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Statistics In The Area Of Research

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Content Outline

  1. Introduction
  2. What is statistics?
  3. Descriptive statistics
  4. Inferential statistics
  5. Types of data
  6. Types of variables 
  7. Summary

Introduction

The word statistics has been derived from the Latin word ‘status’ or the Italian word ‘stastista’ or the German word ‘statistics,’ each of which means a political state. Initially statistics was concerned with economic, political and demographic particulars of a country. Today, statistics has broadened to include many things. It is so important to our way of living that many of us often use statistical analysis in making decisions without even realizing it. In recent years the growth of statistics has made itself felt in almost every phase of human activity. Statistics no longer consists in collection of data and their presentation in charts and tables; it is now considered to encompass the science of basing inferences on observed data and the entire problem of reaching decisions in the face of uncertainty.

Statistics is simply the science of the organization and the conceptual understanding of groups of numbers. This group of numbers is called data. It is the purpose of statistics to take all these numbers or data and present them in a more efficient way, actually in a more comprehensible way. A statistician needs to be a good story teller. A statistician must be able to articulate what was found in an experiment or observational study, why this finding is important and to whom, and what the data from these may mean for us in the future. A statistical background is indispensable in order to understand research reports.

Reasons to Study Statistics
  • Being an informed “Information Consumer
    > Extract information from charts and graphs
    > Follow numerical arguments
    > Know the basics of how data should be gathered, summarized and analyzed to draw statistical conclusions
  • Understanding and Making Decisions
    > Decide if existing information is adequate
    > Collect more information in an appropriate way
    > Summarize the available data effectively
    > Analyze the available data
    > Draw conclusions, make decisions, and assess the risks of an incorrect decision
  • Evaluate Decisions That Affect Your Life
    > Help understand the validity and appropriateness of processes and decisions that affect your life

What is statistics

The most popular, exhaustive and comprehensive definition of statistics in the pluralistic sense is given by Prof Horace Secrist. His definition states that “Statistics may be defined as the aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner, for a predetermined purpose and placed in relations to each other.”

The most crucial aspect of applying statistics consists of analyzing the data in such a way to obtain a more efficient and comprehensive summary of the overall results. To achieve these goals, statistics is divided into two areas, descriptive and inferential statistics.

1. Important Concepts in Statistics
  • Population: This is the entire set of events, people or phenomena about whom the researcher is interested. For instance, the researcher may be interested in all tribal societies in India. Another researcher may be interested in all students in International Baccalaureate schools in India. So we see a population may range from a relatively small set of events, people or phenomena that can be enumerated easily or a very large set that cannot be traced without a significant amount of time, money and personnel. Think back to all that you may have read in the newspapers or heard in the mass media about the Census of India that takes places. This is a once-in-10-years occurrence which involves counting all the people living in India. 
  • Parameters: When we are able to describe key aspects of the population, we are generating population parameters. Some of the population parameters on the Census of India website include literacy, male-to-female ratio and number of persons who report that they are employed.
  • Sample: But most research cannot attempt to undertake census-like operations. So most research is undertaken on smaller sets that are drawn systematically from the population. We call this smaller set of events, people or phenomena a sample. For instance, if you want to check whether there is sugar already in a cup of tea that is served to you in a restaurant, you would usually pick a spoon and sip a little to make sure before adding any more. The little that you taste off that spoon is essentially a sample representing the larger tea-cup. In this case, the tea-cup contains the “population” in which you are momentarily interested. 
  • Statistics and Parameters: Here you will learn another meaning of the term statistics: In this context, it refers to the set of numerical values that the researcher will compute to describe the sample (such as the average value or the range of values). For every population parameter, there is a corresponding sample statistic. The sample mean which is written as X with a bar on top (and read aloud as X-bar) corresponds to the population parameter mu (µ). Sample statistics are always written in roman letter-script while population parameters are written in Greek letters. Statisticians use carefully selected techniques to draw inferences about the larger population from what they know about the sample. How we select our sample will give us confidence to draw conclusions about the larger population of interest. We call this the sampling procedure. For instance, think back to the tasting of that spoon of tea to check for the sugar content in the cup: What happens if you taste a spoonful of tea from the surface but there is actually sugar at the bottom of the cup which has not been mixed in by stirring the cup?

