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# Statistics lesson 1

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### Statistics lesson 1

1. 1. Statistics
2. 2. Statistics <ul><li>Is a scientific body of knowledge that deals with: </li></ul><ul><ul><li>collection of data </li></ul></ul><ul><ul><li>organization or presentation of data </li></ul></ul><ul><ul><li>analysis and interpretation of data </li></ul></ul>
3. 3. <ul><li>Is a statistical procedure concerned with describing the characteristics and properties of group of persons, places or things; it is based on easily verifiable facts. </li></ul>Descriptive Statistics
4. 4. <ul><li>Is a statistical procedure used to draw inferences for the population on the basis of the information obtained from the sample. </li></ul>Inferential Statistics
5. 5. <ul><li>Population. It is the total collection of all the elements (people, events, objects, measurements, and so on) one wishes to investigate. </li></ul><ul><li>Sample. Subgroup obtained from a population. </li></ul><ul><li>Parameter. A numerical value that describes a characteristic of a population. </li></ul>Definitions
6. 6. <ul><li>Statistic. It is a numerical value that describes a particular sample. </li></ul><ul><li>Data. This are facts, or a set of information gathered or under study. </li></ul><ul><li>Quantitative Data are numerical in nature and therefore meaningful arithmetic can be done. </li></ul><ul><ul><li>Ex: age </li></ul></ul>Definitions
7. 7. <ul><li>Qualitative Data are attributes which cannot be subjected to meaningful arithmetic. </li></ul><ul><ul><li>Ex: gender </li></ul></ul><ul><li>Discrete Data assume exact values only and can be obtained by counting </li></ul><ul><ul><li>Ex: number of students </li></ul></ul>Definitions
8. 8. <ul><li>Continuous Data assume infinite values within a specified interval and can be obtained by measurement. </li></ul><ul><ul><li>Ex: height </li></ul></ul><ul><li>Constant is a characteristic or property of a population or sample which makes the member similar to each other. </li></ul>Definitions
9. 9. <ul><li>Variable is a characteristic or property of a population or sample which makes the members different from each other. </li></ul><ul><li>Dependent. A variable which is affected by another variable. </li></ul><ul><ul><li>Ex: test scores </li></ul></ul>Definitions
10. 10. <ul><li>Independent. A variable which affects the dependent variable. </li></ul><ul><ul><li>Ex: number of hours spent in studying </li></ul></ul>Definitions
11. 11. Levels of Measurements <ul><li>Nominal numbers do not mean anything; they just label. </li></ul><ul><ul><li>Ex: SSS Number </li></ul></ul><ul><li>Ordinal numbers are used to label + rank. </li></ul><ul><ul><li>Ex: size of t-shirt </li></ul></ul>
12. 12. Levels of Measurements <ul><li>Interval numbers are used to label + rank; do not have a true zero. </li></ul><ul><ul><li>Ex: temperature </li></ul></ul><ul><li>Ratio numbers are used to label + rank + equal unit of interval; have a true zero </li></ul><ul><ul><li>Ex: number of votes </li></ul></ul>
13. 13. Target Practice <ul><li>A. Determine whether the set of data is qualitative or quantitative. </li></ul><ul><li>Models of cell phones </li></ul><ul><li>Number of subscribers to Philippine Daily News </li></ul><ul><li>Weights of 1000 packs of a brand of noodles </li></ul><ul><li>Yes or No responses to survey question </li></ul><ul><li>Telephone number </li></ul>
14. 14. Target Practice <ul><li>B. Which of the following numbers is discrete or continuous? </li></ul><ul><li>Distance from town A to town B </li></ul><ul><li>Record of absent students in a class in Statistics </li></ul><ul><li>Number of customers in a restaurant </li></ul><ul><li>Number of cars parked in the basement of a building </li></ul><ul><li>Weights of all Grades 1 pupils in the Library School </li></ul>
15. 15. Target Practice <ul><li>C. Identify the level of measurement: nominal(N), ordinal(O), interval(I), or ratio(R) most appropriate for each of the following data. </li></ul><ul><li>Color of the eye </li></ul><ul><li>Number of votes </li></ul><ul><li>Rank of faculty </li></ul><ul><li>Exam score </li></ul><ul><li>Temperature in Baguio last summer </li></ul>
16. 16. Determining the Sample Size Slovin’s Formula: n is the sample size N is the population size e is the margin of error The margin of error is a value which quantifies possible sampling errors.
17. 17. Determining the Sample Size The margin of error can be interpreted by the use of ideas from the laws of probability. In reality, it is what statisticians call a confidence interval. Sampling error means that the results in the sample differ from those of the target population because of the “luck of the draw”.
