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Research Methods in Politics Chapter 15 1 Research Methods in Politics 15 Testing for Association

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Research Methods in Politics Chapter 152 Teaching and Learning Objectives 1. to consider the concept of association between variables 2. to learn how to test for association by the application of correlation analysis and by applying tests of significance to the results 3. to learn how association between variables can be expressed as equations 4. to learn what is meant by regression and how to produce explanatory equations between two or more variables by applying linear regression analysis and multiple linear regression analysis

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Research Methods in Politics Chapter 153 Association univariate statistics, x univariate statistics, x bivariate statistics, x, y bivariate statistics, x, y multivariate statistics, x 1,x 2,x 3,... x n, y multivariate statistics, x 1,x 2,x 3,... x n, y independent variable (cause, driver) x dependent variable (effect, result, outcome) y independent variable (cause, driver) x dependent variable (effect, result, outcome) y expressed as y = f(x) i.e. y is a function of x expressed as y = f(x) i.e. y is a function of x relationship linear, exponential, logarithmic, curvilinear, etc relationship linear, exponential, logarithmic, curvilinear, etc

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Research Methods in Politics Chapter 154 Example: Pay and Union Density: is there any association (relationship)? Pay by Industry Pay as % Unionisation Industryof all industriesUnion Density % Newspaper Printing157.894 Mineral Oil Refining143.259 Underground Workers145.999 Coal Mining133.697 Air Transport130.885 Electricity and Gas122.995 Other Printing120.794 Port and Inland Water119.883 General Chemicals117.559 Aerospace Engineering117.380 Highest Industry Pay ……………………………………………………………………………………………………………………………………………………… Wholesale Distribution86.715Lowest Industry Pay Textiles86.299 Motor Repairs85.560 Industrial Materials85.315 Clothing84.042 Retail Distribution83.615 Woollen Worsted82.347 Education Services80.678 Catering77.9 8 Agriculture72.423 Table 15.1 Pay and union density: Source: Department of Employment, 1981: Table 54

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Research Methods in Politics Chapter 155 X-Y graph of Table 15.1 Union density and pay, 1981

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Research Methods in Politics Chapter 156 Analysis as union density increases, pay appears to increase as union density increases, pay appears to increase association appears to follow a straight line association appears to follow a straight line Pay = P 0 + g. Union Density Pay = P 0 + g. Union Density –where P 0 is pay level where union density is 0 and g is gradient of the straight line relationship can be calculated: coefficient of correlation, r relationship can be calculated: coefficient of correlation, r

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Research Methods in Politics Chapter 157 Regression coefficient of correlation, r coefficient of correlation, r devised by Galton (1822-1911) to measure regression devised by Galton (1822-1911) to measure regression tendency of children to have height etc. nearer the mean – going back tendency of children to have height etc. nearer the mean – going back r measures the tendency of paired data to regress r measures the tendency of paired data to regress relationship between two paired variables can be expressed as a linear regression equation relationship between two paired variables can be expressed as a linear regression equation y = a + bx + έ

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Research Methods in Politics Chapter 158 coefficient of correlation, r r expressed on a scale between +1.00 and -1.00 r = +1.00 perfect positive correlation r = -1.00 perfect negative correlation r = 0.00 no correlation

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Research Methods in Politics Chapter 159 coefficient of correlation, r r = 0.1, the association is termed of small importance r = 0.1, the association is termed of small importance r = 0.3, the association is termed of medium importance r = 0.3, the association is termed of medium importance r = 0.5, the association is termed of large importance r = 0.5, the association is termed of large importance R = 0.7> beware of collinearity: R = 0.7> beware of collinearity:x (concealed variable) z (concealed variable) zy interpretation from coefficient of determination, R 2 – proportion of the variance (change) in one variable that can be attributed to another interpretation from coefficient of determination, R 2 – proportion of the variance (change) in one variable that can be attributed to another evidence of correlation (association) does not necessarily mean causation evidence of correlation (association) does not necessarily mean causation

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Research Methods in Politics Chapter 1510 Calculating Regression Statistics using MS Excel: apply to Pay/ Union Density paired data using MS Excel: apply to Pay/ Union Density paired data –SUMMARY OUTPUT [part] –Regression Statistics –Multiple R0.688452 –R Square0.473966 –Adjusted R Square0.444742 [most reliable R 2] –Standard Error20.01117 –Observations20 – Coefficients Standard Error t Stat P-value Lower 95% Upper 95 % –Intercept 71.48414 9.822873 7.27 9.18E-07 50.84703 92.12124 –X Variable 1 0.564809 0.140249 4.02 0.00079 0.270157 0.859461 Pay = 71.5 + 0.56 Union Density

