All about statistics

Yesterday (August 2, 2013), I am one of the participants in the Seminar-Workshop on Statistical Skills Enhancement conducted by the Commission on Higher Education (CHED) in collaboration with the Philippine Statistical Association (PSA), Region 6 Chapter and the National Statistical Coordination Board (NSCB), held at Central Philippine University, Iloilo City.

Here's the excerpt of my short travel:

I woke up early in the morning to catch up the first fast-craft trip going to Iloilo City. Though it will only take 1 hour or more depending on the weather condition, I opted to be early as possible (I have adopted an attitude of being early especially on events like this) because I wanted to have more time gazing and exploring around the place especially the university.

I was not able to catch up the 6:00 am trip but the other craft in the vicinity will leave by 6:15 am, so I decided to board that one. Not even had my time sitting inside the pre-departure area, we were called to board the craft.

At 7:15, we embarked at Iloilo City port. The weather is real good and no signs of pouring rain or weather disturbance because the clouds were clear and somewhat like cooperating in my short travel. Not seeing any participants from other institutions I knew, I decided to go alone and proceed to the venue.

Upon arrival at the venue, I asked the guard which way is Henry Luce Library and he instructed me. The campus is really wide and I saw lots of cars and motorcycles parked and roam around the roads inside the campus.

I readily went up to the 4th floor and registered myself for the seminar. There were still a quite number of participants arriving at that very moment.

The first thing I always do everytime I attended events like this is to look around for available coffee and indeed I found one. Not having early meal or hot coffee way back home, I decided to pour a cup of brewed coffee and wait for my name to be called after I had registered my name and awaited the official receipt.

Participants from other areas started to come up and registered themselves. I'd seen familiar faces coming from our province and I assumed they took the next trip that I boarded in going to Iloilo City.

The seminar was started with a short prayer and the national anthem afterwhich all participants were introduced. I can't figure well how many had joined the seminar but the tables were filled with participants coming from different higher education institutions.

The first speaker, Dr. Sonia P. Formacion tackles "Introduction to Statistics". Dr. Formacion is the Auditor of PSA 6. Her presentation includes the following sub-topics wherein she explained everything about it and the need for statistics in general:

1. Definition of Statistics

In the plural sense
In the singular sense
In the plural and singular sense

2. General Uses of Statistics

In business
In government
In the academe
In the practice of a profession
In everyday life

3. Fields of Statistics

a. Statistical methods of Applied Statistics

          i. Descriptive Statistics
          ii. Inferential Statistics

     b. Statistical Theory of Mathematical Statistics

4. Type of Data

   a. Qualitative Data
   b. Quantitative Data

A short coffee break and snacks started after Dr. Formacion ended her talks. This is my most favorite part of every seminar.

The next speakers on "Descriptive Statistics" were presented in two topics:

Topic 1 Central Tendency, Dispersion, Graphs - Prof. Jhoanne Marsh Gatpatan, UPV Statistics faculty

Prof. Gatpatan finely presented to us Measures of Central Tendency: is any single value that is used to identify the “center” or the typical value of a data set. It is often referred to as the average.

Part of the exercises that Prof. Gatpatan shared with us is the Arithmetic Mean: Population Mean and the Sample Mean.

The population mean for a finite population with N elements, denoted by the Greek letter (mu), is computed as

The sample mean (read as “X bar”) of n observations is computed as

The sample mean (a statistic) is an estimate of the unknown population mean (a parameter).

The characteristics of the Mean

can be applied in at least interval level
may not be an actual observation in the data set
easy to compute

It possesses two mathematical properties that will prove to be important in subsequent analyses.

The sum of the deviations of the values from the mean is zero.
The sum of the squared deviations is minimum when the deviations are taken from the mean.

If a constant c is added (subtracted) to all observations, the mean of the new observations will increase (decrease) by the same amount c.
If all observations are multiplied or divided by a constant, the new observations will have a mean that is the same constant multiple of the original mean.
affected by the value of every observation. In particular it is strongly influenced by extreme values.

The Median

The positional middle of the arrayed data.
Divides the observations into two equal parts

If the number of observations is odd, the median is the middle number.
If the number of observations is even, the median is the average of the 2 middle numbers.

Characteristics of the Median

It is a positional measure.
It can be applied in at least ordinal leve
It is affected by the position of each item in the series but not by the value of each item. Extreme values affect the median less than the arithmetic mean.

The Mode

the observed value that occurs most frequently
locates the point where the observation values occur with the greatest density
nominal average
generally a less popular measure than the mean or the median

Characteristics of the Mode

It does not always exist; and if it does, it may not be unique. A data set is said to be unimodal if there is only one mode, bimodal if there are two modes, trimodal if there are three modes, and so on.
It is not affected by extreme values.
It can be used for qualitative as well as quantitative data.

Prof. Gatpatan also presented to us Statistics Presentation of Data: Textual and Tabular form.

Textual form of presenting statistics data gives emphasis to significant figures and comparisons and is the simplest and most appropriate approach when there are only a few numbers to be presented while the tabular form is more concise and easier to understand, facilitates comparisons and analysis of relationship among different categories and it presents data in greater detail than a graph.

A formal statistical table includes the following:

Heading
Box Head
Stub
Field
Source note
Footnote

A good graph should posses the following qualities:

Accuracy
Clarity
Simplicity
Appearance

The common types of graphs can be found in Microsoft Excel, the usage of the graphs will depend on how would you present your statistical data.

Topic 2 Percentage, Rates, Estimating Missing Values, Projections - Dr. Cherry T. Nepomuceno, WVSU Statistics faculty

Dr. Nepomuceno presented the following lecture outline:

Percentages

Rates

Npresent - value at current year or period Npast - value at immediate past year or period

The average % growth rate is sum of all % change divided by number of observations or values.

Rates applied to student enrollment data

Missing data

Missing data mechanism Missingness completely at random Probability of missingness is the same for all units
Missingness at random - probability a variable is missing depends only on available information
Missingness depends on unobserved predictors - missingness depends on information that has not been recorded and this information also predicts the missing values
Missingness that depends on the missing value itself