18. 18. Sampling Techniques Sampling is the process of selecting samples from a given population. <ul><li>Probability Sampling </li></ul><ul><li>Non-probability Sampling </li></ul>Types:
19. 19. Sampling Techniques <ul><li>Probability Sampling: Samples are chosen in such a way that each member of the population has a known though not necessarily equal chance of being included in the samples. </li></ul><ul><ul><li>Avoids biases </li></ul></ul><ul><ul><li>It provides the basis for calculating the margin of error. </li></ul></ul>
20. 20. Sampling Techniques <ul><li>Simple Random Sampling: Samples are chosen at random with members of the population having a known or sometimes equal probability or chance of being included in the samples. </li></ul><ul><ul><li>Lottery </li></ul></ul><ul><ul><li>Generation of random numbers </li></ul></ul>
21. 21. Sampling Techniques 2. Systematic Sampling: Samples are chosen following certain rules set by the researchers. This involves choosing the k th member of the population, with k=N/n, but there should be a random start.
22. 22. Sampling Techniques 3. Cluster Sampling: is sometimes called area sampling because it is usually applied when the population is large. In this technique, groups or clusters instead of individuals are randomly chosen.
23. 23. Sampling Techniques 4. Stratified Random Sampling: This method is used when the population is too big to handle, thus dividing N into subgroups, called strata , is necessary. A process that can be used is proportional allocation .
24. 24. Sampling Techniques B. Non Probability Sampling: Each member of the population does not have a known chance of being included in the sample. Instead, personal judgment plays a very important role in the selection. Non-probability sampling is one of the sources of errors in research.
25. 25. Sampling Techniques Types: <ul><li>Convenience Sampling: This type is used because of the convenience it offers to the researcher. </li></ul><ul><li>Quota Sampling: This is very similar to the stratified random sampling. The only difference is that the selection of the members of the samples in stratified sampling is done randomly. </li></ul>
26. 26. Sampling Techniques 3. Purposive Sampling: Choosing the respondents on the basis of pre-determined criteria set by the researcher.
27. 27. Data Gathering Techniques <ul><li>The Direct or the Interview Method: In this method, the researcher has direct contact with the researcher. </li></ul><ul><li>A: Clarification can be done easily. </li></ul><ul><li>D: Costly and time-consuming. </li></ul>
28. 28. Data Gathering Techniques <ul><li>The Indirect or Questionnaire Method: The researcher gives or distributes the questionnaire to the respondents either by personal delivery or by mail. </li></ul><ul><li>A: Saves time and money; large number of samples can be reached. </li></ul><ul><li>D: Problem of retrieval </li></ul>
29. 29. Data Gathering Techniques <ul><li>The Questionnaire (characteristics) </li></ul><ul><li>It should contain a short letter to the respondents which includes: </li></ul><ul><ul><li>a. The purpose of the survey </li></ul></ul><ul><ul><li>b. An assurance of confidentiality </li></ul></ul><ul><ul><li>c. The name of the researcher or writer of the questionnaire </li></ul></ul>
30. 30. Data Gathering Techniques The Questionnaire (characteristics) 2. There is a descriptive title/name for the questionnaire. 3. It is designed to achieve objectives. 4. The directions are clear 5. It is designed for easy tabulation.
31. 31. Data Gathering Techniques The Questionnaire (characteristics) 6. It avoids the use of double negatives. 7. It also avoids double barreled questions. 8. It phrases questions well for all respondents.
32. 32. Data Gathering Techniques <ul><li>Types of Questionnaire </li></ul><ul><li>Open – this type has an unlimited responses </li></ul><ul><li>Closed – this type limits the scope of responses </li></ul><ul><li>Combination – this type is a combination of open and closed types of questionnaire </li></ul>
33. 33. Data Gathering Techniques <ul><li>Types of Questions </li></ul><ul><li>Multiple choice – allows respondent to select answer/s from the list </li></ul><ul><li>Ranking – asks respondents ton rank the given items </li></ul><ul><li>Scales – asks respondents to give his/her degree of agreement to a statement (Likert-scale) </li></ul>
34. 34. Data Gathering Techniques 3.The Registration Method: This method of gathering data is governed by laws. A: Most reliable source of data D: Data are limited to what are listed in the documents
35. 35. Data Gathering Techniques 4. The Experimental Method: This method of gathering data is used to find out cause and effect relationships. A: Can go beyond plain description D: Lots of threats to internal and external validity
36. 36. Presentation of Data Textual Form: Data are presented in paragraph or in sentences. This includes enumeration of important characteristics, emphasizing the most significant features and highlighting the most striking attributes of the set of data.
37. 37. Presentation of Data Tabular Form: A more effective device of presenting data. 1. stem and leaf plots 2. frequency distribution table 3. contingency table
38. 38. Presentation of Data Graphical/Pictorial Form: A most effective device of presenting data. 1. line graph (freq. polygon, ogive) 2. bar graph (histogram) 3. pie chart 4. pictograph 5. statistical maps