1 / 66

Semester II: GC - Generic Compulsory Method Course G VIII

Semester II: GC - Generic Compulsory Method Course G VIII. Social Work Research & Statistical Applications Dr. Jaimon Varghese. G VIII Social Work Research & Statistical Applications. UNIT – 1: Fundamentals of scientific methods and research UNIT - 2: Research design, Sources of data

bina
Download Presentation

Semester II: GC - Generic Compulsory Method Course G VIII

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Semester II: GC - Generic Compulsory Method Course G VIII Social Work Research & Statistical Applications Dr. Jaimon Varghese

  2. G VIII Social Work Research & Statistical Applications UNIT – 1: Fundamentals of scientific methods and research UNIT - 2: Research design, Sources of data UNIT – 3: Data collection and processing UNIT – 4: Statistics for research, techniques and its application UNIT – 5: Presentation and Dissemination of research social work research

  3. Unit 4: Statistics for research, techniques & its application 1 Statistics: Definition, functions, levels of measurements, role and importance of statistics in research. 2 Descriptive statistics: Measures of central tendency (mean, median, mode), 3 Measures of dispersion (standard deviation, coefficient of variation), 4 Measures of correlation 5 Testing of hypothesis. Inferential Statistics: Parametric and Non-Parametric statistical tests. social work research

  4. Unit 4: Statistics for research, techniques & its application • Statistics: Definition: • Science of using numbers to represent facts or describe a situation • Croxton &Cowden, “Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data”. • A.L. Bowley“Statistics may be called the science of counting • “Statistics may be called the science of averages”. social work research

  5. Unit 4: Statistics for research, techniques & its application • Statistics: Definition: • King, “The science of statistics is the method of judging collective, natural or social, phenomenon from the results obtained from the analysis or enumeration or collection of estimates”. • Boddington “the science of estimates and probabilities”. social work research

  6. Unit 4: Statistics for research, techniques & its application • Statistics: Definition: • Horace Secrist“By statistics we mean aggregates of facts affected to a marked extent by a multiplicity of causes numerically expressed, enumerated or estimated according to reasonable standards of accuracy collected in a systematic manner for a predetermined purpose and placed in relation to each other”. social work research

  7. Unit 4: Statistics for research, techniques & its application • Statistics: Characteristics: • 1. Statistics are aggregate of facts • 2. Statistics are affected to a marked extent by a multiplicity of causes • 3. Statistics are numerically expressed, enumrated or estimated • 4. Statistics are numerated or estimated according to reasonable standard of accuracy • 5. Statistics should be collected in a systematic manner for a predetermined purpose • 6. Statistics should be capable of being placed in relation to each other social work research

  8. Unit 4: Statistics for research, techniques & its application Statistics: Functions To present facts in a definite form To simplify unwieldy and complex data To use it as a technique for making comparisons To enlarge individual experience To provide guidance in the formulation of policies To enable measurement of the magnitude of a phenomenon social work research

  9. Unit 4: Statistics for research, techniques & its application Statistics: Limitations The use of statistics is limited numerical studies Statistical methods deal with population or aggregate of individuals rather than with individuals Statistical relies on estimates and approximations Statistical results might lead to fallacious conclusions by deliberate manipulation of figures and unscientific handling social work research

  10. Unit 4: Statistics for research, techniques & its application • role and importance of statistics in research • Sampling • Data analysis • Descriptive statistics • Central tendencies • Derivative statistics • Variance • Correlation • Tests of significance social work research

  11. Levels of measurements –nominal, ordinal, interval and ratio • There are four basic measurement scales that become respectively more precise: nominal, ordinal, interval and ratio. • The precision of each type is directly related to the type of statistical test that can be performed on them. • The more precise the measurement scale, the more sophisticated the statistical analysis can be. social work research

  12. Levels of measurements – nominal • measurement scale in which numbers are used as names of categories; i.e., categorizes without order • Religious / caste / gender status of the people • Only category is referred by the number and there is no rank order or equal distance between the categories social work research

