# Statistic and relationship

### Statistics - Wikipedia

As we have seen throughout this book, most interesting research questions in psychology are about statistical relationships between variables. Recall that there. Correlation is a statistical measure (expressed as a number) that describes the size and direction of a relationship between two or more. Learn more about correlation, a statistical technique that shows how strongly pairs of The latter is useful when you want to look at the relationship between two.

**13-1 Relationships Between Variables**

These inferences may take the form of: Inference can extend to forecastingprediction and estimation of unobserved values either in or associated with the population being studied; it can include extrapolation and interpolation of time series or spatial dataand can also include data mining. Sampling[ edit ] When full census data cannot be collected, statisticians collect sample data by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting through statistical models.

The idea of making inferences based on sampled data began around the mids in connection with estimating populations and developing precursors of life insurance.

## Dating / Relationship Statistics

Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. A major problem lies in determining the extent that the sample chosen is actually representative.

Statistics offers methods to estimate and correct for any bias within the sample and data collection procedures. There are also methods of experimental design for experiments that can lessen these issues at the outset of a study, strengthening its capability to discern truths about the population.

Sampling theory is part of the mathematical discipline of probability theory.

### The relationship between variables - Draw the correct conclusions

Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures. The use of any statistical method is valid when the system or population under consideration satisfies the assumptions of the method.

The difference in point of view between classic probability theory and sampling theory is, roughly, that probability theory starts from the given parameters of a total population to deduce probabilities that pertain to samples.

Statistical inference, however, moves in the opposite direction— inductively inferring from samples to the parameters of a larger or total population. Experimental and observational studies[ edit ] A common goal for a statistical research project is to investigate causalityand in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables.

There are two major types of causal statistical studies: In both types of studies, the effect of differences of an independent variable or variables on the behavior of the dependent variable are observed.

The difference between the two types lies in how the study is actually conducted. Each can be very effective. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.

In contrast, an observational study does not involve experimental manipulation. Instead, data are gathered and correlations between predictors and response are investigated.

While the tools of data analysis work best on data from randomized studiesthey are also applied to other kinds of data—like natural experiments and observational studies [15] —for which a statistician would use a modified, more structured estimation method e.

Experiments[ edit ] The basic steps of a statistical experiment are: Planning the research, including finding the number of replicates of the study, using the following information: Consideration of the selection of experimental subjects and the ethics of research is necessary. Statisticians recommend that experiments compare at least one new treatment with a standard treatment or control, to allow an unbiased estimate of the difference in treatment effects. Design of experimentsusing blocking to reduce the influence of confounding variablesand randomized assignment of treatments to subjects to allow unbiased estimates of treatment effects and experimental error.

At this stage, the experimenters and statisticians write the experimental protocol that will guide the performance of the experiment and which specifies the primary analysis of the experimental data.

Rank correlation coefficients[ edit ] Main articles: If, as the one variable increases, the other decreases, the rank correlation coefficients will be negative.

It is common to regard these rank correlation coefficients as alternatives to Pearson's coefficient, used either to reduce the amount of calculation or to make the coefficient less sensitive to non-normality in distributions. However, this view has little mathematical basis, as rank correlation coefficients measure a different type of relationship than the Pearson product-moment correlation coefficientand are best seen as measures of a different type of association, rather than as alternative measure of the population correlation coefficient.

As we go from each pair to the next pair x increases, and so does y. This means that we have a perfect rank correlation, and both Spearman's and Kendall's correlation coefficients are 1, whereas in this example Pearson product-moment correlation coefficient is 0.

Other measures of dependence among random variables[ edit ] See also: In the case of elliptical distributions it characterizes the hyper- ellipses of equal density; however, it does not completely characterize the dependence structure for example, a multivariate t-distribution 's degrees of freedom determine the level of tail dependence.

You can be sure that your respondents think a rating of 2 is between a rating of 1 and a rating of 3, but you cannot be sure they think it is exactly halfway between.

This is especially true if you labeled the mid-points of your scale you cannot assume "good" is exactly half way between "excellent" and "fair". Most statisticians say you cannot use correlations with rating scales, because the mathematics of the technique assume the differences between numbers are exactly equal. Nevertheless, many survey researchers do use correlations with rating scales, because the results usually reflect the real world.

Our own position is that you can use correlations with rating scales, but you should do so with care. When working with quantities, correlations provide precise measurements. When working with rating scales, correlations provide general indications. Correlation Coefficient The main result of a correlation is called the correlation coefficient or "r". It ranges from If r is close to 0, it means there is no relationship between the variables.

If r is positive, it means that as one variable gets larger the other gets larger. If r is negative it means that as one gets larger, the other gets smaller often called an "inverse" correlation. The square of the coefficient or r square is equal to the percent of the variation in one variable that is related to the variation in the other.

After squaring r, ignore the decimal point. An r value of.

A correlation report can also show a second result of each test - statistical significance.