is the today's session of this module will be class 14 that is statistical treatment
of data and percentile calculations. In last class, we have discussed that the anthropometric
measuring techniques, and before that anthropometric landmarks were discussed. This is specifically
required, when we do not have any ready reference data; for design application we may need to
generate some data, and how to generate the data? Last class we have discussed. And now,
we will be discussing how the statistical treatment can be done, on those collected
data. Now, in last class, we have mentioned that
the basic anthropometric techniques, in using anthropometric rod set, and other equipment's
like a height adjustable tools weight, body weight, and cone for grip diameter, and etcetera.
And measuring circumferences with the help of inextensible or non-elastic measuring tape,
and then using different grids that is that anthropometric measuring boards are used that
can be developed that can be done.
Now, we have discussed a brief measurement procedure using anthropometric rod set, anthropometric
board, and specific measuring devices, as suitable to measure some dimensions like grip,
foot etcetera also. Now, that was basically we discussed for standing measurements, sitting
that is seat desk posture measurement; and sitting on floor posture that is cross legged
squatting; considering static values as well as various dynamic reach values, we have discussed
in last classes.
So, now, today and also we have discussed the indirect methods using photography and
videography techniques and data collection accuracy system. How to make the data accurate?
In various static as well as dynamic postures including various reach values, we have discussed.
And then recent development in this field, using whole body scanner that gives digital
dimensions, that provides us a scope for fast, covering many subjects; that is for the or
anthropometric general survey, it would be very good.
And also we have discussed the easy sampling selection procedure, that is, that if we do
not have a very large number of population, and we need to rely on some small samples;
then it would be better to take around 20 percent eye estimated smaller size people,
20 percent eye estimated larger size of people, and then rest 60 percent randomly selected;
so that, we can make a the both the ends of that population, from smaller dimensions to
largest dimension, we can consider, we can cover it.
So, with all this the today's topic is the statistical analysis of anthropometric data
and the percentile value, means, that when we design something for a single persons use, then we can measure him directly; and
according to those measurements, we can make a design for his use, that is exclusively
for his use say - a chair, a table or a bed, like that; but when, which we can say that
designing for a single person demands his dimensional variations to be well accommodated
in a design. But when designing for a mass use and for unknown individuals use, which
we do not know who will be the intended user, one of the most relevant statistical interpretations
and considerations in this would be the percentile value of the collected data; means, when we
are making a chair, then the popliteal height, means, the opposite side of the knee that
is inner thigh that inner that portion of knee joint or popliteal height.
So, we can say that the chair height should be at per popliteal height, but this popliteal
height from whom we get? A short height people, large height people or an average height people;
so that, most of the people falling within this means small size to largest size everybody
can get comfort.
So, in this situation we need a specific value that is that percentile value of the body
dimensions. Now, what is the percentile value, and how to calculate, and etcetera that we
will discuss now.
Now, what is a percentile? The percentiles are the statistical values of a distribution
of variables transferred into a hundred scales. The population is divided into 100 percentage
categories, ranked from least to highest, with respect to some specific types of body
measurements. Now, the first percentile of any height indicates that 99 percent of the
population would have the heights greater dimensions than, that means, if we measure
some people say 1000 people, we measure their heights; now, the minimum height or the lowest
height what we observed? If we consider it as a one in a hundred scale, one and the highest
value is the hundred in that scale, and rest all the data are arranged within this one
to hundred scale then we can say that the what would be the one person, if we consider
make a door with one percentile height or the this population means what is happen?
