Use of Excel in Statistics: Problem Solving Vs Problem Understanding

International Journal on Integrating Technology in Education (IJITE) Vol.4,No.4,December 2015
DOI :10.5121/ijite.2015.4401 1
USE OF EXCEL IN STATISTICS: PROBLEM SOLVING
VS PROBLEM UNDERSTANDING
Dr.Avanti P. Sethi
Jindal School of Management,University of Texas at Dallas,Texas,USA
ABSTRACT
MS-Excel’s statistical features and functions are traditionally used in solving problems in a statistics class.
Carefully designed problems around these can help a student visualize the working of statistical concepts
such as Hypothesis testing or Confidence Interval.
KEYWORDS
MS Excel, Data Analysis,Hypothesis Testing, Confidence Interval
1.INTRODUCTION
MS Excel is used in a majority of graduate / undergraduate introductory statistics classes,
especially in business schools. Problems related to Regression, ANOVA, difference between two
means, etc. are solved using Excel’s Add-In Data Analysis tool. In addition, students are also
taughtstatisticalfunctions such as AVERAGE, STDEV.S, NORM.DIST, etc.
Books such as Keller [1], Abbott [2] have been written on the use of these functions and tools.
However, the typical focus in these textbooks, as is the case even in Excel-based statistic classes,
ison problem-solving using Excel. For example, the students will use NORM.DIST function to
solve a normal Distribution problem.
Such training is critical since in the real world, packages/ add-ons such as MS Excel, SAS, SPSS,
or R are used in statistical analysis of the data.
Narges [3] has used Excel in generating tests which can be very useful for those who teach
statistics classes. However, what we present here is the use of technology (MS-Excel)to teach
statistics by clarifying the underlying mechanisms. We believe that there is a clear difference
between using a tool to solve a problem and in using it to actually understand the problem-solving
concepts. For example, typical business school students in a statistics class don’t know where the
probability tables come from. They can find a confidence interval for a population mean, but
don’t really understand whyit works. They don’t fully understand why the Null Hypothesis H0:
µ = 50can be rejected in favor of Alternate Hypothesis H1: µ < 50 even when the sample mean

International Journal on Integrating Technology in Education (IJITE) Vol.4,No.4,November 2015
2
‫ݔ‬ = 47 which is less than 50. Or, how does the choice of α impact the confidence level or
Hypothesis testing?
In this paper, our goal is to present a set of simple exercises using MS-Excel thatteachers can use
to demonstrate intuitively what goes on behind the scene when a decision such as the rejection of
the Null Hypothesis is made.
2.PROBABILITY DISTRIBUTION TABLE
Most students, especially in non-technical areas such as business administration, tend to view the
probability tables as entities created by some unknown force.Whether it is the binomial
distribution, normal distribution, or any other, students are given pre-made probability tables and
are asked to use these to find probabilities. At the same time, they also learn Excel’s probability
functions like BINOM.DISTorNORM.DIST. In this paper, wepresent simple manipulations of
the function NORM.S.DISTwhich can be used to demystify the Normal distribution or z-table.
NORM.S.DIST(z)gives the area (probability) from - ∞ to z, z being the number of standard
deviation measured from the mean. As a reference, NORM.S.DIST(1.43)= 0.92364 or 92.364%
which is the probability P(z ≤ 1.43), that is, the area to the left of z = 1.43.
To create our own Normal distribution table, we use NORM.S.DIST($A3+B$2) in cell(3,2) to get
0.5000. Then we copy it across the columns to get the 1st
row followed by copying the row down
to fill the rest of the table. It is simple and intuitive.
A B C D E F G H
1 Area from - ∞
2 z 0 0.01 0.02 0.03 0.04
3 0.0 0.5000 0.5040 0.5080 0.5120 0.5160
4 0.1 0.5398 0.5438 0.5478 0.5517 0.5557
5 0.2 0.5793 0.5832 0.5871 0.5910 0.5948
6 0.3 0.6179 0.6217 0.6255 0.6293 0.6331
7 0.4 0.6554 0.6591 0.6628 0.6664 0.6700
8
Table 1
Many textbooks such as Keller [1] provide multiple z-tables representing probabilitiesfrom
various points such as -∞ (Table 1) or the mean. While teaching introductory undergraduate or
graduate classes, we have realized that the students fail to understand the relationships between
these tables and hence treat them as independent tables. Subtracting 0.5 from the function
NORM.S.DIST($A3+B$2)will create a table (Table 2) where the area is measured from the mean
as seen below. Similarly, a separate table can be created when the z-scores are negative. Such
exercises will make the students realize that the tables are essentially the same, and that any table
can be used to solve a problem.