  13. Levels of measurements – ordinal • measurement scale that categorizes and indicates relative amount or rank-order of a characteristic • Educational status • Place in the occupational hierarchy • Distance between two ranks are not meaningful social work research

  14. Levels of measurements – interval • measurement scale that categorizes, indicates relative amount or rank-order of a characteristic, and has units of equal distance between consecutive points on the scale • Age, temperature • Equal interval, but ratio is meaningless; 80 degree centigrade is not twice as hot as 40 degree, though the value attributed is twice as large • Similarly 20 year old man is not half size as 40 year old man social work research

  15. Levels of measurements – ratio • measurement scale that categorizes, indicates relative amount or rank-order of a characteristic, has units of equal distance between consecutive points on the scale, and compares terms as ratios of one to another (i.e. has a true zero point). • Size, height, weight, income, expenditure • Mostly used in natural sciences social work research

  16. 3. Descriptive statistics: Measures of central tendency (mean, median, mode) • Measures of central tendency refer to estimation of average • Mean (arithmetic) is the total value of observation (frequencies) divided by number of observation; affected by the extremes; it may not represent any observation • Median is the central most observation estimated after arranging the observations in ascending or descending order, affected if the distribution is skewed positively or negatively • Mode is the most popular observation, impossible when all the observations are unique or the similar ones are the extremes • Arithmetic mean is generally considered social work research

  17. Unit 4: Statistics for research, techniques & its application , social work research

  18. Measures of dispersion (standard deviation, coefficient of variation)Dispersion • Dispersion is the measure of the range • Range and inter quartile deviation • Mean deviation & standard deviation • Mean deviation = ∑ (x – x’) / n • X = observation • X’ = mean • n = total number of observation • ∑ = sum total social work research

  19. Dispersion • Standard deviation (SD) = sq rt [∑ (x – x’)2 / (N – 1)] • SD for grouped data = sq rt ∑ f(x – x’)2 / (N – 1) • Coefficient of variation (Standard Error) is the estimated standard deviation of all the sample means from a specific population • Standard error (SE)= SD / sq rt N social work research

  20. Measures of correlation Coefficient of Correlation (r) • Meaning • It ascertains whether a change in one variable is associated with change in another variable. • Whether the higher income of parents is associated with high expectations of children in respect of salaries and the job they will subsequently take up. • Or if lower income of parents is correlated with lower expectation of children in regard to salaries and job they aspire to take up. social work research

  21. Coefficient of correlation (r) …….. • Magnitude/Extent / Strength • The coefficient of correlation (r) changes in value from positive one (+ 1.0) down through zero (0.0) to negative one or unity (- 1.0). • Coefficient of Correlation ranging from : • 1 to 0.7 ‘high’ • 0.7 to 0.4 ‘substantial” • 0.4 to 0.2 ‘low’ • below 0.2 ‘negligible’. social work research

  22. AGE AND ATTITUDE TOWARDS HIV/AIDS social work research

  23. Coefficient of correlation (r) …….. Karl Pearson’s product moment correlation coefficient (r) for normal distribution = ∑ [(x – x’)(y – y’)] / sq rt ∑(x – x’)2 ∑ (y – y’) 2 Spearman’s Rank correlation = 1 – [6 ∑d2 / n(n2 – 1)] where ‘d’ = difference between the ranks of two series Regression coefficient = ∑ [(x – x’)(y – y’)] / sq rt ∑(x – x’)2 ∑ (y – y’) 2 social work research

  24. Regression analysis Regression analysis is used for prediction (interpolation) of one value if the other value is known for two series of data that have good correlation y = a + bx a = y’ – bx’ b = ∑ [(x – x’)(y – y’)] / ∑(x – x’)2 social work research

  25. Coefficient of correlation (r) …….. • Using SPSS…. • To Obtain Bivariate Correlations • From the menus choose: • Analyze • Correlate • Bivariate... social work research

