if your looking to test the significant difference in service quality between the organizations according to service providers (between two groups)! i strongly recommended using The independent-samples t-test (or independent t-test, for short in SPSS) that compares the means between two unrelated groups on the same continuous, dependent variable! also One-way ANOVA will be suitable if you have more than two groups! One-way ANOVA is used to determine whether there are any significant differences between the means of two or more independent (unrelated) groups (although you tend to only see it used when there are a minimum of three, rather than two groups).
In addition, I suggest you to run a F-test, too. It tests for equality of two populations.
In e-commerce, as a quality control, it is not only important that which company has the best average in a specific service. It is also essential to check whether a service provider has a standard for his service quality or not. For example, in a specific service, if the company has bad days and good days, but in average it has the highest quality, it doesn't mean this service provider is doing well.
I hope you consider this test, too. It will increase the validity of your research.
For the purpose of comparison of two independent samples (same as your example) you should use two independent T test. I send you the file in which, you could understand the concept and its method in SPSS.
While these suggestions are all accurate, I would personally recommend using the ANOVA method even if you have only 2 groups. This is because from a technical standpoint, the ANOVA with 2 groups and the independent t test are exactly the same. However, in SPSS, the ANOVA method gives you more options. Specifically, it allows you to choose to automatically calculate the eta squared, so you can immediately get effect size. It is just easier than taking your t-test output and entering it into a third-party tool to get a Cohen's D effect size.
I would also consider two other elements of this question:
1) How closely related are the populations of customers for each provider? For example, are the providers truly providing identical services? If the two providers are offering qualitatively different services, just comparing the satisfaction of their customers may be invalid. For example, it would not be appropriate to compare the satisfaction of buyers of luxury brand cars with the satisfaction of buyers of economy cars. Those are two very different populations, and so their satisfaction may have less to do with the company than their different socioeconomic status. In cases like this, you might need to de-aggregate your populations (by service level provided, for example) and perform a more complex analysis (e.g. a multi-level ANOVA with covariates).
2) There is a growing body of research that "customer satisfaction" is not a useful measure, and does not provide a simple scale of information. In other words, customers rating a 1, 2, or 3 on a 5 point scale may not really be different from each other in how satisfied they are. While the difference between a 3 and a 5 could mean a total reversal in attitude. To get around this, many companies are moving away customer satisfaction to the measure "Net Promoter Score" or NPS. NPS is calculated by first grouping customers according to their overall attitude towards the company into either "detractors," "neutral," or "promoters."
If you have access to the raw data behind NPS scores for the companies you are comparing, I would recommend a multiple logistic regression in which you use the provider, customer SES, and service levels as your predictors and promoter / not promoter as your dependent variable.
Note: This advice comes from the position of having worked as a Customer Experience Data Analyst for a large corporation for several years. I was doing exactly this type of analysis with large data sets of NPS surveys. At the time, I was working in SAS, not SPSS, however. I have honestly never tried to do a multiple logistic regression in SPSS, so I don't know how easy it is in this software.
Beautiful answers above especially from Salah Alhyari and John Hart. In addition, please ensure that your data meets all assumptions for either the independent samples t-test or ANOVA. This will help determine what approach to adopt and if the assumptions are not met, what data manipulation procedures you will need to embark upon.
If your data is normally distributed, you could use Independent Sample t-test. Service quality must have numeric data, and the two different e-commerce sites can be given values.