Lectures one and two What is Statistics? Lecturer: Dr. Madgerie Jameson [email protected]

University of the West IndiesSchool of Education

Introduction To Statistics

Lectures one and twoWhat is Statistics?

Lecturer: Dr. Madgerie [email protected]

Opening ExampleWhere do you shop for clothes and shoes? Do you have a favourite store you shop at? If yes, Why do you shop there? Do you think television commercials have a part to play in your choice of shop? In the US a study was conducted by the National Retail Federation found that 18% of the adults they surveyed said that television commercials influenced them to shop at specific stores. What do you think?

Definition of Statistics• A set of tools and techniques that is used for

describing, organising and interpreting information or data (Salkind, 2008, p.7).

• The methods used to collect, organise, summarise, analyse, interpret and draw collusions from a given data set.

Statistics

Descriptive

Inferential

Descriptive StatisticsUsed to collect, organise, summarise and

present a data set usually presented in graphically. For example the following table shows the names of 12 students and their M.Ed majors. You can use the descriptive data to find the most popular choice of subject. , the average of students enrolled in the course.

Student Major Age Student

Major Age

Joey Reading 35 Bill Curriculum 30

Sarah Curriculum 27 Jane Science Ed 45

Althea Youth Guidance

47 Jeffrey Science Ed 27

Nicole Science Ed 50 Pauline Reading 40

Michael Curriculum 40 Louise Reading 34

Elizabeth Science Ed 27 Jordan Science Ed 35

Inferential StatisticsAre used to make inferences from a given

data set. Inferential statistics are often the next step after you have collected and summarised data.

Inferential Statistics are used to 1.Make generalisations from the sample to the

population using probabilities.2.Perform hypothesis testing.3.Determine relationships among groups.4.Make predictions .

Example Inferential Statistics

Prem Mann, Introductory Statistics, 7/E Copyright © 2010 John Wiley & Sons. All right reserved

POPULATION VERSUS SAMPLE

Definition A population consists of all elements –

individuals, items, or objects – whose characteristics are being studied. The population that is being studied is also called the target population.

A portion of the population selected for study is referred to as a sample.


Figure 1.1 Population and Sample


PopulationPopulation: Includes all objects of interest .

That is the complete set of data elements. For example, In the previous example the population of students would be all the students enrolled in Physics, Chemistry and Biology ( 50 students)

Parameter: Usually seen as the characteristics of the population and denoted with the Greek Letter [ mu (µ), sigma (σ)]

SampleSample: A sample is a portion of the

population selected for further analysis, For example, you may decide to use 20 out of the 50 students for further analysis.

Statistics: are associated with the sample and are usually denoted using the roman letters ( x, s).

ExampleAssume there are 80 students in the research methods class. 20 of the 80 students major is Youth Guidance. Since 20 is 25% of 80, we can say 25% of the students enrolled in the M.Ed programme major in youth guidance. The 25% is a parameter ( not a statistic) of the class because it is based on the entire population of M.Ed students. If we assume that the M.Ed programme is a representative of the entire post graduate programme we treat the 20 students as a sample drawn from a larger population of post graduate students ( Dip Ed, M.Phil) then the 25% becomes a statistic.


Definition A survey that includes every member of the

population is called a census. The technique of collecting information from a portion of the population is called a sample survey.


Example of Sample Survey



Definition A sample that represents the characteristics

of the population as closely as possible is called a representative sample.



Definition A sample drawn in such a way that each

element of the population has a chance of being selected is called a random sample. If all samples of the same size selected from a population have the same chance of being selected, we call it simple random sampling. Such a sample is called a simple random sample.


BASIC TERMS

Definition An element or member of a sample or

population is a specific subject or object (for example, a person, firm, item, state, or country) about which the information is collected.


BASIC TERMS

Definition A variable is a characteristic under study

that assumes different values for different elements. In contrast to a variable, the value of a constant is fixed.


BASIC TERMS

Definition The value of a variable for an element is

called an observation or measurement.

A data set is a collection of observations on one or more variables.


Example Charitable Donations of Six Retailers in 2007


DataFacts, observations and information that come from research.

Data types•Measurement Data are numeric (quantitative). •Categorical data are non numeric ( qualitative).

VariableDefinition: Characteristic or attribute that can

assume different valuesTypes of VariablesIndependent Variable: one that is

manipulated, measured or selected by the researcher.

Dependent variable: one that is not under the researcher’s control. It is observed and measured.

Random variable: A variable whose values are determined by chance.

SUMMATION NOTATION A sample of prices of five literary books: $75, $80, $35, $97, and $88 The variable price of a book: x Price of the first book = x1 = $75

Price of the second book = x2 = $80 … Adding the prices of all five books gives 75+80+35+97+88 = x1+x2+x3+x4+x5 = Σx


Example

Annual salaries (in thousands of dollars) of four workers are 75, 90, 125, and 61, respectively. Find

(a) ∑x (b) (∑x)² (c) ∑x²


Solution

(a) ∑x = x1 + x2 + x3 + x4

= 75 + 90 + 125 + 61 = 351 = $351,000(b) (∑x)² = (351)² = 123,201(c) ∑x² = (75)² + (90)² + (125)² + (61)² = 5,625 + 8,100 + 15,625 + 3,721

= 33,071


Example 2

The following table lists four pairs of m and f values:

Compute the following:

(a) Σm (b) Σf² (c) Σmf (d) Σm²f


Example 2: Solution


Entering data in Excel

http://www.youtube.com/watch?v=3DGxbNf-fyA/



SummaryStatistics is a tool that helps us understand

our world. This is done through the organisation of data that we have collected that permits us to make certain statements about how the features of the data can be related to other settings. Descriptive and inferential statistics work together . The type of statistics you use depends on the questions you want answered.

Documents

Lectures one and two What is Statistics? Lecturer: Dr. Madgerie Jameson [email protected]