The only one percent of this population, those height is within that limit will be able to
pass through without any problem. Now, if we consider the nine, the 50 percentile
means the total population will be divided into two halves; means, 50 percentile means
below this 50 percentile around 50 percent of the body height those who have lower height
than that they will feel no problem, they can pass through that door, but those who
have higher value than that they will have some problem, they may need to bend their
heads to cross that door. If we see that 99th percentile data of that
height, means, what is happen? 99 percent of the population will have lower height than
that only 1 percent, means, 99 above till 100; only 1 percent population will be on
the higher side means over that data. Now, one question comes normally for design
use, in many, everywhere, it is said that - consider the data from 5th percentile to
95th percentile, why not 1 percentile? Why not 100th percentile always? It is said that
- from below the 5th percentile value these are almost free data, and above that height,
above the 95th percentile height is the tallest kind of thing, that is also free data. So,
suppose we want to make a bed for hostel purpose hostel cot, for that if we measure all the
students, then few students may have very short height, and few student may have very
tall height. Now, if we say that - we should make a cot where all the students can sleep
without any problem; then ideally we can say that - take the 100th percentile value with
the tallest person's height of that population, we measured and make a cot; so that, everybody
falling below this height, they will not have any problem. Now, what is happen is from 95th
to 100? This very few people will be there, so if we make all the cots with 100 percentiles
height data, then there will be wastage of material resource; so, for that this 95 percentile
is normally considered as the higher value, and the rest, if it is required to ensure
safety kind of thing, then the maximum thing is necessary, and then allowance maybe given
like. If we do not want someone should touch a top
on overhead hanging some object, no one should touch, at that very time, we should consider
the upper maximum arm reaches, maximum length is the 100 percentile length kind of thing;
so that, below that height or everybody all the people, they will not get touching to
that dangerously hanging thing, in that and then, someone may raise their to, and can
extend their arm reach, and can reach it; in that cases, some extra allowances to be
added in this dimension. So, these are the some of the considerations
that we need to fit; another thing, suppose in one, in certain cases everybody should
get touch, to operate some handle or switch like that, like any control over for any control
operation, in that case, it is that everybody should get touch to that, in that case, we
will try to consider the lower value of this arm dimension; so that, higher person, higher
valued people they will not have any problem. So, in these cases, we should use the lower
percentile value, normally it maybe 5th percentile; why? Now, below the 5th percentile very less
population will be there, representation will be there, and they may touch with extension
of hand means considering the peak data.
So, these are the some common application for percentile value; now, how to calculate
this percentile value from a raw data that we are going to discuss. Now, let us see in
this slide whatever we discussed, let us see the slides for specifically is mentioned here
for reference. The first percentile of any height indicates that 99 percent of the population
would have the heights of greater dimensions than that. Similarly, a 95th percentile height
would indicate that only 5 percent of the study population would have greater heights,
and that 95th percent of the body population would have the same or lesser heights. The
50th percentile value represents closely the average which divides the whole study population
into two similar halves with one half higher and another half with lower values in relation
to the average value; that is the 50th percentile value.
Now, see the this schematic presentation of percentile distribution, with the help of
stature value of a selected population. Now, suppose if we measure, if we see this is a
diagram, some data, 5th body height data, we have taken here for discussion purpose;
these are the data original data collected in millimeter.
Now, here the minimum value is that 1396 millimeter - total body height, and maximum value we
got suppose 1940 millimeter; so, 50 percent's we have measured, and these are the their
data. Now, suppose the 1 percentile, suppose we
did that 1288 millimeter like this, this is a minimum per height; then 50th percentile
is closely average or if our sample is proper then average and 50th percentile will match
together, otherwise it is not the same if our sample size is not proper.
So, average how much 1619 millimeter, and the maximum is the 100 percentile is 1950
millimeter. Now, if we transfer this, in this diagram, in this graph, that suppose, this
is the value in millimeter, so what means, and this the subjects; so, 1 percent data
is here, 50th percentile here, and 100 percent like this, so the total graph is coming like
this; if it is possible, this total bell shape curve is possible if our sample size is proper.
Now, the calculations: the calculation process is described here is an example taking, the
stature values of body height of a group of 50 individuals. This might help designers
in the compilation of special data collection collected by them for special purposes, where
ready sources are not available. It will also help them understand the method. Below is
a reference data of data set to get acquaint with the calculation process.
The stage-I: first stage is that to identification of the two end values, that is the lowest
score is this one, and the highest score is this one, for stage-I. Stage-II is that arrangement
of classes, means, in from, this lowest value and highest value if we arrange, then total
5th value; now, from the highest value to lowest value, if we minus it from the highest
value to lowest value, it comes 544 millimeter, maybe divided into manageable blocks say - if
50 individuals are in this group, then we can say that to from highest to lowest, these
much value is in between divided by 50, so 10.88 classes we can have, means, we can say
that 11, class of 11 of each class interval having 50 scores.
For ease of calculation, a round figure of 350 instead of 1396, 1396 instead that to
make it a round figure we are considering 1350 instead of 1396, means, 1350 we have
taken it as a lower class. So, starting from 1350 with class intervals of 50, classes should
be arranged till the uppermost class attend, the highest score obtained in the original
data; here, we get 12 classes as the following class distribution like this, so minimum we
are taking 1350, and 50 data, then next another 50, another 50, another 50, like this way
we are crossing like this; so, like this way the topmost grade class 1900, 1949, in this
the highest value,, whatever we are originally got 1940 lies in this, and the lowest value
that is 1396 lies here. So, this is called calculation of groups with each class interval
of 50 scores, we have considered arbitrarily these 50 scores.
