Download presentation

Presentation is loading. Please wait.

1
Basic Statistics Correlation

2
**Relationships Associations**

Var Relationships Associations Var Var Var Var

3
**Independent variables**

In Research Information Dependent variable X1 ? Y X2 COvary X3 Independent variables

4
**The Concept of Correlation**

Association or relationship between two variables Co-relate? r relation X Y Covary---Go together

5
**Patterns of Covariation**

Zero or no correlation X Y Correlation Covary Go together X Y X Y Negative correlation Positive correlation

6
**Scatter plots allow us to visualize the relationships**

The chief purpose of the scatter diagram is to study the nature of the relationship between two variables Linear/curvilinear relationship Direction of relationship Magnitude (size) of relationship Scatter Plots

7
**Scatter Plot A Variable Y Variable X high low low high**

Represents both the X and Y scores Variable Y Exact value low low high Variable X An illustration of a perfect positive correlation

8
**An illustration of a positive correlation**

Scatter Plot B high Variable Y Estimated Y value low low high Variable X An illustration of a positive correlation

9
**Scatter Plot C Variable Y Variable X high low low high**

Exact value low low high Variable X An illustration of a perfect negative correlation

10
**An illustration of a negative correlation**

Scatter Plot D high Variable Y Estimated Y value low low high Variable X An illustration of a negative correlation

11
**Scatter Plot E Variable Y Variable X high low low high**

An illustration of a zero correlation

12
**An illustration of a curvilinear relationship**

Scatter Plot F high Variable Y low low high Variable X An illustration of a curvilinear relationship

13
**The Measurement of Correlation**

The Correlation Coefficient The degree of correlation between two variables can be described by such terms as “strong,” ”low,” ”positive,” or “moderate,” but these terms are not very precise. If a correlation coefficient is computed between two sets of scores, the relationship can be described more accurately. A statistical summary of the degree and direction of relationship or association between two variables can be computed

14
**Pearson’s Product-Moment Correlation Coefficient r**

No Relationship Negative correlation Positive correlation Direction of relationship: Sign (+ or –) Magnitude: 0 through +1 or 0 through -1

15
**The Pearson Product-Moment Correlation Coefficient**

Recall that the formula for a variance is: If we replaced the second X that was squared with a second variable, Y, it would be: This is called a co-variance and is an index of the relationship between X and Y.

16
**Conceptual Formula for Pearson r**

This formula may be rewritten to reflect the actual method of calculation

17
**Calculation of Pearson r**

You should notice that this formula is merely the sum of squares for covariance divided by the square root of the product of the sum of squares for X and Y

18
**Formulae for Sums of Squares**

Therefore, the formula for calculating r may be rewritten as:

19
**Calculation of r Using Sums of Squares**

20
An Example Suppose that a college statistics professor is interested in how the number of hours that a student spends studying is related to how many errors students make on the mid-term examination. To determine the relationship the professor collects the following data:

21
**The Stats Professor’s Data**

Student Hours Studied (X) Errors (Y) X2 Y2 XY 1 4 15 16 225 60 2 12 144 48 3 5 9 25 81 45 6 10 36 100 7 8 49 64 56 28 42 18 Total X = 70 Y = 73 X2 =546 Y2=695 XY=429

22
**The Data Needed to Calculate the Sum of Squares**

X Y X2 Y2 XY Total X = 70 Y = 73 X2 =546 Y2=695 XY=429 = /10 = = 56 = /10 = = 162.1 = 429 – (70)(73)/10 = 429 – 511 = -82

23
**Calculating the Correlation Coefficient**

= -82 / √(56)(162.1) = Thus, the correlation between hours studied and errors made on the mid-term examination is -0.86; indicating that more time spend studying is related to fewer errors on the mid-term examination. Hopefully an obvious, but now a statistical conclusion!

24
**Pearson Product-Moment Correlation Coefficient r**

perfect negative correlation Zero correlation Perfect positive correlation -1 +1 Negative correlation Positive correlation

25
Numerical values .73 - .35 Negative correlation Zero correlation Positive correlation Perfect Strong Moderate

26
**The Pearson r and Marginal Distribution**

The marginal distribution of X is simply the distribution of the X’s; the marginal distribution of Y is the frequency distribution of the Y’s. Y Bivariate relationship Bivariate Normal Distribution X

27
**Marginal distribution of X and Y are precisely the same shape.**

Y variable X variable

28
**Interpreting r, the Correlation Coefficient**

Recall that r includes two types of information: The direction of the relationship (+ or -) The magnitude of the relationship (0 to 1) However, there is a more precise way to use the correlation coefficient, r, to interpret the magnitude of a relationship. That is, the square of the correlation coefficient or r2. The square of r tells us what proportion of the variance of Y can be explained by X or vice versa.

29
**How does correlation explain variance?**

Suppose you wish to estimate Y for a given value of X. high How does correlation explain variance? Explained Variable Y Free to Vary 49% of variance is explained Explained low low high Variable X An illustration of how the squared correlation accounts for variance in X, r = .7, r2 = .49

30
**Now, let’s look at some correlation coefficients and their corresponding scatter plots.**

31
**What is your estimate of r?**

32
Y X What is your estimate of r? r = -1.00 r2 = 1.00 = 100%

33
Y X What is your estimate of r? r = +1.00 r2 = 1.00 = 100%

34
**What is your estimate of r?**

35
**What is your estimate of r?**

Similar presentations

OK

Linear Regression and Correlation Chapter 13. 13-2 GOALS 1. Understand and interpret the terms dependent and independent variable. 2. Calculate and interpret.

Linear Regression and Correlation Chapter 13. 13-2 GOALS 1. Understand and interpret the terms dependent and independent variable. 2. Calculate and interpret.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on edge detection in image Ppt on social networking addiction Ppt on 2nd world war countries Download ppt on query processing and optimization Download ppt on rag pickers Ppt on leadership development training Download ppt on data handling for class 7 Human eye anatomy and physiology ppt on cells Ppt online viewer Ppt on series and parallel circuits video