scope and nature of statistics

 

SOME BASIC CONCEPTS 

Statistics may be defined as the body of techniques used to facilitate the collection, organization, presentation, analysis, and interpretation of data to make decisions. The core ideas include.

 (1) Techniques for collecting data

 (2) Techniques for organizing and presenting data 

(3) Techniques for analyzing data 

(4) Interpreting results from analysis for informed decisions.

TYPES OF STATISTICS 

Statistics can be classified into two main branches: descriptive and inferential.

 DESCRIPTIVE STATISTICS Descriptive statistics are used to summarize or describe data in meaningful and useful ways. Descriptive statistics include statistics (or numbers), tables, charts, and graphs. It is important to note that the purpose of descriptive statistics stops at summarizing and describing data. It does not include any attempts to make inferences beyond summarizing and describing. 

 INFERENTIAL STATISTICS Inferential statistics are methods that employ probability theory for deducing and making predictions from the data that has been obtained. 

POPULATION AND SAMPLE Population refer to the number of people or items under study. We could learn about why students are late for school by asking all the students in a school for their reason. Considering all the students for the data collection means you are considering the entire population. However, there are times when considering all the students will be burdensome, so a few of them are selected to represent the whole student body. When a portion of the population is considered in research to represent the entire population, that portion is called a sample.

The main difference between a population and a sample is that a population includes all of the elements from a set of data whiles a sample consists of one or more observations from the population.

 TYPES OF VARIABLES

 A variable refers to an item of data that is liable to vary or change. For example, the age of students, the number of siblings, the color of cars, etc. There are two major types of variables.

 QUANTITATIVE VARIABLES These are variables that can be quantified by either measuring or counting. They are numeric in nature. Examples include age, temperature, weight, height, etc. A quantitative variable can be continuous or discrete variables are variables whose values are obtained by counting. For example, the number of students in a class. Continuous variables refer to variables that are measured. They take any values on a continuous scale. Examples of continuous variables include weight, height, age, temperature, color, and volume.

 QUALITATIVE VARIABLES Qualitative variables cannot be measured or counted. They are therefore non-numeric and can only be described or classified according to the characteristics or attributes they possess. Examples of qualitative random variables include color, sex, rank in the army, marital status, and grade. 

MEASUREMENT SCALES Data can further be classified according to the measurement scale on which they fall -nominal, ordinal, interval, and ratio. 

NOMINAL SCALE The nominal scale is the most limited level of measurement. It applies to qualitative data only. On the nominal scale, no order is required. For example, sex is nominal; so, we can list its categories as male (followed by) female or female (followed by) male. Similarly, marital status is nominal. This is because there is no unique order in which its categories married, single, divorced, widowed, etc. are listed. On the nominal scale, categories are mutually exclusive and exhaustive. Categories are said to be mutually exclusive if an individual or item can belong to one and only one category. In other words, once an individual or item has been included in one category, it must be excluded from any other category. Categories are said to be exhaustive if an individual or item can belong to at least one of them. 

ORDINAL SCALE The next higher scale of measurement is the ordinal scale which also applies to qualitative data only. On the ordinal scale, order is necessary; meaning that one category is lower than the other or vice versa. For example, Grades are ordinal, as excellent is higher than very good, which in turn is higher than good, and so on interval and ratio.

 NOMINAL SCALE The nominal scale is the most limited level of measurement. It applies to qualitative data only. On the nominal scale, no order is required. For example, sex is nominal; so, we can list its categories as: male (followed by) female or female (followed by) male. Similarly, marital status is nominal. This is because there is no unique order in which its categories married, single, divorced, widowed, etc. are listed. On the nominal scale, categories are mutually exclusive and exhaustive. Categories are said to be mutually exclusive if an individual or item can belong to one and only one category. In other words, once an individual or item has been included in one category, it must be excluded from any other category. Categories are said to be exhaustive if an individual or item can belong to at least one of them. 

