Data Interpretation II

How is effect size measured?

(1) standardized mean difference (2) odd ratio (3) correlation coefficient

The stronger the association of the two variables...

-The closer the Pearson correlation coefficient r will be to +1 or -1 -The Pearson correlation coefficient is typically used for jointly normally distributed data (data that follow a bivariate normal distribution)

What is used to measure heterogeneity?

-This chi-squared test assesses whether observed differences in results are compatible with chance alone. A low P value (or a large chi-squared statistic relative to its degree of freedom) provides evidence of heterogeneity of intervention effects -Both Chi-square and I2 statistic can be found at the bottom of the table in a forest plot

What is heterogeneity in EBM?

-Variability in data -Systematic reviews and meta-analyses aim to capture the overall effects of an intervention or treatment when it has been tested in multiple trials -Ideally, if multiple trials are testing the same intervention, the effects of the intervention should be consistent across all studies. Unfortunately, this is rarely the case, because many factors can affect the results of a trial, such as a researcher bias, problems with data collection, or measurement of outcomes.

vWhen two variables are seen moving in the same direction. Increase in the value of the X variable results in an increase in the Y variable or vice versa

Positive correlation

What tells yo the overall significance of regression?

R^2 •This statistic indicates the percentage of the variance in the dependent variable that the independent variables explain collectively •R-squared measures the strength of the relationship between your model and the dependent variable on a convenient 0 - 100% scale. -v0% represents a model that does not explain any of the variations in the response variable around its mean. The mean of the dependent variable predicts the dependent variable as well as the regression model. v100% represents a model that explains all the variations in the response variable around its mean -P value for the regression

-A statistical technique based on the average mathematical relationship between two or more variables -Provides a more detailed analysis that includes an equation that can be used for prediction and/or optimization. •Y is called the dependent variable •X is called independent or predictor variable -It estimates the change in the metric of the dependent variable due to the change in one or more independent variables -It plays an important role in forecasting past, present, or future events based on past or present events

Regression

Three methods used to compute the value of co-efficient of correlation

§1. Scatter Plot §2. Pearson's Product Moment Co-efficient of Correlation §3. Spearman's Rank Order Co-efficient of Correlation

Considerations in choosing or measuring effect size

1. Effect sizes from the different studies should be comparable to one another (or at least measure approximately the same thing) 2. Estimates of the effect size should be computable from the information reported in a published article. Therefore, it should not require the re-analysis of the raw data 3. Effect size should have good technical properties. For example, variances and confidence intervals can be computed 4. Effect size should be substantively interpretable and meaningful

Types of regression

1.Linear Regression, which uses R^2 (predicts continuous values or dependent variable is continuous. Example: BMI, weight, length of stay in the hospital) 2.Logistic Regression, which uses odds ratio (predicts binary classification or categorical variable is continuous or discrete value. In other words, can it only have one of two values? Example: obese: yes or no, disease: yes or no, either 0 or 1, true or false, black or white)

A statistical concept that measures the strength of the relationship between two variables or the difference between two groups on a numeric scale The larger the effect size the stronger the relationship between two variables

Effect size

Is a statistical measure that quantifies the direction and strength of the relationship between two numeric variables, X and Y, and always lies between -1.0 and 1.0

Correlation

How is the degree of association measured?

Correlation coefficient denoted by r and is called Pearsons correlation coefficient and is measured from +1 to 0 to -1

Correlation vs Regression

Correlation just investigates whether a relationship between x and y exists Regression is to explore HOW x predicts y

In meta analysis, what influences the measurement of effect size?

Different study designs Types of outcome variables

How is effect size calculated?

Generally, effect size is calculated by taking the difference between the two groups (e.g., the mean of treatment group minus the mean of the control group) and dividing it by the standard deviation of one of the groups

Is a low heterogeniety good?

In MAs and SRs, yes However, in IND or RCTs, prefer studies to have high heterogeniety.

- This analysis produces estimates for the slope and intercept of the linear equation predicting an outcome variable, Y, based on values of a predictor variable, X. Y = B0 + B1 * X The intercept, b0, is the predicted value of Y when X=0. The slope, b1, is the average change in Y for every one unit increase in X In simple or multiple linear regression, the coefficient size for each independent variable gives you the effect that variable is having on your dependent variable, and the sign on the coefficient (positive or negative) gives you the direction of the effect.

Linear regression

What is a low I^2 and a high I^2?

Low = <25% Moderate = 25-50% High = >50%

When two variables are seen moving in a different direction. Increase in the value of the X variable results in a decrease in the Y variable or vice versa

Negative correlation

Do correlations show cause and effect?

No, just association

If differences are caused by chance, what can we have confidence in? If the differences are not caused by chance, what must we infer?

Resuls of meta analysis Cautious interpreting results of the MA

-Is the nonparametric version of the Pearson correlation coefficient -For non-normally-distributed continuous data, for ordinal data, or for data with relevant outliers, a correlation can be used as a measure of a monotonic association. It measures the strength and direction of association between two ranked variables (ordinal, interval, or ratio). This correlation determines the strength and direction of the monotonic relationship between two variables rather than the strength and direction of the linear relationship between your two variables, which is what Pearson's correlation determines

Spearmans correlation

If any change in one variable is not dependent on the other

Zero correlation