Now, the stage number 3: refinement of the class intervals, what is the refinement of
class interval? That is that refinement of the class intervals and frequency distribution
of scores are according to the classes and calculations of calculative or cumulative
frequency - that is *** *** f - for each class. The cumulative frequency for the lowest score
containing class will be the same original frequency and the rest will be by adding gradually
the lower class interval's cumulative frequency will be the total number of the sample size.
Cumulative percentage frequency is the next step to calculate, corresponding to the cumulative
frequency considering the highest cumulative frequency value as 100. Now, we see the graph.
Show here, what this is, the class interval number 1, class interval 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12, so total 12 class intervals; so, within this class interval, how many scores
we have? How many tally? So, here if we go back to the original class, from here we can
say that there will be 2, from this we can find out that, 2 scores are falling within
this. So, like this we have to consider that here 2 frequencies tally are here; so, counting
this how many scores are falling within this 2, here a 4, in this 3, like that we found
it, the tally number; means, the original scores falling within this classes.
Now, means the frequency in these groups are 2, 2, 4, 3, 6, 1, 2, 7, 7, 1, 3, 2, 1, 2 like
that; now, the cumulative frequency is that, suppose in this group, in this class, only
2 are there, in this class 2, but if we consider that 1, 4, 4, 9, this value, below this value,
total 4 are there, this 2 from the below and 2 of this class so total 4, so this 4 will
be below this; so, this is called by adding one after another, it is the cumulative frequency
like that the total 50 here will be below this. Now, this is the cumulative frequency
by adding one after another, means, then this we have considered 50 percentile, this 50
individuals.
Now, the 50 data we got it now for percentile, we are transferring this to a 100 scale; 100
scales, means, what is happen? Then if the top it should be 100 means, in this case,
it is just 2 multiplications. So, this cumulative percentage frequency would be 50 will be 100,
40 into 2 is the 96, like that, so 47 into 2 is 94, like that maybe 11 into 2 is 22 like
that way, 2 into 2 equal to 4 something like that, this is the cumulative frequency; from
this cumulative frequency and this is our main calculation starts.
Now, if we look at the bar diagram next; this is the examples, now if we see the bar diagram
here, then what it says? Now, our class intervals where 1350 to 1399, next class interval was
1400 to 1449 like that. Now, if we see this one, then we can say that in... Now, we are
making these classes in a graph. Now, in this is the graph where the lowest
value is 1350 and highest is that 1390; so, next group starts from 1400 and higher value
of this class is 1449, but if we make a graph, then there this portion remains blank which
data from here 1350 to 1449, this portion remains vacant for that purpose; like this
way, it is distributed for that a specific case has been considered that, consider from
what is the gap here? In this case, from 1399 to 14001 is there, so divide it by 2, because
it is this for this dimension, one- dimension one value is divide distributed between these
2; so, if we divide by 2 that is 0.5. So, this specific group if we start 0.5 below,
means, the score class it starts with the true limit of this group is, the true limit
will be 1349.5 instead of 1350, and upper value of this group would be 1399.5, means,
adding 0.5. The next one, just below minus 0.5 it will be 1399.5 instead of 1400; means,
this point is being shared by both the groups. So, what is happen? All the groups like I
said, then there will be a fixed, so no gaps will be there.
So, the true value of the classes is 1349.5 to 1399.5, the next 1449 like that, and the
scores are there, as per within this 2 scores, within this 4 scores, within this 6 scores
like this; after this, the main calculation part comes, the calculation is that we have
to that we see here; so, these were the original group class, we mentioned.
Now, if we from or this if we read this slide what it says - if we look at the bar diagram
that we have seen right now or the distribution, then if any individual score is between 1399
and 1400, it is not counted either in class 1st or in 2nd. To accommodate this in the
proper group, the mid value that 1 - 1 point between the upper value of the lower class
and lower value of the next higher class maybe considered as the true limit of these two
class intervals; that just now we have seen through this graph.
Hence, the true lowest value of the class second 1400 - 1449, would be 1349.5, like
this; the same value also would be true highest value of this class. If there is no possibility
of its happening in manner or if that minute consideration is not required, these step
maybe avoided in percentile calculation also.