ORDINAL SCALE The next higher scale of measurement is the ordinal scale which also applies to qualitative data only. On the ordinal scale, the order is necessary; meaning that one category is lower than the other or vice versa. For example, Grades are ordinal, as excellent is higher than very good, which in turn is higher than good, and so on It is important to note, however, that differences between categories cannot be determined or are meaningless. If 4 denotes excellent, 3 denotes very good, 2 denotes good and 1 denotes fair; it does not mean that an employee who is rated excellent is twice as competent as an employee who is rated good, just because excellent is denoted by 4 and good is denoted by 2. As with the categories in nominal data, categories in ordinal data are mutually exclusive and exhaustive.

 INTERVAL SCALE The interval scale is the next higher scale of measurement and applies to quantitative data only. The interval scale has all the properties of the ordinal scale, with the additional property that there is a meaningful difference between categories. There is no natural zero starting point. An example of a variable on an interval scale is temperature. 

RATIO SCALE The ratio scale is the highest scale of measurement. It applies to quantitative and has all the properties of an interval scale. In addition, the ratio scale has a meaningful zero starting point and a meaningful ratio between two numbers. An example is weight. A weighing scale that reads 0 kg, for example, gives an indication that there is absolutely no weight on it; and so, the zero starting point is meaningful. 

SOURCES OF STATISTICAL DATA

 Sources of data can be classified into two main groups depending on their origin. These two main groups are primary sources and secondary sources. Data that are derived from primary sources are called primary data and those obtained from secondary sources are called secondary data. In this session, you will learn about primary and secondary sources of data. 

PRIMARY SOURCES OF DATA Primary data are data originally generated by an investigator or researcher for use by himself or herself. The choice of method for collecting primary data is largely influenced by the nature of the problem at hand and the availability of money and time.

 ADVANTAGES OF PRIMARY DATA

 1. Targeted issues are addressed.

 2. Data interpretation is better

 3. Efficient spending for information

 4. Greater control

 DISADVANTAGES OF PRIMARY DATA

 1. High cost

 2. Time-consuming

 3. Inaccurate feedback

 4. More resources are required

SECONDARY SOURCES OF DATA

 Secondary data are data that have already been gathered or published by someone else before and for a purpose other than the current project. Ordinarily, secondary data is faster to collect and less expensive compared with primary data. Secondary data are available in libraries, government agencies' internet, and so on.

 ADVANTAGES OF SECONDARY DATA

 1. Less expensive

 2. Easily accessible 

3. Immediately available. 

4. Targeted issues are addressed.

 DISADVANTAGES OF SECONDARY DATA

 1. Not specific to the researcher's needs. 

2. Problems with incomplete information.

 3. Can adversely affect the quality of research.

 METHODS FOR COLLECTING DATA

 Methods for collecting data refer to the various ways data can be gathered. They include.

 DIRECT OBSERVATION 

This is a method of data collection where the researcher monitors the parameter, whose data is being collected. Direct observation has been used by some sociologists, particularly in areas where interviews and the use of questionnaires are not suitable.

SURVEYS

 In surveys, the investigator or researcher's task is to find a way to obtain information from individuals who are often referred to as respondents. A survey conducted on an entire population is called a census or complete enumeration; whilst those conducted on samples are called sample surveys. Surveys involve mainly the use of questionnaires and/or interviews to obtain the required information from respondents. In using the interview method, an investigator personally asks for the required information and obtains verbal responses to his/her questions. A questionnaire may consist of questions or statements or a mixture of the two which the respondents have to answer. Questionnaires are particularly useful when the respondents must remain anonymous. This is because they can be administered in ways that the respondents can feel confident that their identities are not known. A questionnaire is, therefore, very important and by far the most popular method for collecting data.

 EXPERIMENTS

 Primary data may also be generated by researchers through experiments. Experimental research is concerned with cause-and-effect relationships. An experiment can be conducted in laboratory or in a field setting.

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