Cronbach's Alpha: A Tool for Assessing the Reliability of Scales

RefsCortina, J.M. (1993). What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, 78, 98-104. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika. 16, 297-334.Hatcher, L. (1994). A step-by-step approach to using the SAS(R) system for factor analysis and structural equation modeling. Cary, NC: SAS Institute.Miller, M.B. (1995). Coefficient alpha: A basic introduction from the perspectives of classical test theory and structural equation modeling. Structural Equation Modeling, 2(3), 255-273.Nunnaly, J. (1978). Psychometric theory. New York: McGraw-Hill.Reuterberg, S.E., & Gustafsson, J.E. (1992). Confirmatory factor analysis and reliability: Testing measurement model assumptions. Educational and Psychological Measurement, 52, 795-811.Santos, J.R.A., Lippke, L., and Pope, P. (1998). PROC FACTOR: A tool for extracting hidden gems from a mountain of variables. Proceedings of the 23rd Annual SAS Users Group International Conference. Cary, NC: SAS Institute Inc.Zimmerman, D.W., Zumbo, B.D., & Lalonde, C. (1993). Coefficient alpha as an estimate of test reliability under violation of two assumptions. Educational and Psychological Measurement, 53, 33-49.

alphaWe judge the reliability of data tables by estimating how well the items that reflect the same construct yield similar results. We are looking at how consistent the results are for different items for the same construct within the measure. N is equal to the number of items and r-bar is the average inter-item correlation among the items. One can see from this formula that if you increase the number of items, you increase Cronbach's alpha. Additionally, if the average inter-item correlation is low, alpha will be low. As the average inter-item correlation increases, Cronbach's alpha increases as well. This makes sense intuitively - if the inter-item correlations are high, then there is evidence that the items are measuring the same underlying construct. This is really what is meant when someone says they have "high" or "good" reliability. They are refering to how well their items measure a single unidimensional latent construct. Note, that a reliability coefficient of 0.80 or higher is considered as "acceptable" in most Social Science applicationshttp://trochim.human.cornell.edu/kb/reltypes.htmhttp://www.nsoe.uconn.edu/siegle/research/Instrument/Reliability/Reliability.htmN=4Sum Var=15.1836734694Alpha=0.9949977262var4.24489795923.34693877553.34693877554.244897959259.836734693915745212685625378672845745215675624624129713116

answerbased upon p75 Heyes application of Pearsonx1x2x1-meansqrdx2-meansqrdDxDybestfit.htm120215.934.815.328.0931.27297-5.126.01-8.775.6944.3731419-0.10.013.310.89-0.3341310-1.11.21-5.732.496.2751013-4.116.81-2.77.2911.0761417-0.10.011.31.69-0.13718223.915.216.339.6924.57815190.90.813.310.892.9791114-3.19.61-1.72.895.271017152.98.41-0.70.49-2.03112.9210.1123.3mean14.115.7r=0.8005769455r=0.8005769455reliability or prediction

8-24-0.9344597166Pearson Product Moment Correlation (takes into account the mean value)-0.9032032993Spearman Rank Correlation Coefficient (considers only the rank order)testassesstestassess155101Is there a correlation?7921820484Correlation does not prove causal effect.1859123464Non-correlation indicates no connection.2157160336622285535659248

based upon p75 Heyes application of Pearsonx1x2x1-meansqrdx2-meansqrdDxDy1202129731419413105101361417718228151991114101715

mean14.115.7r=r=0.8005769455

sdxx-m(x-m)229-1112131-98140004111499815010100384>64.00>86n40meanERROR:#N/Amode40.5median8sd 68%meansd612152025303520.46.5614151617183517.33.960120150200250300350156.065.366.00.066.00.0

cfagecopy and sortuse frequency functionalt data23230234545245656574645451252343416413434193456562045656556454552343449353548565652545447242448494906145452948787839456565495439395939555565next5514.6

mmmABCD112020453120414051456056705481209145100230.636.8mean40 > 25b442.5mediang620mode8.2 not experimental design 8.14 common mistake

introPrinciples: significance; reliability; descriptive; inferential; Cohen & Manion p38-44Number: nominal; ordinal; interval; ratio7.12 worked example of poor tables of dataCodable data (nursery) mmm