  26. Coefficient of correlation …. • Select two or more numeric variables. • The following options are also available: • For quantitative, normally distributed variables, choose the Pearson correlation coefficient. • If your data are not normally distributed or have ordered categories, choose Kendall’s tau-b or Spearman, which measure the association between rank orders. social work research

  27. Coefficient of correlation …. • Flag significant correlations. • Correlation coefficients significant at the 0.05 level are identified with a • single asterisk, and those significant at the 0.01 level are identified with two • asterisks. • Click OK in the main dialog box to run the procedure. social work research

  28. Interpretation of Coefficient of Correlation (r) • First of all see if Coefficient of Correlation is statistically significant. • Explain the nature of Correlation • Explain the strength of Correlation • When interpreting your results, be careful not to draw any cause-and-effect conclusions. social work research

  29. Testing of hypothesis. Inferential Statistics: Parametric and Non-Parametric statistical tests. Test of Significance • Tests of significance and applied usually for normal distribution (parametric tests). Tests for skewed or non normal distributions are known as non parametric tests (sign test & chi square test). • You can select two-tailed or one-tailed probabilities. • If the direction of association is known in advance, select One-tailed, otherwise, select Two-tailed. social work research

  30. Various Tests of Significance Parametric Tests (Lal Das, 2000:328-340) Two standard deviation method Sign Test (proportions) Paired T-test T-test for Independent Samples ANOVA Non Parametric Tests (Lal Das, 2000:314-325) Chi-square Kolmogorov Smirnov Test Sign Test The Wilcoxon Sign Test The Mann-Whitney U Test social work research

  31. Tests of significance (t-test & chi-square) • Tests of significance assumes that the distribution is normal • What is normal distribution? • Normal distribution is a frequency distribution of which 95.4 % of the observations lie within the distance of 2 standard deviations from the mean (68.2 % lies within 1 SD; 95 % lies within 1.96 SD and 99 % lies within 2.575 SD) social work research

  32. What is level of significance? • If the statistically derived value is above 1.96 (for two tailed) or 1.645 (for one tailed), but below 2.575 it is significant at 5 % level (0.05) (there is only 5 % chance for the occurrence of sample mean in comparison with the population mean) and the studied hypothesis is rather significant • If the statistically derived value is beyond 2.575 it is significant at 1 % level (0.01) (there is only 1 % chance for the occurrence of sample mean in comparison with the population mean) and the studied hypothesis is highly significant • 0.00380 social work research

  33. What is level of significance? • If the statistically derived value (level of significance) is greater than 0.05 and the studied hypothesis is not significant • If the statistically derived value (level of significance) is less than 0.05and greater than 0.01(there is only 5 % chance for the occurrence of sample mean in comparison with the population mean) the studied hypothesis is moderately significant • If the statistically derived value (level of significance) is less than 0.01, the studied hypothesis is highly significant(there is only 1 % chance for the occurrence of sample mean in comparison with the population mean). • 0.380 social work research

  34. What is level of significance? Example: • Hypothesis is that there is a gender difference with regard to time management skills. However, the chi-square test conducted upon Table 2.6 (Time management skills and Gender) shows that the level of significance is 0.380. Since the derived value is greater than 0.05 level of significance, there is no significant gender difference with regard to time management skills. social work research

  35. T- Tests • It is used for examining whether two samples differ significantly. • Types of t –tests: • Paired t – test • T – test for Independent Samples • Both the tests are used to assess significance of difference. social work research

  36. T – test for Independent Samples • T–test for independent samples is used for the scores (values) of two independent groups (two samples). • That means there is no logical relationships between the scores (values) that have been obtained for one group when compared with other group. social work research

  37. The Paired t – test • The test is used when the researcher draws two random samples from the same population, introduces a treatment to one group while holding the other without the treatment, and then compares the groups to see whether there is a statistically significant difference between the groups. social work research