3
A B C D E F G H
1 Area from Mean
2 z 0 0.01 0.02 0.03 0.04
3 0 0.0000 0.0040 0.0080 0.0120 0.0160
4 0.1 0.0398 0.0438 0.0478 0.0517 0.0557
5 0.2 0.0793 0.0832 0.0871 0.0910 0.0948
6 0.3 0.1179 0.1217 0.1255 0.1293 0.1331
7 0.4 0.1554 0.1591 0.1628 0.1664 0.1700
8
Table 2
The students can even be assigned homework problems where they have to use Excel’s built-in
functions to create such tables, and then use these tables to solve general normal distribution
problems. Similarly, function BINOM.DIST can be used to create binomial distribution table for
desired number of trials and probability of success. Likewise, T.DISTcan be used to create T-
table.
3.SAMPLING DISTRIBUTION
Excel’s Add-In Data Analysis can be used to make students visualize concepts such as Central
Limit Theorem, Confidence Interval, or Hypothesis Testing. Data Analysis, a collection of many
useful statistical tools built into Excel, is normally hidden from Excel’s menu as most users do
not need it. It can be turned on by going into Excel’s Option menu.
The instructor can create a multistep homework assignment where the 1st
step is to generate a
distribution-based population. Here are some suggestions.
3.1.Generate a population
A uniform distribution can be generated by simply using Excel’s RANDBETWEEN function.
For example, to generate a population between 120 and 180, use RANDBETWEEN(120, 180)
and copy it down to say, 2000 times, to get a population of size N = 2000 and mean µ ≈ 160.
A normal distribution population can be generated in a similar fashion by using
NORM.INV(RAND(),160,15) which will give a mean µ ≈ 160 and standard deviation σ ≈ 15.
Since newer versions of Excel no longer have a Random Seed, these 2000 random numbers will
be continuously changing. One can use Excel’s special copying feature to copy the values only
which will not change anymore.
Alternatively, one can generate a population of desired distribution by using Excel’s Add-In Data
Analysis bygoing to Data Analysis>Random Number Generation and puttingin the necessary
parameters.

4
Fig 1. Generate a population
Sometimes it is helpful to gray-out the population numbers in the Excel column to give the
students the impression that the population, in general, is not accessible in its entirety.
3.2.Standard deviation σ vs. Standard error of the sample mean ࣌/√࢔:
Now that a population is available (in Column 1), Data Analysis>Sampling can be used (Fig 2) to
generate, as an example,12 samples of size n = 30 from this population in columns B through M.
Fig 2: Select a Random Sample

5
The students are asked to find the mean of each sample(as shown in the Table 3) using
AVERAGE. What they will see is that the sample mean is a good estimate of the population
mean. Now, they have to find the standard deviation of the sample means using STDEV.S
function and compare this with the standard deviation of the population (STDEV.P). For our
dataset, the corresponding numbers are 2.88(standard error of sample mean) and 15.26
(population standard deviation).
A look at the table will allow the students visualize why standard error (deviation) of the sample
mean is smaller than the standard deviation of the population. They can then be asked to compare
this calculated value of 2.88 to the theoretical value of the standard errorߪ/√݊ = 15.26/√30
which happens to be 2.79. The difference between these two valuesof 2.88 and 2.79 will become
smaller / larger as the sample size n increases / decreases.
Mean 160.53 158.50 164.97 156.73 157.63 160.20 158.07 158.00 157.07 163.43 158.20 154.63
1 155 186 173 131 164 128 171 146 153 166 167 180
2 200 165 160 165 124 163 147 158 164 149 153 175
3 170 146 151 160 162 200 164 176 165 176 146 151
4 155 149 148 163 141 160 141 152 120 141 152 148
5 205 160 153 153 145 147 168 189 160 162 166 159
6 138 146 172 153 164 163 165 154 176 183 178 168
7 163 139 159 167 169 136 131 151 158 133 134 155
8 158 133 161 134 154 185 149 160 142 167 159 149
9 165 167 184 175 194 147 163 175 162 180 184 128
10 155 145 162 160 162 165 158 164 151 164 156 136
11 130 175 169 164 164 170 150 169 158 152 185 168
12 - -. -.
13 - - -
Table 3
3.3.Confidence Interval
Confidence interval, associated with a Confidence level, is the interval in which the population
parameter, such as the mean µ, is expected to fall. To see how this works,the students are asked
to calculate a Confidence interval around each of the sample mean in our table with a Confidence
interval of 90%. The population mean is expected to fall in most of these intervals (90% to be
exact). Thus, with z = 1.645, our interval will be given by ‫ݔ‬ ± 1.645 × 15.26/√30 where ‫ݔ‬ is
the mean of each sample and 15.26/√30 represents the standard error of the sample mean ߪ/√݊.
The following table gives the calculated upper (UCL) and the lower (LCL) levels.

