Statistics lesson 1

StatisticsStatistics• Is a scientific body of Is a scientific body of

knowledge that deals with:knowledge that deals with:

collection of datacollection of data

organization or organization or presentation of datapresentation of data

analysis and interpretation analysis and interpretation of dataof data

• Is a statistical procedure Is a statistical procedure concerned with describing concerned with describing the characteristics and the characteristics and properties of group of properties of group of persons, places or things; it persons, places or things; it is based on easily verifiable is based on easily verifiable facts.facts.

Descriptive Descriptive StatisticsStatistics

• Is a statistical procedure Is a statistical procedure used to draw inferences for used to draw inferences for the population on the basis the population on the basis of the information obtained of the information obtained from the sample. from the sample.

Inferential StatisticsInferential Statistics

• Population.Population. It is the total collection of It is the total collection of all the elements (people, events, all the elements (people, events, objects, measurements, and so on) objects, measurements, and so on) one wishes to investigate.one wishes to investigate.

• Sample.Sample. Subgroup obtained from a Subgroup obtained from a population.population.

• Parameter.Parameter. A numerical value that A numerical value that describes a characteristic of a describes a characteristic of a population.population.

DefinitionsDefinitions

• Statistic.Statistic. It is a numerical value that It is a numerical value that describes a particular sample.describes a particular sample.

• Data.Data. This are facts, or a set of This are facts, or a set of information gathered or under study.information gathered or under study.

• Quantitative DataQuantitative Data are numerical in are numerical in nature and therefore meaningful nature and therefore meaningful arithmetic can be done.arithmetic can be done.

Ex:Ex: age age


• Qualitative DataQualitative Data are attributes which are attributes which cannot be subjected to meaningful cannot be subjected to meaningful arithmetic.arithmetic.

Ex:Ex: gender gender

• Discrete DataDiscrete Data assume exact values assume exact values only and can be obtained by countingonly and can be obtained by counting

Ex:Ex: number of students number of students


• Continuous DataContinuous Data assume infinite assume infinite values within a specified interval and values within a specified interval and can be obtained by measurement.can be obtained by measurement.

Ex:Ex: height height

• ConstantConstant is a characteristic or is a characteristic or property of a population or sample property of a population or sample which makes the member similar to which makes the member similar to each other.each other.


• VariableVariable is a characteristic or is a characteristic or property of a population or sample property of a population or sample which makes the members different which makes the members different from each other.from each other.

• Dependent.Dependent. A variable which is A variable which is affected by another variable.affected by another variable.

Ex:Ex: test scores test scores


• Independent.Independent. A variable which A variable which affects the dependent variable.affects the dependent variable.

Ex:Ex: number of hours spent in number of hours spent in studyingstudying


Levels of Levels of MeasurementsMeasurements• Nominal numbersNominal numbers do not mean do not mean

anything; they just label.anything; they just label.

Ex: Ex: SSS NumberSSS Number

• Ordinal numbersOrdinal numbers are used to label + are used to label + rank.rank.

Ex: Ex: size of t-shirtsize of t-shirt

Levels of Levels of MeasurementsMeasurements• Interval numbersInterval numbers are used to label + are used to label +

rank; do not have a true zero.rank; do not have a true zero.

Ex:Ex: temperature temperature

• Ratio numbersRatio numbers are used to label + are used to label + rank + equal unit of interval; have a rank + equal unit of interval; have a true zerotrue zero

Ex:Ex: number of votes number of votes

Target PracticeTarget PracticeA. Determine whether the set of data is A. Determine whether the set of data is qualitative or quantitative.qualitative or quantitative.

1.1. Models of cell phonesModels of cell phones2.2. Number of subscribers to Philippine Daily Number of subscribers to Philippine Daily News News 3.3. Weights of 1000 packs of a brand of Weights of 1000 packs of a brand of noodles noodles 4.4. Yes or No responses to survey questionYes or No responses to survey question5.5. Telephone number Telephone number

Target PracticeTarget PracticeB. Which of the following numbers is B. Which of the following numbers is discrete or continuous?discrete or continuous? 1.1. Distance from town A to town BDistance from town A to town B

2.2. Record of absent students in a class Record of absent students in a class in in StatisticsStatistics

3.3. Number of customers in a restaurantNumber of customers in a restaurant

4.4. Number of cars parked in the Number of cars parked in the basement of basement of a buildinga building5.5. Weights of all Grades 1 pupils in the Weights of all Grades 1 pupils in the Library School Library School

Target PracticeTarget PracticeC. C. Identify the level of measurement: Identify the level of measurement: nominal(N), ordinal(O), interval(I), or ratio(R) nominal(N), ordinal(O), interval(I), or ratio(R) most appropriate for each of the following most appropriate for each of the following data.data.