Descriptive statistics:

Historically, this is the older area, and supplies several tools, such as tables, graphs, and basic description of number such as averages or means. These tools help in collecting, classifying and summarizing information about a collection of actual observations. Tables listing the different types of crimes against women reported in your state in the past one year, a graph showing the daily movement of the rupee in the last two weeks, and the grade point average in your mark sheet are all examples of statistical tools that organize and summarize information about a collection of actual observations. The most well-known statistics are the mean (that is the statistical average) and the mode (the most frequently occurring value). Knowledge of this aspect of Statistics enables us to evaluate critically the information presented in reports, articles, etc

Inferential statistics:

Inferential statistics is primarily a product of the twentieth century and supplies several tools for generalizing beyond actual observations. It involves informed and calculated making guesses (inferences) about a large group of data (called the population) from a smaller group of data (called the sample). Typically, sample data is randomly drawn from the population or larger group of data. The concept of random sampling means that every person in the population has an equal chance of being chosen for the limited size sample.

Types of data:

A statistical analysis is performed on data, that is, on a collection of actual observations from a survey or experiment. The precise form of a statistical analysis often depends on whether the data are numbers or words
  • Quantitative data:
    When, among a set of observations, any single observation is a number that represents an amount or a count, the data are quantitative. The weights of the hundred trucks recorded as per our earlier example are quantitative data, because any single observation represents an amount of weight.
  • Qualitative data:
    When, among a set of observations, any single observation is a word or code that represents a class or category, the data are qualitative. For instance, if a survey records the response of students with the code Y for Yes and N for No, to the question "Do you drink?" the resulting data is qualitative since each individual observation is a code that represents a particular class of replies. Often numbers are assigned to the Yes and No replies to permit computer processing. But we cannot derive a statistical average of these numbers. We can only report the most frequent value, or the relative percentage of values. 

Types of variables:

Another distinction from the realm of research methods is based on two types of variables. A variable is a characteristic or property that can take on different values. Weights of trucks or the replies (Y or N) are examples of variables but any single observation can be described as a constant, because it takes on only one value.
  • Independent variable:
    When a variable is manipulated by an investigator in an experiment, it is an independent variable
  • Dependent variable:
    When a variable is measured, counted or recorded by the investigator, it is a dependent variable. It is not manipulated. Instead it represents an outcome: the data produced by an experiment in relation to changes in the independent variable. Thus the values that appear for the dependent variable cannot be specified in advance.
  • Predictor and Criterion variables:
    Let us look at another example: empowerment of women. Social work researchers may be interested to see which women are able to achieve economic stability and/ or independence: Are younger women more likely to achieve economic stability? Are more educated women likely to achieve economic stability? The answer is that younger women are more likely to be educated. So is it age or is it education that is the special ingredient that leads to independence? Here researchers are not able to manipulate these variables. They can only draw inferences from observational or archival data sources. So we speak instead of predictor and criterion variables.
  • Predictor variables
    A predictor variable is one “from which a prediction is made” (Howell, 1999, p.144). In our example, age and education are predictor variables.
  • Criterion variables
    A criterion variable is one which is “to be predicted” (Howell, 1999, p.144). In our example, empowerment is the criterion variable. While depicting these variables graphically, we will traditionally designate the predictor variables as X (or X1, X2 and so on) and we will plot it on the X axis (the horizontal axis). Criterion variables as designated as Y (or Y1, Y2 and so on) and we will plot it on the Y axis (the vertical axi 

Summary

  • It is an acknowledged fact that learning statistics, one can interpret the statistical messages of everyday life, understand references in research reports and plan a simple statistical analysis of one’s own research. Statistics consists of two main subdivisions: descriptive and inferential statistics. 

References

  • Howell, D.C. (1999). Fundamental Statistics for the Behavioral Sciences (4th ed.). Pacific Grove, CA, USA: Duxberry Press.


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