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# Basic Statistics for Social Science Research * Dr. A. Asgari

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### Transcript of "Basic Statistics for Social Science Research * Dr. A. Asgari"

1. 1. BASIC STATISTICS FOR SOCIAL SCIENCE RESEARCH Dr. Azadeh Asgari Statistics in Research
2. 2. Purpose of Statistics <ul><li>To describe phenomena, </li></ul><ul><li>To organize and summarize our result more conveniently and meaningfully, </li></ul><ul><li>To make inference or make certain predictions, </li></ul><ul><li>To make explain, and </li></ul><ul><li>To make conclusion. </li></ul>
3. 3. Type of Statistics <ul><li>1. Descriptive Statistics: </li></ul><ul><li>Concerned with summarizing the distribution of single variable or measuring relationship between two or more variables (eg: Frequency distribution, measure of central tendencies, measures of dispersion and so on) </li></ul><ul><li>2. Inferential Statistics: </li></ul><ul><li>Concerned with making generalization from sample to population (eg: T-test, Analysis of Variance and Chi-square and so on). </li></ul>
4. 4. Concepts in Statistics <ul><li>a. Population </li></ul><ul><li>The entire group being observed, almost always assumed to be infinite in size </li></ul><ul><li>The total collection of all cases in which the researcher is interested and wishes to understanding. </li></ul><ul><li>Group or set of human subjects or other entities (eg: all student at the UPM, all members at government ) </li></ul><ul><li>b. Sample </li></ul><ul><li>The sub-group of population </li></ul><ul><li>Generalizations based on samples can accurately represent the population </li></ul>
5. 5. Concepts in Statistics (Cont.) <ul><li>Population </li></ul><ul><li>Basic unit of interest </li></ul><ul><li>Known as universe </li></ul><ul><li>Large in numbers </li></ul><ul><li>Difficult to observed </li></ul><ul><li>Dynamic </li></ul><ul><li>Sample </li></ul><ul><li>A portion of defined population </li></ul><ul><li>Small in numbers </li></ul><ul><li>Observable </li></ul><ul><li>Can draw inference about population </li></ul>
6. 6. Concepts in Statistics (Cont.) <ul><li>VARIABLE </li></ul><ul><li>As an observable characteristic of an object or event that can be described according to certain classification or scales of measurement. </li></ul><ul><li>Independent Variable: In bi-variate relationship, the variable is taken as cause, normally represented by symbol X. </li></ul>
7. 7. <ul><li>1. Dependent variable: In a bi-variate relationship, the variable is taken as the effect, normally represented by symbol Y. </li></ul><ul><li>2. Continuous variable/data: A variable/data with a unit of measurement that can be subdivided infinitely. e.g: height = 150.3 cm </li></ul><ul><li>3. Discrete variable/data: A variable with a basic unit of measurement that cannot be subdivided. </li></ul><ul><li>e.g: sex (1 = Male, 2 = Female ) </li></ul>Concepts in Statistics (Cont.)
8. 8. Measurement <ul><li>… is the process of assigning a number to object, place or person. </li></ul><ul><li>Level of Measurement </li></ul><ul><li>The mathematical characteristic of a variable as determined by the measurement process. A major criterion for selecting statistical procedures or techniques. </li></ul>
9. 9. Level of Measurement (Type of Data) <ul><li>1. Nominal </li></ul><ul><li>Sorting elements with respect to certain characteristics </li></ul><ul><li>Sort into categories that are at homogenous as possible </li></ul><ul><li>Lowest level of measurement </li></ul><ul><li>classification, naming, labeling </li></ul><ul><li>2. Ordinal </li></ul><ul><li>Grouping or classification of elements with degree of order or ranking </li></ul><ul><li>May not be able say exactly how much they possess </li></ul><ul><li>Can be arrange or placed in single continuum </li></ul><ul><li>e.g: Likert scale </li></ul>
10. 10. <ul><li>3. Interval </li></ul><ul><li>Ordering elements with respect to the degree to which they possess certain characteristics </li></ul><ul><li>Indicates the exact distance between them </li></ul><ul><li>Zero does not means absence </li></ul><ul><li>e.g: 0 degrees Celsius </li></ul><ul><li>4. Ratio </li></ul><ul><li>Ordering elements with respect to the degree to which they possess certain characteristics </li></ul><ul><li>Indicates the exact distance between them </li></ul><ul><li>Zero means absence – absolute </li></ul>Level of Measurement (Type of Data)
