Unit 1 - Introduction

Statistics For Social Sciences – MATH1208

https://sites.google.com/a/pcc.edu.jm/ statistics-for-social-sciences/about-me

Resources needed:

 Graph Book/Graph Papers

 Geometry Set

 Scientific Calculator

 Folder Leaves

 Hardcover Notebook for class

 At Least Five Current Past Papers

Websites

http://www.worldofstatistics.org/

http://www.examiner.com/article/community- college-students-and-the-international-year-of-statistics https://www.youtube.com/watch?

v=yxXsPc0bphQ&list=PLA6598DFE68727A9 C https://www.youtube.com/watch?

v=HKA0htesJOA

Online Platform

Google Classroom Code

uqzcnqs

Unit 1 – Introduction

Statistics

Statistics is concerned with the scientific

reasonable decisions on the basis of such analysis.

Population and Sample

A population can be finite or infinite. For

example, the population consisting of all bolts produced in a factory on a given day is finite. Whereas, the population consisting of all

possible outcomes of tossing a die in successive tosses is infinite.

The sample is a set of data taken from the

population to represent the population.

Important conclusions about the population can be inferred from the analysis of the sample.

https://www.youtube.com/watch?v=ehIKql_jz_4

https://www.youtube.com/watch?v=20NpnXa4UlI

Inductive Statistics or Statistical Inference

The phase of statistics dealing with the

consideration under which such inference is valid is called inductive statistics or statistical inference. The language of probability is often used in stating the conclusion because such inference cannot be absolutely certain.

Now, suppose you need to collect data on a very large population. For example, suppose you

want to know the average height of all the men in a city with a population of so many million residents. It isn't very practical to try and get the height of each man. Instead of using the entire population to gather the data, the statistician will collect a sample or samples from the millions of residents and make inferences about the entire population using the sample. This is where

inferential statistics comes into play.

In inferential statistics, the answers are never 100% accurate because the calculations use a sample taken from the population. The sample does not include every measurement from the population, and the methods use probability to fill in missing gaps.

Deductive or Descriptive Statistics

The phase of statistics that seeks only to

describe, organize and summarize the data for a given group without drawing any conclusions or inference about a larger group is called

descriptive or deductive statistics.

a collection of information. It gives information

that describes the data in some manner. For example, suppose a pet shop sells cats, dogs, birds and fish. If 100 pets are sold, and 40 out of the 100 were dogs, then one description of the data on the pets sold would be that 40% were dogs.

This same pet shop may conduct a study on the number of fish sold each day for one month and determine that an average of 10 fish were sold each day. The average is an example of

descriptive statistics.

Some other measurements in descriptive

statistics answer questions such as 'How widely dispersed is this data?', 'Are there a lot of

same?', 'What value is in the middle of this

data?', 'Where does a particular data value stand with respect with the other values in the data set?'

A graphical representation of data is another method of descriptive statistics. Examples of this visual representation are histograms, bar graphs and pie graphs, to name a few. Using these methods, the data is described by

compiling it into a graph, table or other visual representation.

This provides a quick method to make

purchased most in the summer, a graph might be a good medium to compare the number of each type of pet sold and the months of the year.

Qualitative (Or Categorical) and Quantitative Variable

Variables can be divided into two main types – qualitative (or categorical) and quantitative.

Quantitative variable is defined as a variable which can be given a numerical value.

Quantitative variables are said to be of two distinct types – discrete or continuous.

number of mangoes on a tree must be a definite value. On the other hand shoe size can be

bought only in ‘a whole number size’ or ‘a size and a half’. For example, size 8 and size 8 ,

regardless of the actual size of the person’s feet. Hence, a person with a size 8.25 feet will buy a 8 .

A continuous variable is a variable which can take any value within a given range. It can be obtained by measurement. For example, a

A qualitative (categorical) variable is defined as a variable which describes a characteristic. For example, the height of a person can be described as tall, short or average.

Exercise

State whether the following variables are qualitative or quantitative. If the variable is quantitative, state whether it is discrete or continuous.

1. The weight of a baby during its first year of life on earth.

2. The number of students in an examination.

4. The body temperature of a normal person.

5. The scores of a football team in five matches.

6. The speed of a bird in flight.

7. The number of apples on a tree.

8. The smell of flowers in a garden.

9. The number of males in my class.

10. The electricity used by a household throughout the year.

Uses of Statistics

 Organize and summarize data

 Generalize from knowledge of sample data

 Test hypothesis

 Make predictions from existing data

Abuses of Statistics

 Quoting statistics based on non-representative sample

 Formatting graphs to mislead the eye

 Designing questions to be used on a survey that will facilitate bias results

Data Collection Methods

Some methods of collecting data are assessment (test), questionnaire, use focus groups, survey, interviews, observational data and using

Activity

Use an example to explain one of the strengths and one of the weaknesses for each data

collection method below.

Strengths and Weaknesses of the different Data Collection Methods

Assessments/Tests

Assessment is the process of gathering and discussing information from multiple and diverse sources in order to develop a deep

Strengths of Tests

 It can provide measures of many characteristics of people.

 It is often standardized, i.e., the same stimulus is provided to all participants.

 It allows comparability of common measures across research populations.

 It facilitates strong psychometric properties (high measurement validity).

Weaknesses of Tests

 Nonresponse to selected items on the test.

 Tests are sometimes biased against certain groups of people.

 Open-ended questions and probing not available.

Questionnaires

A questionnaire is a research instrument

consisting of a series of questions and other prompts for the purpose of gathering

information from respondents.

Strengths of Questionnaires

 It is good for measuring attitudes from the research participant.

 It gives a quick turnaround response.

 Ease of data analysis for closed-ended items.

 Useful for exploration as well as confirmation.

