The use and interpretation of a multiple regression model depends implicitly on the assumption that the explanatory variables are not strongly interrelated. In most regression applications the explanatory variables are not orthogonal. Usually the lack of orthogonality is not serious enough to affect the analysis. However, in some situations the explanatory variables are so strongly interrelated that the regression results are ambiguous. Typically, it is impossible to estimate the unique effects of individual variables in the regression equation....
Diagnostics and Remedial Measures
The interpretation of data based on analysis of variance (ANOVA) is valid only when the following assumptions are satisfied:
1. Additive Effects: Treatment effects and block (environmental) effects are additive.
2. Independence of errors: Experimental errors are independent.
3. Homogeneity of Variances: Errors have common variance.
4. Normal Distribution: Errors follow a normal distribution.
Also the statistical tests t, F, z, etc. are valid under the assumption of independence of errors and normality of errors. The departures from these assumptions...
Web Analytics - An Overview
Web analytics is the practice of measuring, collecting, analysing and reporting online data for the purposes of understanding how a web site is used by its visitors and how to optimise its usage. The focus of web analytics is to understand a site’s users, their behaviour and activities.
The study of online user behaviour and activities generates valuable marketing intelligence and provides:
• performance measures of the website against targets
• insights on user behaviours and needs, and how the site is meeting those needs
• optimisation...
Test of Significance
In applied investigations, one is often interested in comparing some characteristic (such as the mean, the variance or a measure of association between two characters) of a group with a specified value, or in comparing two or more groups with regard to the characteristic. For instance, one may wish to compare two varieties of wheat with regard to the mean yield per hectare or to know if the genetic fraction of the total variation in a strain is more than a given value or to compare different lines of a crop in respect of variation between...
Statistical Terms
A
Acceptance Error, Beta Error, Type II Error - An error made by wrongly accepting the null hypothesis when the null is really false.
Acceptance Region - Opposite of the Rejection Region. It is better to call this the "Fail to Reject Region." In the case of a two-tailed hypothesis t-test, it is shaded in light blue on the picture below. If the test statistic falls between -tcritical and tcritical then we fail to reject the null hypothesis....
Probability Applied to Landing Page Testing
So how does probability apply to landing page optimization?
The random variables are the visits to your site from the traffic sources that you have selected for the test. The audience itself may be subject to sampling bias. You are counting whether or not the conversion happened as a result of the visit. You are assuming that there is some underlying and fixed probability of the conversion happening, and that the only other possible outcome...
Testing of Statistical Hypothesis
Understanding the Results
The null hypothesis in probability and statistics is the starting assumption that nothing other than random chance is operating to create the observed effect that you see in a particular set of data. Basically it assumes that the measured effects are the same across the independent conditions being tested. There are no differences or relationships between these independent variables and the dependent outcomes—equal until...