11. 11. <ul><li>These four scale of measurement can be generalized into TWO categories: </li></ul><ul><li>1. Non-metric: includes the nominal and ordinal scales of measurement. </li></ul><ul><li>2. Metric: include interval and ratio scales of measurement. </li></ul>Level of Measurement (Type of Data)
12. 12. 1. Descriptive Statistics <ul><li>Frequency Distribution </li></ul><ul><li>Measure of Central Tendency </li></ul><ul><li>Measure of Dispersion </li></ul><ul><li>Measure of Association </li></ul>
13. 13. Data Presentation <ul><li>Basic function of statistics to organize and summarize data: </li></ul><ul><li>Frequency table </li></ul><ul><li>Graphic presentation </li></ul><ul><li>- Pie Chart </li></ul><ul><li>- Bar Chart </li></ul><ul><li>- Histogram </li></ul><ul><li>- Polygon </li></ul><ul><li>- Line Graph </li></ul>
14. 14. General Guides <ul><li>Use mode when variable are nominal; you want to present quick and easy measure for ordinal, interval and ratio data/variables. </li></ul><ul><li>Use median when variable are ordinal; you want to report the central score and the scores measured at interval and ratio levels have badly skewed distribution. </li></ul><ul><li>Use mean when variables are interval or ratio (except for badly skewed distribution); you want to report the typical score and you anticipate additional statistical analysis. </li></ul>
15. 15. 2. Inferential Statistics <ul><li>To enable researcher to make statement or summary or decision about the population based on the sample </li></ul><ul><li>To enable researcher to make statement or summary or decision on the unseen data based on the empirical data </li></ul><ul><li>To enable researcher to make statement or summary or decision on the large group based on data from the small group. </li></ul>
16. 16. Two Main Procedures of Inferential Statistics <ul><li>1. ESTIMATES </li></ul><ul><li>2. HYPOTHESIS TESTING </li></ul>
17. 17. Statistical Assumption <ul><li>A set of parameters, guidelines indicating the conditions under which the procedures can be most appropriately used. </li></ul><ul><li>Every test has own assumption that should not be violated </li></ul><ul><li>Four main assumption of Inferential Statistics </li></ul>
18. 18. Main Assumption of Inferential Statistics <ul><li>Random sample </li></ul><ul><li>Characteristics are related to true population </li></ul><ul><li>Multiple random sample from same population yield similar statistics that cluster around true population parameters </li></ul><ul><li>Can calculate the sampling error associated with a sample statistics </li></ul>
19. 19. Normal Distribution <ul><li>The normal probability distribution is a continuous probability distribution. </li></ul><ul><li>Data in the normal distribution are measured in terms of standard deviation from mean and are called standard scores or Z score. </li></ul><ul><li>Characteristics of Normal Distribution: </li></ul><ul><li>1. It is a continuous probability distribution. </li></ul><ul><li>2. Symmetrical or bell-shaped with the mode, median and mean are equal. </li></ul><ul><li>3. The distribution contains an infinite number of cases. </li></ul><ul><li>4. The distribution is asymptotic – the tails approach abscissa: range from negative to positive infinity. </li></ul><ul><li>5. About 95% of distribution lies within 2 standard deviation from the mean. </li></ul>
20. 20. Hypothesis Testing <ul><li>Hypothesis is a tentative statement about something. </li></ul><ul><li>Statement concerning: </li></ul><ul><li>Differences between groups </li></ul><ul><li>Relationship or association between variables </li></ul><ul><li>Changes that occurs </li></ul><ul><li>Statement related to our prediction about population characteristics or relationship </li></ul><ul><li>Statement related to research question </li></ul><ul><li>Statement must be testable or verifiable </li></ul>
21. 21. Hypothesis Testing <ul><li>Hypothesis Statement And Testing Help Us On: </li></ul><ul><li>Drawing Conclusion </li></ul><ul><li>Making Implication </li></ul><ul><li>Making Suggestion </li></ul>
