what is Correlations

Correlation And Trend Analysis

Presented by : Miftahuddin Bin MisriHP120048

Correlation Coefficient 

• Correlation refers to any of a broad class of statistical relationships involving dependence.

• One of the most frequently used statistics – Important to be able to interpret it correctly

• Fundamental to theory building • Basis of many meta-analyses• Building block for more sophisticated methods – e.g., Multiple

Regression, Factor Analysis, Structural Equation Modelling

Why is correlation important?

Choose a Procedure:

• Bivariate Correlations

• Partial Correlations

• Distances

BIVARIATE CORRELATIONS

• In Bivariate Correlations, the relationship between two variables is measured. The degree of relationship (how closely they are related) could be either positive or negative.

• The maximum number could be either +1 (positive) or -1 (negative). This number is the correlation coefficient. A zero correlation indicates no relationship.

• Examples. Are a student’s grade and the amount of studying done correlated? You might find that these variables are positively correlated.

PARTIAL CORRELATIONS

• The Partial Correlations procedure computes partial correlation coefficients that describe the linear relationship between two variables while controlling for the effects of one or more additional variables. Correlations are measures of linear association.

• Example. Is there a relationship between healthcare funding and disease rates? Although you might expect any such relationship to be a negative one, a study reports a significant positive correlation: as healthcare funding increases, disease rates appear to increase. Controlling for the rate of visits to healthcare providers, however, virtually eliminates the observed positive correlation.

DISTANCES

• This procedure calculates any of a wide variety of statistics measuring either similarities or dissimilarities (distances), either between pairs of variables or between pairs of cases. These similarity or distance measures can then be used with other procedures, such as factor analysis, cluster analysis, or multidimensional scaling, to help analyze complex data sets.

• Example: Is it possible to measure similarities between pairs of automobiles based on certain characteristics, such as engine size, MPG, and horsepower? By computing similarities between autos, you can gain a sense of which autos are similar to each other and which are different from each other.

Other Forms of correlations

• Spearman correlation coefficient – Less influenced by outliers

• – Converts data to ranks before correlating

• Point-Biserial correlation

– One binary and one metric variable

• Let see :

Trend Analysis

• When a quantitative factor is used, trend analysis is very useful

Why Trend Analysis Studies Used

1.  Allows us to describe a historical pattern

2. Able to make projections on past patterns, past or

future trends

3. In most instances, it allows us to eliminate trend

component of the series

• Standard form of ANOVA could be applied but would not capitalize on the quantitative information available

• By assuming a linear model, the following fit is obtained

• In statistics, trend analysis often refers to techniques for extracting an underlying pattern of behaviour in a time series which would otherwise be partly or nearly completely hidden by noise.

• A simple description of these techniques is trend estimation, which can be undertaken within a formal regression analysis.

• The independent variable is a continuous variable representing the amount of weekly reading hours, while the dependent variable is a continuous variable representing reading achievement scores.

• Research question: Is there a linear trend between the amount of weekly reading hours and reading achievement?

• We usually plot the entire set of treatment means on a graph, connect the points, and examine the display for any underling shape or trend.

• Trend analysis is a specialized form of single-df comparisons when a quantitative independent variable is manipulated.

• Analyze…Compare Means…One-Way ANOVA

• See :

Thank You

Miftahuddin Bin Misri

published by CEFMcefmCEFM