6
UCL 165.28 163.25 169.71 161.48 162.38 164.95 162.81 162.75 161.81 168.18 162.95 159.38
LCL 155.79 153.75 160.22 151.99 152.89 155.45 153.32 153.25 152.32 158.69 153.45 149.89
Mean 160.53 158.50 164.97 156.73 157.63 160.20 158.07 158.00 157.07 163.43 158.20 154.63
So, if we took the first sample, we expect the population mean to be somewhere between 155.79
and 165.28. But if our sample happened to be the last one, the corresponding interval will be
(149.89, 159.38). Which of these is correct? Now we can see the dilemma – for each interval,
we are 90% confident that the population mean µ will fall in that interval, but the intervals
themselves are so different!
Since in our example, we have access to the whole population, we can calculate its mean µ which
in this case is 159.43. By scanning the 12 confidence intervals, we find that interval number 3
and number 12 do NOT include the population mean.Do we expect that? Yes,because 90%
Confidence interval implies that we expect the mean NOT to fall in 1 out of 10 intervals.
In a real life scenario,where normally we draw only one sample at any given time, which sample
could we be drawing? If we drew sample number 1, then we would be right about the interval
estimation of the population mean. But if we drew sample number 3, we would come to a wrong
conclusion about the population mean. Such is the life of a statistician!
We can increase the confidence level to 95%, use z = 1.96, but then our interval size increases
making it less useful. As a parallel statement, we can be 100% confident that the outside
temperature in Septemberin Boston will be between 0 and 100 degrees, but what good is that?
3.4 Hypothesis Testing
A two-tail hypothesis testing is another form of Confidence Interval. Since we know the
population mean here, we can set up a Hypothesis test as shown below:
H0: µ = 159.43
H1: µ ≠ 159.43
Let us keep our level of significance = α = 10% which gives us z = 1.645. Now, our lower and
upper cut-off points can be calculated to be 159.43 ± 1.645 × 15.26/√30 = (154.84, 164.01)
In other words, if the sample mean is less than 154.84 or more than 164.01, we will reject the null
hypothesis claiming that the true population mean is not equal to 159.43. With our α = 10% , we
are taking a 10% risk of rejecting the true null – that is, of committing a Type I error. Now, if we
look at our sample means, sample number 3 (mean = 164.97) and number 12 (mean = 154.63)
will make us reject the true null and make us commit a Type 1 error.

7
4.CONCLUSION
MS-Excel and Add-In Data Analysis are commonly used in solving statistic problems in a
classroom setting. The purpose of this paper is to show how the same tools can be used to make
the students actually visualize the underlying concepts.
REFERENCES
[1] Keller, Gerald, Statistics for Management and Economics, Cengage Publishing, 10th Edition, ISBN-
10: 1285425456
[2] Abbott, Martin, Understanding Educational Statistics Using Microsoft Excel and SPSS, Wiley, ISBN:
978-0-470-88945-9
[3] NargesAbbasi, ShahramDokoohaki, An Initiative in Making Tests for Statistics Lessons, Asian
Journal of Education and eLearning, Vol 1, No. 5, 2013
Author
Dr. Avanti Sethi, a faculty member at Jindal School of Management at UT
Dallas, received his MS and Ph. D. in Operations Research from Carnegie-
Mellon University in Pittsburgh, USA.

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