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Research Methods in Politics Chapter 1511 Null Hypothesis H 0 no relationship between pay and Union Density H 0 no relationship between pay and Union Density H 1 relationship between pay and Union Density H 1 relationship between pay and Union Density refer back to summary output refer back to summary output – Coefficients Standard Error t Stat P-value Lower 95% Upper 95 % –Intercept 71.48414 9.822873 7.27 9.18E-07 50.84703 92.12124 –X Variable 1 0.564809 0.140249 4.02 0.00079 0.270157 0.859461 –P-value is observed level of significance – 0.05 in Politics –if p value is low, then H 0 can go –P-values are below 0.05 –Null Hypothesis can be refuted –There is an association between Pay and Union Density

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Research Methods in Politics Chapter 1512 Multiple Regression Analysis y = A + B 1 x 1 + B 2 x 2 + B 3 x 3 +... + B n x n y = A + B 1 x 1 + B 2 x 2 + B 3 x 3 +... + B n x n where x 1,x 2,x 3,...x n are independent variables where x 1,x 2,x 3,...x n are independent variables additional data for Pay/Union Density shows additional data for Pay/Union Density shows Multiple linear regression equation is Multiple linear regression equation is – y = 35.2 + 0.46x1 + 0.14x2 + 0.31x3 + 0.21x4 + ε –Relative Pay % = 35.2 + 0.46 [Union Density%] + 0.14 [%Workers in plants of 500+] – + 0.31 [%male workers] + 0.18 [%UK market share] + residual error

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Research Methods in Politics Chapter 1513 R-matrix X1X1X1X1 X2X2X2X2 X3X3X3X3 X4X4X4X4 X5X5X5X5 X1X1X1X11 X2X2X2X20.6881 X3X3X3X30.1200.5851 X4X4X4X40.5370.1990.2261 X5X5X5X50.3290.169-0.5230.3141

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Research Methods in Politics Chapter 1514 Questions for Discussion or Assignments 1. Correlation does not necessarily mean causation. Discuss. Explain how you would investigate a high correlation for causation 2.The table below shows paired data for the total number of UK workers registered as unemployed and membership of the British Communist party, 1929-39. yearUK unemployed (000s)BCP membership 19291,216 3,200 1930 1,917 2,555 1931 2,630 6,279 19322,745 5,600 19332,521 5,700 19342,159 5,800 19352,036 7,700 19361,75511,500 19371,48412,250 19381,79115,570 19391,51417,756

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Research Methods in Politics Chapter 1515 Questions for Discussion or Assignments II 2.(Continued) Is there any evidence of association between unemployment and party membership between 1929 and 1939? Using Excel, draw an X-Y graph of unemployment on the x-axis and CP membership on the y-axis. Calculate the coefficient of correlation. Calculate the linear regression equation. Calculate the contribution made by unemployment to CP membership. Test the statistical significance of the calculation. Can the null hypothesis be dismissed? The data shows that, after 1934, CP membership increased whilst unemployment fell. What other causes of increasing CP membership can you suggest and why?

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Research Methods in Politics Chapter 1516 Questions for Discussion or Assignments III 3.Read carefully the extract from the publication by Rallings, C., and Thrasher, M., (1997) Local Government Elections in Britain, London, Routledge, pp. 46-63. Examine the relevant 2001 census data for the wards of a UK city of your choice from web-site www.neighbourhood.statistics.gov.uk www.neighbourhood.statistics.gov.uk On the basis of the information given in the selected text and the census data available, set out an hypothesis to the research question: which three factors are most likely to have affected electoral turnout in local elections in your chosen city? Find and save the most recent headline election data for ward turnout for all of the wards in your selected city from its web-site www.[selected city].gov.uk Select three independent/collinear variables from the census information for testing your hypothesis. Transpose the data for ward names, turnout and your three selected census variables into a single spreadsheet. Produce X-Y charts of the data. Using Microsoft Excel spreadsheet software, create a spreadsheet consisting of all wards, the turnout data and the three variables you have selected from the census data. Calculate the coefficients of correlation between turnout and selected census characteristics. What inferences can you draw from the association of turnout and selected census data? Are the data significant? What limitations do you attach to these inferences? Using the appropriate formula within Excel, calculate the multiple linear regression equation between ward turnout (Y) and the independent variables (X1.. Xn). Your submission should be no less than 2,000 words in report form. It must critically review the text by Rallings and Thrasher and clearly justify your choice of potential independent variables. You must then explicitly describe, justify and explain the analytic techniques you have adopted, the results, the linear regression equation calculated and the limitations attached to the output.

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Section 10.2-1 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Chapter 10 Correlation and Regression 10-2 Correlation 10-3 Regression.

Section 10.2-1 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Chapter 10 Correlation and Regression 10-2 Correlation 10-3 Regression.

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