Editing Quantitative marketing research (section)

==Statistical analysis==

The data acquired for quantitative marketing research can be analysed by almost any of the range of techniques of [[statistical analysis]], which can be broadly divided into [[descriptive statistics]] and [[statistical inference]]. An important set of techniques is that related to [[statistical survey]]s. In any instance, an appropriate type of statistical analysis should take account of the various types of error that may arise, as outlined below.

===Reliability and validity===

Research should be tested for [[reliability (psychometric)|reliability]], generalizability, and [[validity (psychometric)|validity]].

'''Generalizability''' is the ability to make inferences from a sample to the population.

'''Reliability''' is the extent to which a measure will produce consistent results.
* ''Test-retest reliability'' checks how similar the results are if the research is repeated under similar circumstances. Stability over repeated measures is assessed with the Pearson coefficient.
* ''Alternative forms reliability'' checks how similar the results are if the research is repeated using different forms.
* ''Internal consistency reliability'' checks how well the individual measures included in the research are converted into a composite measure. Internal consistency may be assessed by correlating performance on two halves of a test (split-half reliability). The value of the [[Pearson product-moment correlation coefficient]] is adjusted with the [[Spearman–Brown prediction formula]] to correspond to the correlation between two full-length tests. A commonly used measure is [[Cronbach's alpha|Cronbach's α]], which is equivalent to the mean of all possible split-half coefficients. Reliability may be improved by increasing the sample size.

'''Validity''' asks whether the research measured what it intended to.
* ''[[Content validity|Content validation]]'' (also called face validity) checks how well the content of the research are related to the variables to be studied; it seeks to answer whether the research questions are representative of the variables being researched. It is a demonstration that the items of a test are drawn from the domain being measured.
* ''[[Criterion validity|Criterion validation]]'' checks how meaningful the research criteria are relative to other possible criteria. When the criterion is collected later the goal is to establish predictive validity.
* ''[[Construct validity|Construct validation]]'' checks what underlying construct is being measured. There are three variants of construct validity: ''convergent validity'' (how well the research relates to other measures of the same construct), ''discriminant validity'' (how poorly the research relates to measures of opposing constructs), and ''[[Nomological network|nomological validity]]'' (how well the research relates to other variables as required by theory).
* ''Internal validation'', used primarily in experimental research designs, checks the relation between the dependent and independent variables (i.e. Did the experimental manipulation of the independent variable actually cause the observed results?)
* ''External validation'' checks whether the experimental results can be generalized.

Validity implies reliability: A valid measure must be reliable. Reliability does not necessarily imply validity, however: A reliable measure does not imply that it is valid.

===Types of errors===


'''Random sampling errors:'''
*sample too small
*sample not representative
*inappropriate sampling method used
*[[errors and residuals in statistics|random errors]]
'''Research design errors:'''
*bias introduced
*measurement error
*data analysis error
*sampling frame error
*population definition error
*scaling error
*question construction error
'''Interviewer errors:'''
*recording errors
*cheating errors
*questioning errors
*respondent selection error
'''Respondent errors:'''
*non-response error
*inability error
*falsification error
'''Hypothesis errors:'''
*[[Type I and type II errors#Type I error|type I error]] (also called alpha error)
**the study results lead to the rejection of the null hypothesis even though it is actually true
*[[Type I and type II errors#Type II error|type II error]] (also called beta error)
**the study results lead to the acceptance (non-rejection) of the null hypothesis even though it is actually false