WEBVTT WEBVTT Kind: captions Language: en 00:00:00.030 --> 00:00:06.450 Coefficient alpha sometimes called cronbach's  alpha or tau-equivalent reliability is one of   00:00:06.450 --> 00:00:09.750 the most commonly used reliability  indices in social science research. 00:00:09.750 --> 00:00:14.130 It may not be the best index for  every scenario but it is commonly   00:00:14.130 --> 00:00:17.670 used and therefore it is important  to understand what it quantifies   00:00:17.670 --> 00:00:21.300 and under which assumptions it  is a good reliability index. 00:00:21.300 --> 00:00:28.440 Coefficient alpha is sometimes referred to as  internal consistency reliability. What that means   00:00:28.440 --> 00:00:35.640 is that is based on or its calculated based on  how consistent the indicators are interrelated. So   00:00:35.640 --> 00:00:41.310 basically it means how highly the indicators are  correlated. And this index is calculated from the   00:00:41.310 --> 00:00:46.860 correlation matrix of the indicators or covariance  matrix depending on which equation you apply. 00:00:46.860 --> 00:00:54.360 Coefficient alpha quantifies what is the  reliability of a scale score calculated as   00:00:54.360 --> 00:00:59.640 a sum of the scale items. So if you  have a scale of five items or five   00:00:59.640 --> 00:01:03.630 measures that are supposed to measure  the same thing and then you take a mean   00:01:03.630 --> 00:01:10.020 or a sum of those five items then alpha  quantifies the reliability of that sum. 00:01:10.020 --> 00:01:17.070 The part about internal consistency  is very important because while alpha   00:01:17.070 --> 00:01:22.920 is an internal consistency measure in  terms that it quantifies how strongly   00:01:22.920 --> 00:01:28.200 the indicators are correlated it doesn't  test where the internal consistency holds. 00:01:28.200 --> 00:01:35.490 So here's an example of six indicators.  We have indicators x1 x2 and x3 that are   00:01:35.490 --> 00:01:40.320 designed to measure one thing. So they're  highly correlated because they measure the   00:01:40.320 --> 00:01:46.710 same thing. x4 x5 and x6 are designed  to measure something else and they are   00:01:46.710 --> 00:01:52.650 highly correlated with one other because  they measure the same thing. But these   00:01:52.650 --> 00:01:59.640 two groups of indicators x1 x2 x3 and x4  x5 x6 are uncorrelated with one another   00:01:59.640 --> 00:02:04.500 because they are designed to measure two  distinct things that are not correlated. 00:02:04.500 --> 00:02:10.770 So this set of six indicators measures  two different dimensions or two different   00:02:10.770 --> 00:02:17.490 things. Yet if we calculate coefficient  alpha using this correlation matrix we   00:02:17.490 --> 00:02:24.210 get the value of 0.7. So the fact that we  got an alpha value that is acceptable for   00:02:24.210 --> 00:02:32.010 some researchers doesn't guarantee that the scale  is a uni-dimensional internally consistent one. 00:02:32.010 --> 00:02:36.600 The important thing here is that  internal consistency is something   00:02:36.600 --> 00:02:43.140 that alpha assumes and it is based on  that assumption. High alpha doesn't   00:02:43.140 --> 00:02:46.710 guarantee that you have an internally  consistent uni-dimensional scale. 00:02:46.710 --> 00:02:53.280 So alpha is a reliability index and it relies  on the classical test theory assumptions.   00:02:53.280 --> 00:02:59.130 Basically it means that your scale that  goes into the Alpha the indicators must   00:02:59.130 --> 00:03:05.850 be uni-dimensional and there is a no other error  there except unreliability which is random noise. 00:03:05.850 --> 00:03:11.670 Then it doesn't provide any test of the  classical test theory assumptions. So   00:03:11.670 --> 00:03:17.640 before you apply alpha at least you have to  check uni-dimensionality and you also can   00:03:17.640 --> 00:03:23.190 check the tau covariance which basically means  whether the indicators are equally reliable. 00:03:23.190 --> 00:03:32.010 The classical test theory states that the measures  score X is a sum of the true score T plus the   00:03:32.010 --> 00:03:39.270 measurement error E. In greek letters the T is tau  and therefore it's tau equivalent. Every indicator   00:03:39.270 --> 00:03:44.100 has the same amount of true score various in  it. That's what the tau equivalence means. 00:03:44.100 --> 00:03:51.810 While alpha is commonly used there are also  common misconceptions that you seen in research. 00:03:51.810 --> 00:03:59.280 The first misconception is that it was developed  by Cronbach. That's not the case. It was developed   00:03:59.280 --> 00:04:05.820 a couple of decades before Cronbach widely sited  paper. It just happens to be the first index in   00:04:05.820 --> 00:04:10.440 his paper where he discussed many different  reliability indices and therefore he got   00:04:11.070 --> 00:04:18.420 the coefficient alpha and it got his name. But  Cronbach himself says that this index probably   00:04:18.420 --> 00:04:24.210 shouldn't carry his name. So that's why we call  it coefficient alpha instead of cronbach's alpha. 00:04:24.210 --> 00:04:28.230 Also alpha does not necessarily equal reliability.   00:04:28.230 --> 00:04:33.510 It is an estimate of reliability under  the assumptions of classical test theory.   