APEC Schools 2018-2019 Reviewers

Intro to STAT

Introduction to Statistics:

What is Statistics?

Everywhere we look, we are surrounded by information--how many people are inside the room, what grades we get in the different subjects, and our favorite ice cream flavor, just to name a few--and this information can answer just about any question we can ask. Statistics offers a way to make this happen.Statistics is the study of collecting data (the information), handling it appropriately, and analyzing it to come up with a generalization or conclusion (the answer to the question). Data may come in the form of numbers or characteristics. The former is referred to as quantitative data; the latter, qualitative data.

Example 1: When 200 college graduates are asked at what age they began going to school, the data collected (age) is quantitative in nature. The respondents who went to school at age 1 or 2 may be asked for what they feel are the advantages or disadvantages of starting school at such an early age.

Their responses to this question will be collected as qualitative data.

Example 2: In the context of business, quantitative data may come in the form of sales volume or employee salaries. Examples of qualitative data include customer feedback and consumer preferences.

Why do I need to study Statistics?

Are you a sports buff? Do you wish to be an entrepreneur? Do you have an advocacy? Are you curious about anything? Are you passionate about something? If your answer to any of the above questions is yes, then there is reason for you to study Statistics. Historically, people studied and used Statistics to keep track of birth and mortality rates to predict death rates due to various diseases, and to improve the quality of medical care during the time of war. More recently, people have been using Statistics for a much wider range of purpose, such as to better understand the world we live in. We use it to answer questions such as, "What are the concrete effects of climate change?" and "What makes Metro Manila traffic horrible, and what can we do to make it better?"

There are 2 types of Statistics, which can answer questions in different ways. 

Descriptive Statistics, as the name implies, is the type of Statistics that uses data to describe a certain group of people or a phenomenon. It uses mostly quantitative data, summarized and organized in a visual presentation, with the numbers telling a story about the population being studied. Descriptive statistics gives information like what number can be considered a central value that represents the entire data set, how widely spread the data points are, and whether or not there are outliers or extreme values.

Example 1: A study was conducted by educational researchers on Canadian students' level of stress and depression, and the results are summarized below. Of the more than 43,000 students who were surveyed, about 30% reported that they felt "felt very lonely" within the past 2 weeks, while nearly half the students felt debilitatingly depressed, with 44% saying they "felt so depressed that it was difficult to function."

This information uses statistics to describe the current state of emotional health of students in Canadian universities. The data may be useful for school officials and policy makers, who are expected to take into consideration every aspect of the students' development.

Example 2: A restaurant owner can determine the best-selling dish in the menu by keeping a record of the number of times an order is placed for each dish. Using the same data, he can determine dishes that are not popular and may not be worth keeping in the menu.

Inferential Statistics, on the other hand, uses data to study patterns, and to make conclusions and predictions based on these patterns. Generally, it is not possible to gather data from an entire population, say, all the people in the Philippines. Therefore, a subset of this population, say a group of some people from Luzon, some from Visayas, and some from Mindanao, is taken. The observations taken from the subset are then generalized to be true for the entire population.

Example 1: To check the lifespan of batteries manufactured, a company may opt to take a certain number of batteries from each shipment and test the lifespan of these. They may then claim that the average lifespan of all the batteries they manufacture falls within the observed range.

Statistics aims to answer any question you may have about anything under the sun. It can serve whatever purpose you intend it to--from satisfying your curiosity to making a positive change in the world.

How do I do the Statistical method?

Every statistical research begins with a problem, usually formulated as a question.

Example 1: Suppose you wish to look into the amount of time high school students spend on social media sites. Here are some things you can study.

-the amount of time they spend on social media sites

-what they do on social media sites

-the effect that time spent on social media may have on their school performance

Thus, you may ask the following research questions:

"How much time on the average does a high school student spend on social media sites?"

"What social media activity takes up most of their time?"

"Is there a correlation between the amount of time a high school student spends on social media sites and his performance in school?"

The last research question gives rise to 2 types of variables--the independent variable, and the dependent variable.

The independent variable is the variable to which respondents can assign random values. In the given example, the amount of time spent on social media sites is an independent variable.

The dependent variable, on the other hand, is the variable whose value depends on the independent variable. In the case of the given example, the dependent variable is performance in school, since the researcher would like to know if a student's performance in school is affected by the independent variable.

The next step in the process is to collect the data. At this point, a researcher must take note of three things--that the data is relevant to the research question, that it is collected from a fair group of respondents, and that it is collected using the appropriate method.

After the data are collected, it is summarized and converted into a visual form that can be read and interpreted by both the researcher and his intended audience. This is done using tables, charts, and graphs, depending on the information that the researcher wishes to highlight. The data are then analyzed using various statistical methods. 

Descriptive statistics usually involves averages and measures of variance. Comparison and correlation between constructs may also be made. For qualitative data, responses may be divided into thematic categories and analyzed accordingly. Results are then presented, often accompanied by recommendations for further study or a discussion of the limitations of the study. The statistical process may be illustrated by the following diagram.

Statistics is a powerful tool for inquiry, for as long as it is used judiciously. It can have powerful adverse effects when misused and abused. This could happen intentionally or unintentionally. When outliers or extreme values are disregarded, for instance, the data does not show a complete and honest picture. When data is manipulated to show only numbers that are favorable to a desired conclusion, the audience is misled by the statistics presented. When data is collected from a biased sample, the outcome becomes predictable. These are only a few examples of how Statistics can be used to mislead and misinform, and why a researcher must aim to present the most accurate and unbiased findings possible.