  38. Self Esteem Scores of 10 Students social work research

  39. T– test for Independent Samples • The t – test for two independent samples examines the difference between their means to see how close or apart they are. social work research

  40. T – test for Independent Samples Continues….. • The data compares scores obtained by two groups of students, say for example, a group of Master degree students and a group of Bachelor’s degree students on a scale designed to measure attitude towards AIDS patients social work research

  41. ATTITUDE TOWARDS AIDS PATIENTS social work research

  42. Tests of Hypotheses: T – test ‘t’ score = (x – y)/SE where x = sample mean y = population mean SE = standard error Standard error (SE) = SD / sq rt N If total number of observation is less than 30 the derived value has to be compared to the table value for (N – 1)th row at 0.05 / 0.01 probability level. If the observations exceed 30 consider 1.96 and 2.575 as table values for 5 % and 1 % probability levels respectively social work research

  43. Standard Error & Z score • The distribution of sample means will normally follow normal distribution. Mean of the sample means will be the same as population mean. • Standard deviation of sample means is known as standard error (SE) • Z score = (sample mean – population mean)/SE • A variable where the observations have been converted into z-scores is known as a standardised variable. Z score measures the number of standard deviations an observation is away from the mean. The mean of z scores is zero and the SD is one. The mean z scores of different variables for an individual is his / her index value (indicator of excellence) social work research

  44. T test for proportions & Sign Test ‘t’ score for proportions = (x – y)/SE where x = sample (mean) proportion y = population (mean) proportion SE = standard error Standard error (SE) for proportions = sq rt {[p (1 – p)] / n} Sign test is non parametric test (skewed distribution, not normal) where median is used instead of mean; + sign is given to distributions above median and – sign is given for distributions below. Proportion of + signs upon the total distribution is considered for t test. social work research

  45. Confidence interval Confidence interval is the estimation of the interval (range) where the population mean lies in respect to the sample mean for a normal distribution. 95 % confidence interval = x’ +/- 1.96*SE 99 % confidence interval = x’ +/- 2.575*SE social work research

  46. Chi-square Test • The 2 (Greek letter 2 and pronounced as Ki-square) test provides us with a method to evaluate whether or not frequencies which have been empirically observed differ significantly from those which would be expected under a certain set of theoretical assumption. social work research

  47. Chi-square Test …… SEXUAL ABUSE OF STREET CHILDREN BY GENDER social work research

  48. Chi-square Test • Chi-square can be used only for tables containing counts • Each expected value should be five or more (modify the table conveniently combining some columns or rows • Standardized residual (r) beyond +/- 1.96 are significant • Standard residual (r) = (O – E) / sq rt E social work research

  49. Chi-square Test 2= ∑ [(O – E) 2 / E] O = observed frequency in each cell of a cross table (bi-variate) E = expected frequency for each cell from the contingency table where, E = (C x R)/T C = Column total; R = Row total; T = Grand total df = (k – 1) (r – 1); df is degree of freedom, k = number of columns and r = number of rows. Find the table value for the df at the required probability level (5 % or 1 %) compare it with the derived value, which, if found greater, the difference in the observation is significant. social work research

  50. Analysis of Variance (ANOVA) • Application of Chi-square and t-test is limited to bi-variate analysis. When there are more than two sets of scores are available, ANOVA is used to test the significance. • Total sum of squares (TSS) • = (∑ x2 + ∑ y2 + ∑ z2) – (∑ x + ∑ y + ∑ z) 2 /N • Between sum of squares (BSS) • = (∑ x)2 / n1 + (∑ y)2 / n2 + (∑ z)2 / n3 – (∑ x + ∑ y + ∑ z) 2 /N • Within sum of squares (WSS) = TSS – BSS • Between df (numerator) = k – 1 Within df (denominator) = N – k • mean squares between group = BSS / (k – 1) • mean squares within group = WSS / (N – k) • F = mean squares between groups / mean square within groups • Compare the derived value with F table value at DF [(k – 1)/(N – k)] social work research

More Related