To sort out the true lower value and higher value of any class, this could be 0.5 less
than the original lower value and 0.5 more than the original higher value, is the true
value. By this it could be said that an individual score of 1399.4 would be continuing, will
be counted in the true class of 1349.5, and 1399.7 would be in the class of this.
Now, the calculation, first I will discuss this table, and then we will go for the its
description. Now, the thing is that, this is the original class minus 0.5 plus 0.5,
this is the true value like this, is a true value, it is a true higher value; this is
the original frequency as we have seen earlier to in these class 2, 2, 4 like this way; cumulative
frequency the same thing, now whatever we got in adding this 2 plus 2 equal 2 plus 0,
if this a to the 4, 2 plus 2 equal to 4 like this way, and 4 plus 4 equal to 8 like that,
by this way adding we are coming to 50; now with this 50, this is the cumulative frequency
is there. Now, we would like to see, suppose I, we want
to measure or to calculate 25th percentile value, what will be the 25th percentile value
of this 50 percents data? We can say that 50, 20 percentile, so with this cumulative
frequency the 25 is falling within this, means, below this true limit there are 22 percent
people, above this there will be other people, and 25th are within this true value somewhere.
How to find i? It like, still 22, this is the upper value, then from this value to this
value, what are 50 scores are there, originally 6 percents are here, frequency is 6; so, 50
by 6.
Now, if we see the calculation part here. Percentile 25, the 25th percentile value corresponding
cumulative percentage frequency falls in the class of 1550 - 1599, in this case; in this
the true class of 1549.5- 1599.5 and correspondingly to the cumulative percentage frequency, 25th
percent position of the cumulative frequency, will be the 25th percent of the total number
in that is 12.5th cumulative frequency rank; means, we want 25, in this case what is happen?
We have taken the double, double means into 2, like this have you got it from cumulative
frequency, cumulative percentage frequency. So, 25 if we require, then 25 divided by 2
equal to 12.5; so, in this original cumulative frequency, it would be it would be 12.5 score.
So, till 11 is this is there, so from 11 to 12.5 how far we should go? That is that below
1549.5 score limit there are 11 persons, 22 percent of the population. To get 25th percentile
figure of this score we have to go to the score that corresponds to the 12.5 cumulative
corresponds to the 12.5 cumulative frequency levels, that means, 12.5 minus 11 is equal
to 1.5 frequency score to the class; means, here is 11, so we have to go to 12.5 means
1.5, we have cross here; so, within this 50, there are total 6, so 50 by 6 for one score,
for one frequency how much it crosses, then into 1.5 where it matches. Here, that will
be the 25th percentile value, means, the class this has a frequency of 6. Each frequency
carries 50 score, whether in one class divided by 6 is equal to 8.33 score value, for each
frequency. Hence, adding 12.50, means, if this is for
1, then 1.5 multiplied to this, then it becomes 12.50; so, with the lowest value here, with
the lowest value, this one below this 11 are there, then this one plus 12.50 whatever is
coming from here, if we add it means 1.45.5 plus 12.5, you have to 1562 millimeter it
would be the 25th percentile score of this population group, where 75 percent of this
survey of the population mentioned above or the first, will be larger stature than this
value and the rest will be the below this value; so like, this all the percentile figures
we can calculate accordingly like.
Now, this is by a calculation, we have done arithmetic calculation. Now, by a graph, in
this graph, we can say that suppose we are measuring a graph, this is the true cumulative,
the true class values, in this class values, this is the cumulative percentile percentage
frequency; the frequency we are putting adding like this way. So if we want to see that where
the 8, this is 4, this is 8, this is 16, like that as per the, now if we want to have a
25 th mark in this graph which is 25 th, then where it falls this.
So, count the measurement here, and then make a this each row is the... So, what is from
this interval to this interval? 50 data, 50 is there, so 1, 2, 3, 4, 5, so means, each
dimension is a 10 th; so, then what would be corresponding figure matches here, that
would be the percentile.
