Correlated time and space analysis is a research technique that uses ordered data (in this case, pairs of data about one or more variables) in order to draw statistical conclusions about the relationships among the variables. The main advantage of using correlated time and space analysis is that it can be used to examine time trends, but it may also be applied to many other situations, such as the relationship between time and prices for a product or service. This paper reviews the theoretical foundations of the two methods and the associated limitations. Finally, an analysis is performed on real data.

## Conducting Correlated Studies

One way of performing a correlational study is called a non-parametric approach. In this method, all relationships are identified using a set of correlated variables, without the need for a priori knowledge of the underlying variables. A related method, the principal component analysis, involves identifying a set of correlated variables based on one or more predictor functions. However, using predictor functions does not allow us to examine the statistical association of the variables themselves. In this case, we use another approach: the multivariate approach.

Most papers about correlational research describe the procedure in terms of means and correlation. Means is the probability that the random variables chosen will mean the main predictor variable, and correlation is the probability that the main predictor variable will follow the mean values of the correlated variables. The most commonly used statistical procedures in correlational research use a one-way or two-way correlation. One-way correlations indicate that the results obtained from the main dependent variable and its dependent variables are significantly different from each other (a negative correlation suggests that there is no significant relationship between the two variables).

### Correlational research

Before looking at the various limitations of this scientific methodology, let us review what is meant by successful correlational research. First, researchers need to select appropriate and reliable predictor functions, and they must ensure that these functions do not have unexpected negative effects on the main dependent variable. Second, the researchers need to examine the distribution of the dependent variable and make sure that it follows a normal distribution (or variance), so that their results are meaningful.

A two-way or two-sided correlation occurs when the slopes of the correlation lines are different from zero (i.e., the slope of one of the predictor variables is greater than the slope of the corresponding variable on the left side of the regression line). This situation can only occur if the values for the predictor variables are normally distributed. The slope of the regression line will therefore deviate from zero, indicating that the predictor variable has a nonzero slope, implying that the results obtained through the correlational research are reliable. For consistency, researchers choose to assume that the slope of the line on the x axis is equal to zero (i.e., the data distribution is centered around the predictor variable).

Assuming these requirements, researchers then perform principal components analysis. This requires the researcher to select the two variables that are most strongly related to the dependent variable by averaging their effect together, taking into account the standard deviation of the mean value of each variable. By calculating and comparing the slopes of the correlated variables, researchers can estimate the strength and sign of the association between the predictor variables.

Due to the multiple stages involved in conducting a correlational study, smaller sample sizes generally lead to significant results that are more precise and reliable than traditional experiments. However, in some cases, this is not possible, especially for longer-term relationships, such as those that may be revealed by latent classificatory factors, such as stereotypes. Therefore, researchers choose to perform a correlational study that involves smaller numbers, at the expense of considerably increased time involvement. Conversely, larger samples are also able to yield stronger associations and results are more consistent with smaller degrees of predictive power.

If an investigator chooses to perform a correlational study using a traditional or Likert scale, he/she must first prepare the questionnaires and instruments used in the study. The questionnaires must be accurately constructed and should contain all pertinent information on the subject matter, thus it is important that the respondent answer the questions truthfully and completely. The Likert questionnaire is then manually analyzed by the researcher, following which a conclusion regarding the main statistical relationship between the variables is reached. A more comprehensive description of the process can be found in appendix A.