If you have only two questions is natural to have a low alpha, because the model is sensitive to the number of parameters (items), this might imply that the Cronbach's alpha model is does not suit well your measurement model. 

This paper might help you to figure out the right model to assess internal consistency of your questions:

Streiner, DL (2003)Being Inconsistent About Consistency: When Coefficient Alpha Does and Doesn’t Matter. JOURNAL OF PERSONALITY ASSESSMENT, 80(3), 217–222

Thank you very much for sharing that reference with me; it is probably exactly what I need and I will review it and get back if there are further issues. I really appreciate your help. 

Just two small points.

PCA is not a latent variable method. In fact, two manifest variables are just not enough to identify a latent variable.

@Luis: Alpha is not really a model based coefficient, at least if used a lower bound to reliability. Furthermore, the appropriateness of alpha as a reliability measure is not related to the number of items.

Please also note that Cronbach's alpha only increases with increasing item numbers when the errors are uncorrelated (see Spearman-Brown formula). Therefore, small alpha values may not necessarily indicate inconsistency even in scales with more items, but may also indicate issues with correlated errors.

Priciple component analysis (PCA) is a method to reduce the number of variables in the analysis. The method divides the variables in to K groups which in all groups the variables have a high correlations together and there is a low relationships between variales in different group. The method makes a linear conbination between the variables in every group such that:

F1=a1X1+a2X2+...+akXk

where x1 to xk are the variables in the first group and a1 to ak are some numbers. Therefore, we have a few linear conbination such as F1, F2, f3 etc.

About Cronbach alpha, if you have a multichoice queationaire and you want to find the internal consistancy of the questions its possible to use Cronbach alpha. Its similar to correlation and at most it is one. If Cronbach alpha is near one its mean that the questionair has a good condsistancy otherwise you need to delete those questions which reduce Cronbach alpha and therefore the internal consistancy.

Thereare many books and papers regading to the above titles.

Regards

I used the principal component analysis only for the assessment of a scale I had been constructing. In such instances, the  number of items put to  the analysis was just too big, and my aim was to/ reduce that quantity to some reasonable size. Alpha Cronbach's coefficient was usually growing up with the reduction of those items,which did not match. But there was always the point, here the alpha was going down again. Not to many items can be disregarded. 

In this respect, the Alpha plays  the positive role. When you need to make a choice betwen two items or question, alpha is not a proper coefficient. Definitely the preceding colleagues are right. Follow their advice.

@Anna-Lena: In principle you are right, but to decrease alpha the measurement errors on different items should correlate negatively. In my (admitedly only intuitively based) opinion, such a negative correlation is not a situation often encountered in practice (?).

Rupert,

using Cronbach's alpha is generally not a good idea as this measure is based on some very restrictive assumptions, such a tau-equivalence of the measures, unidimensionality, and uncorrelated errors. With two items you could just report the correlation between the two items.

I would not use PCA for identifying scales, instead pricipal axes factor analysis may be a better alternative.

Here are some references with regard to alpha:

Starkweather, J. (2012). Step out of the past: Stop using coefficient alpha; there are better ways to calculate reliability. (Online document) Available at: http://www.unt.edu/rss/class/Jon/Benchmarks/Omega_JDS_Jun2012.pdf

Sijtsma, K. (2009) . On the use, the misuse, and the very limited usefulness of Cronbach's alpha. Psychometrika, 74(1), 107-120. doi:10.1007/s11336-008-9101-0

@Karin: If you use coefficient alpha as a lower bound (which is what alpha has originally been constructed for by Guttman (1945)), then you only need uncorrelated errors. But you need uncorrelated errors for more or less all reliability estimates.

I think, there are few reverse items in your questionnaire. if you recode these items, your alpha will increase. alpha approximately is the average of between items correlations and reverse items produce negative correlations and finally reduce the average.

Low cronbach alpha indicates low inter-item correlations. Maybe there are some issues with the correlated errors. Suggest  checking yr items, should some reverse item involved.

Dear Rupert, I understand you have two questions! In that case PCA and reliability analysis are useless. Correlation is enough, but when it is below .45, you need a large number of cases to assume strength of association.