So, if we require 50 percentile like this way, if we require 75 th, 2 percentile, 3
percentile, it is like this way. So, it is a graphical system to measure that so percentile
calculations by cumulative percentage frequency curve, another is that. Now, if we see whatever
the mathematical calculations we have, arithmetic calculation we have discussed, the formula
would be that preferred percentile rank P p equal to l plus P N minus F divided f p
into I; P p means required percentile rank; if we require 5th percentile, then P p would
be 5 p 5. Then lowest value of the class interval, if we go to this, in the this is the five,
means, it is here; so, this is the lowest percentile, lowest interval of the class,
lowest interval of the class plus to 2.5, means, this is that cumulative frequency in
relation to the P p point, means, we want 5. So, in that table we have calculated 2
multiplications from the cumulative frequency to the percentage frequency; so, 5 divided
by 2 to 0.5. So, below that class only two are there, so
point five level, we have to, and divided by f p; means, f is that cumulative frequency
below the lowest value of P p class, and f p is that actual frequency the P p class,
in our discussion, it is 50; so, the actual frequency to the class, is that, it is number
2, in this case, in this actually the 2. Now, then into I, I means class interval score;
in our case, we have taken the class interval of 50 scores, so like this way, so 1412 would
be a percentile 5 value, in this distribution; so, accordingly p percentile 10, 25, 50, etcetera
will be one can calculate it.
Now, the shorter the class interval, the more accurate will be the results. Now, Mean, Median,
and Percentiles: the mean is the best is average, is the best measure of the central tendency
of the distribution. In the above scores, 50 scores individuals, we have measured value
comes to 1637.5, but as per our percentile 50th percentile concern, it comes to 1632.8
means 1633 millimeter, but here we can see that average is different, this may be due
to non-appropriate sample size. So, wherever this possibility is there, it
would be better to take, mean, 5th percentile value, 50th percentile value for this. The
median is the mid-point of a score arrangement from the lowest to the highest order, which
would be the 50th percentile figure. In the above case, whatever data concern we are discussing,
it is 1632.8, and its graphical presentation is shown here below. So, roughly, for the
purpose of a survey of anthropometric data, the subject number is vast, and hence, the
references, when addressing the 50th percentile value, the term average is also used; this
normally for anthropometric survey a vast population size is considered
Now, in this case, the graphical representation if we see, now earlier what is happened? We
have seen this graph, this bar diagram, we have seen. Now, the centre points, if we do
like, then we will get the curvature; we will get the curvature like this.
So, the in the graphical presentation, of this distribution pattern of scores, of a
sample survey, that reference data used here, in A is the class mid-point; these are the
class mid points, means, minus it divided by 2 that comes the mid-point. Bar diagram
with class true limits, and original frequency is the B, this structure; the blocks are the
bar diagram with true class intervals. C curve, this is the C curve, this one, C curve using
class mid points and original frequency; and this is the D curve, a smooth curve using
class mid points and smoothening the frequency.
How to make the smoothening of the curve? True class intervals, then see that in this
class interval, what was that group ranks, and then original frequency, and then by adding.
the So, these system the calculations, calculation for smooth frequency of a corresponding group
is that two times the original frequency of the original group plus frequency of the group,
just above the original group plus divided by the frequency of the group, just below
the original group, if you see and divided by 4, this will be the smoothening points;
by these, from with using this details, the smoothening of the curve is made and shown
here.
Now, the standard deviation and sketch: these are the standard deviation of a diagram, that
in any statistical book or reference book, this will be, these are given there. So, this
is the bell shaped curve, the Gaussian curve, the ideal sample distribution showing, mean,
values and standard and plus minus S D relationships; so, like this, so from this mean value, if
we have 1 S D minus and 1 S D plus, then it calculates 34 plus 34 is 68 percent of the
population, will lie within this range, and then rest like accordingly this chart it can
be seen.
Now, in certain cases, if we see that the curves are in different structures; so, this
cuteness it shows that if our subjects sampling is not proper, then these type of curves are
possible.
Now, if most of the source is concerned near the mean value, then it is termed as a leptokurtic
curve. If the curve follows a short height and spreads towards the both the ends it is
termed as platikurtic curve. The normal bilaterally symmetric curve termed as Gaussian curve,
and would always be mesokurtic.
Anthropometric data are normally presented in percentile figures with range of minimum
and maximum values, and sometimes with mean plus minus SD to understand the data distribution
pattern in a particular study population group. It helps in selecting the required data of
design relevance.
Now, with this we can say that - today we are completing the module number 3 that is
human physical dimension concern, and the next a new module we will start as a module
4 that posture and movement concern. So, with this we are concluding today's session; so,
next session we will go for posture and movement and its design relevances.
Thank you very much.