00:04:33.510 --> 00:04:39.960 If those assumptions don't hold then  alpha can underestimate reliability. 00:04:39.960 --> 00:04:44.550 Your statistical software when you  calculate alpha also gives you an   00:04:44.550 --> 00:04:49.770 estimate of how much the alpha would  be if you omit one of the indicators. 00:04:49.770 --> 00:04:53.370 For example it would say that if  you have five indicators going   00:04:53.370 --> 00:04:58.350 to the Alpha dropping one of those  indicators could increase the alpha. 00:04:58.350 --> 00:05:04.710 Should you drop the indicator? The answer  to that question is not necessarily because   00:05:04.710 --> 00:05:10.950 dropping an indicator from the... while it  increases the alpha value it can also mean that   00:05:10.950 --> 00:05:16.320 you're just capitalizing on chance factors.  So the actual reliability doesn't increase. 00:05:16.320 --> 00:05:21.090 Remember that alpha is not equal to  reliability. It is an estimate of reliability. 00:05:21.090 --> 00:05:28.230 And we could just have an alpha value that is  slightly overestimated because of random factors. 00:05:28.230 --> 00:05:35.850 Then there are misconception about  cut-offs. So if alpha equals zero   00:05:35.850 --> 00:05:39.120 point seven you're okay if it's zero point  sixteen then your study is unpublishable. 00:05:39.120 --> 00:05:46.650 So that of course doesn't hold true. What  the reliability - what kind of reliability   00:05:46.650 --> 00:05:51.360 you require depends on the context or if you are  measuring something that no one has ever measured   00:05:51.360 --> 00:05:56.280 before then it's perhaps more acceptable  to have an alpha of maybe even less than   00:05:56.280 --> 00:06:01.320 0.7 if you're studying something that others  have studied and have used scales with the   00:06:01.320 --> 00:06:07.500 reliability of 0.85 then 0.7 is not gonna cut  it because there are better scales available. 00:06:07.500 --> 00:06:11.430 Also it is not about yes or no decision. You have   00:06:11.430 --> 00:06:17.670 to explain what the reliability of 70%  or 80% means for your study results. 00:06:17.670 --> 00:06:21.420 So what kind of systematic error  do you expect when your measures   00:06:21.420 --> 00:06:24.540 are unreliable. So it's not about the cutoff. 00:06:24.540 --> 00:06:31.290 And then the final misconception is that alpha  is the best reliability coefficient. People may   00:06:31.290 --> 00:06:36.930 think that it's the best because it's widely  used but sometimes we use a statistic simply   00:06:36.930 --> 00:06:41.970 because they have been used in the past and  if we just used something that's been used in   00:06:41.970 --> 00:06:48.540 the past - it means that we use the oldest thing.  And there are many other reliability indices that   00:06:48.540 --> 00:06:54.780 have been introduced after coefficient alpha  that are more modern and better than alpha. 00:06:54.780 --> 00:07:00.960 Here's a list of some from a paper by  McNeish from psychological methods. He   00:07:00.960 --> 00:07:05.610 starts with alpha and then he goes  and explains omega which is relaxes   00:07:05.610 --> 00:07:12.540 some of the assumptions then he goes on and  explains others that relax the assumptions. 00:07:12.540 --> 00:07:17.670 The important assumptions in alpha were  that the indicators are uni-dimensional. If   00:07:17.670 --> 00:07:23.760 you relax that assumption then you can go with  some of these hierarchical omega coefficients. 00:07:23.760 --> 00:07:30.480 Also another important assumption is that  indicators are both equally reliable. If you relax   00:07:30.480 --> 00:07:36.870 that assumption you can go with Omega coefficient  which is also known as composite reliability. 00:07:36.870 --> 00:07:46.530 Cho's paper presents this nice decision diagram  of which reliability index to choose from. So he   00:07:46.530 --> 00:07:54.210 starts by checking is the scale uni-dimensional  and if the scale is uni-dimensional and he   00:07:54.210 --> 00:07:59.280 measures one thing then you check are the  indicators about equally reliable - do   00:07:59.280 --> 00:08:04.230 they have the same true score. If yes then  you're going to be OK with coefficient alpha. 00:08:04.230 --> 00:08:13.170 If no the second step then you go with  coefficient omega or composite reliability index. 00:08:13.170 --> 00:08:19.020 If on the other hand you don't have  uni-dimensionality then you apply a   00:08:19.020 --> 00:08:24.870 factor model in which case you are do higher omega   00:08:24.870 --> 00:08:30.420 or on a variant of alpha that  doesn't use the factor model. 00:08:30.420 --> 00:08:38.460 So it's a not that you would always use alpha  but instead you have to make a decision based   00:08:38.460 --> 00:08:43.170 on the nature of your data and you have to  - if you use alpha you have to justify the   00:08:43.170 --> 00:08:46.950 uni-dimensionality assumption which  you do with the factor analysis. And   00:08:46.950 --> 00:08:53.040 then you have to justify the Tau equivalence  assumption which basically means that all the   00:08:53.040 --> 00:08:57.270 indicators are equal reliable. Which  you also do with the factor analysis. 00:08:57.270 --> 00:09:02.010 And if those assumptions don't hold  then alpha is not the ideal but you   00:09:02.010 --> 00:09:04.410 have to look at these other coefficients instead.