If this is not the case (you have several variables from each domain, timing and quantity or whatever), and you get two clear components, then a general alpha should be low, while high for each specific scale. My opinion is that alpha from the overall questionnaire (set of measures) is useless and when several measures within each domain are avaliable, any reliability statistic should be reported for each domain.

yes, reverse items produce negative correlations and transforming these correlations to positive, lead to  increasing total sum of inter- item correlation that finally increase alph.

Hello Rupert, here are some clues and references to interpretate Cronbach's alpha:

The Cronbach's alpha (1947, 1951) is a good measure of the internal consistency of a latent variable; Acceptable values are normally above 0.70 (Nunnally, 1978). However, relatives of 0.60 values can be accepted (Hair, Black, Anderson and Tatham, 2006), especially if the variable is measured with few items. George and Mallery (2003, p 231) propose the rules of thumb 'to interpret the following Cronbach's alpha: unacceptable 0.89. It is possible that two observed variables measure a single latent variable, but this can lead to problems of identification of the conceptual model thereafter (Brown, 2006; Kline, 2005). It is advisable to have a minimum of 3 items or better 4 items (Hair, et al., 2006). The interpretation of the alpha coefficient is based on the number of items, most of items there, the more alpha coefficients may be higher yet with inter-item correlations rather average (Cortina, 1993; Worthington and Whittaker, 2006).

References:

• Brown, T. (2006). Confirmatory Factor Analysis for Applied Research. New York: The Guiford Press.

• Cortina, J.M. (1993). What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, Vol 78(1), 98-104.

• Cronbach, L. J. (1947). Test "reliability": lts meaning and determination. Psychometrika, 12. 1 - 16.

• Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334.

• Georges et Mallery, (2003). SPSS for Windows step by step: A simple guide and reference. 11.0 update (4th ed.). Boston: Allyn & Bacon

• Hair, J., Black, W., Babin, B., Anderson, R., & Tatham, R. (2006). Multivariate Data Analysis (6th ed.). New Jersey: Pearson Educational, Inc.

• Kline, R. (2005). Principles and Practice of Structural Equation Modeling (2nd ed.). New York: The Guilford Press.

• Nunnally, J. C. (1978). Psychometric theory. New York: McGraw-Hill Inc.

• Worthington, R., & Whittaker, T. (2006). Scale Development Research. A Content Analysis and Recommendations for Best Practices. The Counseling Psychologist, 34(6), 806-838.

How many variables are you factoring? If you have just a few, then the PC loadings will be very high compared to the actual correlations which could be producing your result. In that case, principle factors is the better approach (Gorsuch, R. (1983/2014). Factor Analysis. Taylor & Frances).

Do both of the items contain valid but slightly different information? If so, it may be useful to have 2 measures for them, the first would be the sum of the two items and the second would be the difference between items. (Internal consistency reliabilities - such as alpha -- are irrelevant in this situation and would be misleading to report; test-retest reliability would be the ones to report).

I agree with the comments that two items are not enough for either alpha or PCA. In that case, you have only a single correlation, so the Alpha is just an algebraic manipulation of that correlation, and there is no way that you can legitimately derive two factor loadings from one correlation coefficient.

In addition, the value of .45 that you give indicates that these two items share only about 20% of their variance. If you follow the classic assumptions of Alpha and PCA, that means that you have much more random variance ("error") in each variable than you have shared content ("covariance").

I suspect it is more likely, however, you are in a situation where your two variables actually measure different aspect of the phenomenon, in which case they shouldn't be combined. This situation will be obvious in a regression, where each of the two variables would be significant as predictors of a dependent variable.

@David: I don't really agree that "two items are not enough for either alpha or PCA."

First, Guttman's split-half coefficient is technically alpha for two items. So it's not incorrect to compute alpha from two measurements.

Second, PCA sometimes makes sense even with two variables. Namely, in this case the first PC is simply the (standardized) sum of standardized values of both variables. This often makes sense in practice. Of course, it tells you nothing about the latent structure...