22. 22. Type of Hypothesis <ul><li>We are not going to prove the hypothesis is true, but we are to prove that is not true or false. </li></ul><ul><li>Statistical test is to test the hypothesis </li></ul><ul><li>Two Types Of Hypothesis: </li></ul><ul><li>Null Hypothesis ( Ho ) </li></ul><ul><li>Alternative/Research Hypothesis </li></ul><ul><li> ( Ha or H1 ) </li></ul>
23. 23. Type of Hypothesis <ul><li>Null Hypothesis: </li></ul><ul><li>A statement of no difference or no association (among variables, samples etc). </li></ul><ul><li>Alternative/Research Hypothesis: </li></ul><ul><li>A statement asserting that there is difference or association (among variables, samples, etc). </li></ul>
24. 24. Forms of Hypothesis <ul><li>There Are TWO Forms Of Hypothesis: </li></ul><ul><li>1. Directional Hypothesis: </li></ul><ul><li>e.g.: Ha: μ >230 or </li></ul><ul><li>Ha: μ < 230 </li></ul><ul><li>2. Non-directional Hypothesis: </li></ul><ul><li>e.g.: Ha: μ = 230 </li></ul>
25. 25. 5 Step Model for Hypothesis Testing <ul><li>Step 1: Making assumption </li></ul><ul><li>Samples selected randomly </li></ul><ul><li>Defined population </li></ul><ul><li>Interval-ratio data </li></ul><ul><li>Sampling distribution – normal </li></ul><ul><li>Step 2: State the null and research hypothesis </li></ul><ul><li>Step 3: Selecting the appropriate distribution such as z, t, f and χ ² and establishing the level of significance as well as critical region. Calculate the test statistics </li></ul>
26. 26. <ul><li>Step 4: State the level of significance and critical region </li></ul><ul><li>Level of significance or alpha level commonly used 0.05 </li></ul><ul><li>Critical region will determine the rejection or failure to reject the null hypothesis </li></ul><ul><li>Step 5: Making decision </li></ul><ul><li>If test statistic falls in the critical region, reject the null hypothesis. </li></ul><ul><li>If test statistic does not fall in the critical region, we fail to reject the null hypothesis at predetermined alpha level. </li></ul>5 Step Model for Hypothesis Testing
27. 27. <ul><li>a. Type I Error (ALPHA ERROR): </li></ul><ul><li>The probability of rejecting a null hypothesis that is in fact true. </li></ul><ul><li>b. Type II Error (BETA ERROR) </li></ul><ul><li>The probability of failing to reject the null hypothesis in fact false. </li></ul>Type I and Type II Error
28. 28. Level of Significance (Alpha Level) <ul><li>The probability of area under the sampling distribution that contains unlikely sample outcomes given that the null hypothesis is true. Also, the probability of type I error </li></ul><ul><li>Commonly expressed as 90%, 95% or 99% or written as alpha = 0.10, 0.05 or 0.01 </li></ul><ul><li>95%, refers to alpha 0.05 which means that we are 95% sure of making the right decision and 5% error. </li></ul>
29. 29. Critical Region <ul><li>The area under the sampling distribution that, in advance of the test itself, is defined as including unlikely sample outcome given that the null hypothesis is true. </li></ul><ul><li>Critical value of the test statistic to reject null hypothesis. </li></ul><ul><li>Critical value is defined from the test statistic table corresponding to its level of significance and degree of freedom. </li></ul>
30. 30. One-tailed and Two-tailed Test <ul><li>Critical region on one side or both sides of the distribution depending on the nature of alternative or research hypothesis. </li></ul><ul><li>e.g.: Ho: a = b (Two-tailed) </li></ul><ul><li>Ha: a ≠ b </li></ul><ul><li>Ha: a > b (One-tailed) </li></ul><ul><li>Ha: a < b </li></ul>
31. 31. One-tailed Test <ul><li>A type of hypothesis test used when the direction of the difference between variables or samples can be predicted (Directional hypothesis). </li></ul><ul><li>One-tailed test has a one critical region that correspond to the direction of the research hypothesis. </li></ul>
32. 32. Two-tailed Test <ul><li>A type of hypothesis test used when direction of difference between variables or samples cannot be predicted (Non-directional hypothesis). </li></ul><ul><li>Two-tailed test has a two critical regions on both sides of the distribution </li></ul>