# Relationship between 2 continuous variables in research

### What statistical analysis should I use? Statistical analyses using SPSS

The correlation between two variables can be positive (i.e., higher levels of one close to zero suggests no linear association between two continuous variables. association (r=0,2) that we might expect to see between age and body mass A small study is conducted involving 17 infants to investigate the association. The correlation between two variables can be positive (i.e., higher levels of one A correlation close to zero suggests no linear association between two continuous variables. Scenario 2 depicts a weaker association (r=0,2) that we might A small study is conducted involving 17 infants to investigate the. Using the hsb2 data file, let's see if there is a relationship between the type of school a Fisher's exact test on a 2×2 table, and these results are presented by default. pairs (like a case-control study) or two outcome variables from a single group. . Because prog is a categorical variable (it has three levels), we need to .

A canonical correlation measures the relationship between sets of multiple variables this is multivariate statistic and is beyond the scope of this discussion. Regression An extension of the simple correlation is regression. In regression, one or more variables predictors are used to predict an outcome criterion. Data for several hundred students would be fed into a regression statistics program and the statistics program would determine how well the predictor variables high school GPA, SAT scores, and college major were related to the criterion variable college GPA.

Not all of the variables entered may be significant predictors. R2 tells how much of the variation in the criterion e. The regression equation for such a study might look like the following: For example, someone with a high school GPA of 4.

Universities often use regression when selecting students for enrollment. I have created a sample SPSS regression printout with interpretation if you wish to explore this topic further. You will not be responsible for reading or interpreting the SPSS printout.

Non Parametric Data Analysis Chi-Square We might count the incidents of something and compare what our actual data showed with what we would expect. Suppose we surveyed 27 people regarding whether they preferred red, blue, or yellow as a color.

If there were no preference, we would expect that 9 would select red, 9 would select blue, and 9 would select yellow.

We use a chi-square to compare what we observe actual with what we expect. If our sample indicated that 2 liked red, 20 liked blue, and 5 liked yellow, we might be rather confident that more people prefer blue.

If our sample indicated that 8 liked read, 10 liked blue, and 9 liked yellow, we might not be very confident that blue is generally favored. Chi-square helps us make decisions about whether the observed outcome differs significantly from the expected outcome.

### ANOVA, Regression, and Chi-Square | Educational Research Basics by Del Siegle

Just as t-tests tell us how confident we can be about saying that there are differences between the means of two groups, the chi-square tells us how confident we can be about saying that our observed results differ from expected results.

In Summary Each of the stats produces a test statistic e. Ultimately, we are interested in whether p is less than or greater than.

It all boils down the the value of p. Model Building Thanks to improvements in computing power, data analysis has moved beyond simply comparing one or two variables into creating models with sets of variables.

Structural Equation Modeling SEM analyzes paths between variables and tests the direct and indirect relationships between variables as well as the fit of the entire model of paths or relationships.

## What statistical analysis should I use? Statistical analyses using SPSS

For example, a researcher could measure the relationship between IQ and school achievment, while also including other variables such as motivation, family education level, and previous achievement. The example below shows the relationships between various factors and enjoyment of school.

The figure below is a scatter diagram illustrating the relationship between BMI and total cholesterol. Each point represents the observed x, y pair, in this case, BMI and the corresponding total cholesterol measured in each participant. Note that the independent variable BMI is on the horizontal axis and the dependent variable Total Serum Cholesterol on the vertical axis.

BMI and Total Cholesterol The graph shows that there is a positive or direct association between BMI and total cholesterol; participants with lower BMI are more likely to have lower total cholesterol levels and participants with higher BMI are more likely to have higher total cholesterol levels. For either of these relationships we could use simple linear regression analysis to estimate the equation of the line that best describes the association between the independent variable and the dependent variable.

The simple linear regression equation is as follows: The Y-intercept and slope are estimated from the sample data, and they are the values that minimize the sum of the squared differences between the observed and the predicted values of the outcome, i.

## Introduction

These differences between observed and predicted values of the outcome are called residuals. The estimates of the Y-intercept and slope minimize the sum of the squared residuals, and are called the least squares estimates.

That would mean that variability in Y could be completely explained by differences in X.

- ANOVA, Regression, and Chi-Square
- Introduction to Correlation and Regression Analysis

However, if the differences between observed and predicted values are not 0, then we are unable to entirely account for differences in Y based on X, then there are residual errors in the prediction. The residual error could result from inaccurate measurements of X or Y, or there could be other variables besides X that affect the value of Y. Based on the observed data, the best estimate of a linear relationship will be obtained from an equation for the line that minimizes the differences between observed and predicted values of the outcome.

The Y-intercept of this line is the value of the dependent variable Y when the independent variable X is zero.