A Study On Effects Of The Numbers Of Scale Steps And Items On Reliability

Object: Establish a method of simulating scale scores. Explore the effects of the sample size ,the numbers of response items and scale steps on Cronbach?a coefficient under the normal, skewed and uniform distributions for giving references to scale design in practice. Conduct the pilot study of two other internal consistency reliability 0 and Q coefficients for further research in the future. Method: The sample size n was calculated according to Streiner and Norman抯 method. The times of simulation t were determined with the equation ?=1.96 s/VT when variation of the error c was stable. Scale scores were simulated by random programs of MATLAB. Software packages MATLAB and SPSS 10.0 were employed in the study. Resu Its: The simulated scale scores coincided with the expectations. Changes of reliability under positive and negative skewness distributions showed little differences. To keep the reliability loss less than 2% for 3,4,5,6 and 7-point scales, the numbers of items should be higher than 30,25,15,10 and 5 respectively if the distribution is normal; higher than 350,350, 35,20 and 10 respectively if the distribution is skewed; and higher than 90,150,10,5 and 5 respectively if the distribution is uniform. The reliability loss would be under 2% and even equal to 0 if the scale steps was large enough (e.g. ~ 8). No matter what the sample size was, the curves of reliability loss were close to each other or even overlapped under the different distributions. The a and 0 coefficients were nearly equal under various situations, but the loss of Q coefficient was less than the former two coefficients, especially when the number of scale steps was lower. Conc I us i ons: A method of simulating scale scores was proposed. The more the scale steps were, the less the reliability loss was. For 5,6 and 7-point scales, only smaller numbers of items were needed (the low limits were from 5 to 35) to keep the reliability loss lower (e.g. lower than 2%). -2- So they were recommended for applications in practice. The sample size had no significant effect on reliability. The Q coefficient was higher than a and 0 coefficients.