Strenth and Direction

The real point of the last lecture is that these are hugely important concepts, and if you get these, you'll be able to understand the research synopses that you read in any journal (if you read between the lines, basically, and look for them).

Strength is the degree to which one variable is related to another. We used the example of senility and age. The higher the age, the more the senility is the likely outcome of a bivariate study on this topic.

The hypothesis there could be,

If a person is in his 90's, he is likely to suffer more senile dementia than if a person is in his 40's.

OR If people reach retirement and beyond, then the degree of senile dementia will be proportional to their age.

OR People over the age of 65 will have more senile dementia than people 65 years old and younger.

This study, with only 2 variables, is called a bivariate study. I think I mistakenly called it binary in class.

Now if you were to tell me, but maybe it isn't aging that is responsible for dementia, but poverty, because people get poorer as they age, then you're thinking that there's an extraneous variable involved that you had better control for so you don't mistakenly say that it's all about age.

Now you have a multivariate study. You have 2 independent variables and one dependent variable. You measure all three. Then you check to see which variables are related to one another, in other words, when the measurement of one of them goes up, then the other goes up (or down if the relationship is negative, meaning inverse).

That going up when one goes up, or down when the other goes up, is the DIRECTION of the relationship. How much one goes up when the other goes up, or down when the other goes up, is the STRENGTH. We measure this with one statistic, usually the Pearson r.

And when the computer spits out this statistic, there's a plus sign or a minus sign that tells us the direction. It's really not a plus sign, there's just no sign for a positive relationship, but there is a minus sign to indicate a negative relationship. And the r will only be between -1 and +1. i.e., -.72, or .98, or -.01

-.01 is a very tiny relationship, hardly any at all. If the strength of the relationship between senility and age were -.01 then we would know, intuitively, that the two variables are not related.

And it could be that the relationship between aging and poverty turned out to be significant, too, maybe .62. That would mean that neither of the two independent variables predicted the dependent variable.

NOW. You would also check to see if the two independent variables were related, poverty and aging. And there's yet another test to see if each of them contributes something different to the dependent variable (assuming they're both significantly related to the dependent variable).

We'll get to that later. Enough for now.

Univariate, Bivariate, and Multivariate Data

In other words, data analysis all depends upon how many variables you're analyzing

Univariate analysis is about analysis of one variable. Usually we'll find descriptive statistics (measures of central tendency), or measures of variability, i.e. the range, SD and variance. We'll often make frequency distributions to see how often a certain variable popped up in the data.

Bivariate and multivariate analysis attempt to do more than describe. They explain relationships between one or more variables: which variables are related, and how.

Bivariate implies an analysis of only two.

Multivariate analysis helps us to specify the conditions under which relationships hold. We simultaneously analyze relationships between variables.

Often we use cross-tabulations to tabulate the joint occurrence of 2 or more variables. The result is called a contingency table.

Employed Not employed Total
Men 75 25 100
Women 25 75 100

Total 100 100 200


Here you can see that with univariate analysis, you would have found that there are 100 men, or 100 women, or 100 are employed, and 100 are not employed.

A bivariate analysis allows us to say that three-fourths of the men are employed, and only one-quarter of the women are employed.

A contingency table like the one above allows you to “see” data. Another way, some might consider a more refined way to look at of looking at is to create a scatterplot. You should be able to identify one of these.

Read the post below to refresh your memories