 It can provide information about the participants way of thinking.

 Interviewers may respond in a way that is socially desirable.

 Nonresponse to selective items.

 Data analysis can be time consuming for open-ended items.

 Open-ended items may reflect differences in verbal ability, obscuring the issues of

interest.

Focus Groups

A focus group is a small, but demographically diverse group of people whose reactions are

studied especially in market research or political analysis in guided or open discussions about a new product or something else to determine the reactions that can be expected from a larger

population. It is a form of qualitative

group of people are asked about their

perceptions, opinions, beliefs, and attitudes towards a product, service, concept,

advertisement, idea, or packaging. Questions are asked in an interactive group setting where

participants are free to talk with other group members. During this process, the researcher either takes notes or records the vital points he or she is getting from the group. Researchers should select members of the focus group carefully for effective and authoritative responses.

Strengths of Focus Groups

 Can examine how participants react to each other.

 Allows for interaction and probing.

 Useful for exploring ideas and concepts.

 Provides window into the participants’ internal thinking.

Weaknesses of Focus Group

 May be dominated by one or two participants.

 Data analysis can be time consuming for open-ended data.

 Reactive and investigator effects may occur if participants feel they are being watched or studied.

 Sometimes expensive.

Interviews

An interview is

word "interview" refers to a one-on-one

conversation with one person acting in the role of the interviewer and the other in the role of the interviewee. The interviewer asks questions, the interviewee responds, with participants

taking turns talking. Interviews usually involve a transfer of information from interviewee to interviewer, which is usually the primary

purpose of the interview, although information transfers can happen in both directions

simultaneously.

One can contrast an interview which involves

bi-directional communication with a one-way flow of information, such as a speech or oration.

technologies such as the Internet have enabled conversations to happen in which parties are separated geographically, such as

with videoconferencing software,[2] _{and of}

course telephone interviews can happen without visual contact. Interviews almost always

involve spoken conversation between two or more parties, although in some instances a

"conversation" can happen between two persons who type questions and answers back and forth. Interviews can range from unstructured or free-wheeling and open-ended conversations in

which there is no predetermined plan with prearranged questions, to

order. They can follow diverse formats; for example, in a ladder interview, a respondent's answers typically guide subsequent interviews, with the object being to explore a

respondent's subconscious motives. Typically the interviewer has some way of recording the

information that is gleaned from the

interviewee, often by writing with a pencil and paper, sometimes transcribing with

a video or audio recorder, depending on the

context and extent of information and the length of the interview. Interviews may have a

duration, in the sense that the interview has a beginning and an ending.

 It is good for measuring attitudes and other content of interest

 It allows probing and posing of follow-up questions by the interviewer.

 It can provide information about the

participants’ internal meanings and ways of thinking.

 Telephone and e-mail interviews provide very quick turnaround.

 A relatively high response rate are often attainable.

Weaknesses of Interviews

 Reactive effects – Interviewees may try to show only what is socially desirable.

 Investigator effects may occur – untrained interviewers may distort data because of

 Interviewees may not recall important information and may lack self-awareness.

 Data analysis can be time consuming for open-ended items.

Observational Data

Observation is the active acquisition

of information from a primary source. In living beings, observation employs the senses. In

science, observation can also involve the

recording of data via the use of instruments. The term may also refer to any data collected during the scientific activity. Observations can

be qualitative, that is, only the absence or

a numerical value is attached to the

observed phenomenon by counting or measuring

Strengths of Observational Data

 It allows to directly see what people do

without having to rely on what they say they do.

 It provides first-hand experience, especially if the observer participates in the activities.

 The observer can determine what does not occur.

 The observer may see things that escape the awareness of people in the setting.

Weaknesses of Observational Data

 Reactive effects may occur when

 Cannot observe large or dispersed populations.

 Data analysis can be time consuming.

 Personal bias – the observer may only record what they perceive to be important.

Secondary/Already Existing Data (e.g. documents in a library)

Strengths of Documents and Physical Data

 Can provide insight into what people think and what they do.

 Can be collected for time periods occurring in the past (e.g. historical data).

 Provides useful background and historical data on people, groups and organizations.

 Reactive and investigator effects are very unlikely.

 It is may be incomplete.

 It may not apply to general populations.

 It may be representative only of one perpective.

 It may not provide insight into the

participants’ personal thinking for physical data.

Archived Research Data

An archive is an accumulation of historical

records or the physical place they are

located. Archives contain primary source documents that have accumulated over the course of an individual or organization's

lifetime, and are kept to show the function of that person or organization. The encyclopedia is an archive of world history.

 They are available on a wide variety of topics.

 It is inexpensive.

 Often reliable and valid.

 It can be used to study trends.

Weaknesses of Archived Research Data

 It may not be available for the population of interest to you.

 The data may be outdated.

 It may not be available for the research questions of interest to you.

 It may not address certain key issues of interest to you.

There are five stages in a statistical investigation:

1. Collection: Utmost care must be exercised in collecting data because they form the foundation of statistical analysis. If data are faulty, the

conclusion drawn can never be reliable. The

2. Organization: Data from published sources are generally in organized form. Data from

survey needs organization. The first step is data editing so that the omissions, inconsistencies, irrelevant answers and wrong computation in the returns may be corrected or adjusted. The

second step is to classify data and the last step is tabulation of data-arrange data in rows and

columns.

3. Presentation: After the data have been collected and organized, they are ready for presentation. It facilitates statistical analysis.

4. Analysis: Data are analyzed mostly in tabular form. Methods used are numerous ranging from simple observation of data to complicated,

sophisticated and highly mathematical techniques.

5. Interpretation: Drawing conclusions from the data collected and analyzed. It is a

degree of skills and experience. Correct