One Sample Test
A one-sample test, also known as a goodness of fit test, shows whether the collected data is useful in making a prediction about the population.
One sample tests are used when we have a single sample and wish to test the hypothesis that it comes from a specified population.
In this case, the following questions are encountered:
• Is there a difference between observed frequencies and the frequencies we would expect, based on some theory?
• Is there a difference between observed and expected proportions?
• Is it reasonable to conclude that sample is drawn from a population with some specified distribution (normal, etc.).
• Is there significant difference between some measures of central tendency (X bar) and its population parameter (μ).
A number of tests may be appropriate in this situation, i.e. Parametric test and Non-parametric test.
Parametric Tests
Parametric tests are more powerful because their data are derived from interval and ratio measurements.
Assumptions for parametric tests include the following:
• The observations must be independent.
• The observations should be drawn from normally distributed populations.
• These populations should have equal variances.
• The measurement scales should be at least interval so that arithmetic operations can be used with them.
Parametric tests place different emphasis on the importance of assumptions. Some tests are quite robust and hold up well despite violations. For others, a departure from linearity or equality of variance may threaten the validity of the results. Assessing the consequences of violating a statistical assumption requires a lot of tacit knowledge with regard to the data used and the field one investigates. As outlined above, violations of the assumptions are the rule rather than the exception in business research. Therefore, interpretation of the results should never be based blindly on the statistical results. Rather the statistical results form a solid base for
One sample tests are used when we have a single sample and wish to test the hypothesis that it comes from a specified population.
In this case, the following questions are encountered:
• Is there a difference between observed frequencies and the frequencies we would expect, based on some theory?
• Is there a difference between observed and expected proportions?
• Is it reasonable to conclude that sample is drawn from a population with some specified distribution (normal, etc.).
• Is there significant difference between some measures of central tendency (X bar) and its population parameter (μ).
A number of tests may be appropriate in this situation, i.e. Parametric test and Non-parametric test.
Parametric Tests
Parametric tests are more powerful because their data are derived from interval and ratio measurements.
Assumptions for parametric tests include the following:
• The observations must be independent.
• The observations should be drawn from normally distributed populations.
• These populations should have equal variances.
• The measurement scales should be at least interval so that arithmetic operations can be used with them.
Parametric tests place different emphasis on the importance of assumptions. Some tests are quite robust and hold up well despite violations. For others, a departure from linearity or equality of variance may threaten the validity of the results. Assessing the consequences of violating a statistical assumption requires a lot of tacit knowledge with regard to the data used and the field one investigates. As outlined above, violations of the assumptions are the rule rather than the exception in business research. Therefore, interpretation of the results should never be based blindly on the statistical results. Rather the statistical results form a solid base for