1.1. Color of the eyeColor of the eye 2.2. Number of votesNumber of votes 3.3. Rank of facultyRank of faculty 4.4. Exam scoreExam score5.5. Temperature in Baguio last summer Temperature in Baguio last summer

Determining the Determining the Sample SizeSample SizeSlovin’s Formula:Slovin’s Formula:

21

Nn

Ne

nn is the sample size

NN is the population size

ee is the margin of error

TheThe margin of error margin of error is a value which is a value which quantifies possible sampling errors.quantifies possible sampling errors.

Determining the Determining the Sample SizeSample SizeTheThe margin of error margin of error can be interpreted can be interpreted

by the use of ideas from the laws of by the use of ideas from the laws of probability. In reality, it is what probability. In reality, it is what statisticians call a statisticians call a confidence confidence interval.interval.

Sampling error Sampling error means that the results means that the results in the sample differ from those of the in the sample differ from those of the target population because of the target population because of the “luck of the draw”.“luck of the draw”.

Sampling TechniquesSampling TechniquesSamplingSampling is the process of selecting is the process of selecting

samples from a given population.samples from a given population.

1.1. Probability SamplingProbability Sampling

2.2. Non-probability SamplingNon-probability Sampling

Types:Types:

Sampling TechniquesSampling TechniquesA.A. Probability Sampling: Probability Sampling: Samples are Samples are

chosen in such a way that each chosen in such a way that each member of the population has a member of the population has a known though not necessarily equal known though not necessarily equal chance of being included in the chance of being included in the samples.samples.

- Avoids biasesAvoids biases

- It provides the basis for calculating It provides the basis for calculating the margin of error.the margin of error.

Sampling TechniquesSampling Techniques1.1.Simple Random Sampling:Simple Random Sampling: Samples Samples

are chosen at random with members are chosen at random with members of the population having a known or of the population having a known or sometimes equal probability or sometimes equal probability or chance of being included in the chance of being included in the samples.samples.

a.a. LotteryLottery

b.b. Generation of random numbersGeneration of random numbers

Sampling TechniquesSampling Techniques2. Systematic Sampling: 2. Systematic Sampling: Samples are Samples are

chosen following certain rules set by chosen following certain rules set by the researchers. This involves the researchers. This involves choosing the kchoosing the kthth member of the member of the population, with k=N/n, but there population, with k=N/n, but there should be a random start.should be a random start.

Sampling TechniquesSampling Techniques3. Cluster Sampling: 3. Cluster Sampling: is sometimes is sometimes

called called area samplingarea sampling because it is because it is usually applied when the population usually applied when the population is large.is large.

In this technique, groups or In this technique, groups or clusters instead of individuals are clusters instead of individuals are randomly chosen.randomly chosen.

Sampling TechniquesSampling Techniques4. Stratified Random Sampling: 4. Stratified Random Sampling: This This

method is used when the population method is used when the population is too big to handle, thus dividing N is too big to handle, thus dividing N into subgroups, called into subgroups, called stratastrata, is , is necessary. necessary.

A process that can be used is A process that can be used is proportional allocationproportional allocation..

Sampling TechniquesSampling TechniquesB. Non Probability Sampling:B. Non Probability Sampling: Each Each

member of the population does not member of the population does not have a known chance of being have a known chance of being included in the sample. Instead, included in the sample. Instead, personal judgment plays a very personal judgment plays a very important role in the selection.important role in the selection.

Non-probability sampling is one of Non-probability sampling is one of the sources of the sources of errorserrors in research. in research.

Sampling TechniquesSampling TechniquesTypes:Types:1.1.Convenience Sampling: Convenience Sampling: This type is This type is

used because of the convenience it used because of the convenience it offers to the researcher.offers to the researcher.

2.2.Quota Sampling:Quota Sampling: This is very similar This is very similar to the stratified random sampling. to the stratified random sampling. The only difference is that the The only difference is that the selection of the members of the selection of the members of the samples in stratified sampling is samples in stratified sampling is done randomly.done randomly.

Sampling TechniquesSampling Techniques3. Purposive Sampling:3. Purposive Sampling: Choosing the Choosing the

respondents on the basis of pre-respondents on the basis of pre-determined criteria set by the determined criteria set by the researcher. researcher.

Data Gathering Data Gathering TechniquesTechniques1.1.The Direct or the Interview Method: The Direct or the Interview Method:

In this method, the researcher has In this method, the researcher has direct contact with the researcher.direct contact with the researcher.

A: Clarification can be done easily.A: Clarification can be done easily.

D: Costly and time-consuming.D: Costly and time-consuming.

Data Gathering Data Gathering TechniquesTechniques1.1.The Indirect or Questionnaire The Indirect or Questionnaire

Method: Method: The researcher gives or The researcher gives or distributes the questionnaire to the distributes the questionnaire to the respondents either by personal respondents either by personal delivery or by mail.delivery or by mail.

A: Saves time and money; large A: Saves time and money; large number of samples can be reached.number of samples can be reached.

D: Problem of retrievalD: Problem of retrieval

Data Gathering Data Gathering TechniquesTechniquesThe Questionnaire The Questionnaire (characteristics)(characteristics)

1.1. IItt sshhoouulldd ccoonnttaaiinn aa sshhoorrtt lleetttteerr ttoo tthhee rreessppoonnddeennttss wwhhiicchh iinncclluuddeess::

a. The purpose of the surveya. The purpose of the survey

b. An assurance of confidentialityb. An assurance of confidentiality

c. The name of the researcher or c. The name of the researcher or writer of the questionnairewriter of the questionnaire


2. There is a descriptive title/name for 2. There is a descriptive title/name for the questionnaire.the questionnaire.

3. It is designed to achieve objectives.3. It is designed to achieve objectives.

4. The directions are clear4. The directions are clear

5. It is designed for easy tabulation.5. It is designed for easy tabulation.


6. It avoids the use of double 6. It avoids the use of double negatives.negatives.

7. It also avoids double barreled 7. It also avoids double barreled questions.questions.

8. It phrases questions well for all 8. It phrases questions well for all respondents.respondents.

Data Gathering Data Gathering TechniquesTechniquesTypes of QuestionnaireTypes of Questionnaire

• OpenOpen – this type has an unlimited – this type has an unlimited responsesresponses

• ClosedClosed – this type limits the scope of – this type limits the scope of responsesresponses

• CombinationCombination – this type is a – this type is a combination of open and closed combination of open and closed types of questionnairetypes of questionnaire

Data Gathering Data Gathering TechniquesTechniquesTypes of QuestionsTypes of Questions

• Multiple choice Multiple choice – allows respondent – allows respondent to select answer/s from the listto select answer/s from the list

• RankingRanking – asks respondents ton rank – asks respondents ton rank the given itemsthe given items

• ScalesScales – asks respondents to give – asks respondents to give his/her degree of agreement to a his/her degree of agreement to a statement (Likert-scale)statement (Likert-scale)

Data Gathering Data Gathering TechniquesTechniques3.The Registration Method: 3.The Registration Method: This This

method of gathering data is governed method of gathering data is governed by laws.by laws.

A: Most reliable source of dataA: Most reliable source of data

D: Data are limited to what are listed D: Data are limited to what are listed in the documentsin the documents

Data Gathering Data Gathering TechniquesTechniques4. The Experimental Method: 4. The Experimental Method: This This

method of gathering data is used to method of gathering data is used to find out cause and effect find out cause and effect relationships.relationships.

A: Can go beyond plain descriptionA: Can go beyond plain description

D: Lots of threats to internal and D: Lots of threats to internal and external validityexternal validity

Presentation of DataPresentation of DataTextual Form: Textual Form: Data are presented in Data are presented in

paragraph or in sentences. This paragraph or in sentences. This includes enumeration of important includes enumeration of important characteristics, emphasizing the characteristics, emphasizing the most significant features and most significant features and highlighting the most striking highlighting the most striking attributes of the set of data.attributes of the set of data.

Presentation of DataPresentation of DataTabular Form: Tabular Form: A more effective device A more effective device

of presenting data.of presenting data.

1. stem and leaf plots1. stem and leaf plots

2. frequency distribution table2. frequency distribution table

3. contingency table3. contingency table

Presentation of DataPresentation of DataGraphical/Pictorial Form: Graphical/Pictorial Form: A most A most

effective device of presenting data.effective device of presenting data.

1. line graph (freq. polygon, ogive)1. line graph (freq. polygon, ogive)

2. bar graph (histogram)2. bar graph (histogram)

3. pie chart3. pie chart

4. pictograph 4. pictograph

5. statistical maps5. statistical maps

Statistics lesson 1

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Transcript of Statistics lesson 1