Because the spacing between the four levels of educational experience is very uneven, the meaning of this average would be very questionable. In short, an average requires a variable to be numerical.
If we cannot be sure that the intervals between each of these five values are the same, then we would not be able to say that this is an interval variable, but we would say that it is an ordinal variable. However, in order to be able to use statistics that assume the variable is numerical, we will assume that the intervals are equally spaced.
When you are doing a t-test or ANOVA, the assumption is that the distribution of the sample means are normally distributed. One way to guarantee this is for the distribution of the individual observations from the sample to be normal. However, even if the distribution of the individual observations is not normal, the distribution of the sample means will be normally distributed if your sample size is about 30 or larger.
If you are doing a regression analysis, then the assumption is that your residuals are normally distributed. One way to make it very likely to have normal residuals is to have a dependent variable that is normally distributed and predictors that are all normally distributed; however, this is not necessary for your residuals to be normally distributed.
You can see the following resources for more information:. Second, we discuss the difference between experimental and non-experimental research. Finally, we explain how variables can be characterised as either categorical or continuous. An independent variable, sometimes called an experimental or predictor variable, is a variable that is being manipulated in an experiment in order to observe the effect on a dependent variable, sometimes called an outcome variable.
Imagine that a tutor asks students to complete a maths test. The tutor wants to know why some students perform better than others. Whilst the tutor does not know the answer to this, she thinks that it might be because of two reasons: 1 some students spend more time revising for their test; and 2 some students are naturally more intelligent than others.
As such, the tutor decides to investigate the effect of revision time and intelligence on the test performance of the students. The dependent and independent variables for the study are:.
The dependent variable is simply that, a variable that is dependent on an independent variable s. For example, in our case the test mark that a student achieves is dependent on revision time and intelligence.
Whilst revision time and intelligence the independent variables may or may not cause a change in the test mark the dependent variable , the reverse is implausible; in other words, whilst the number of hours a student spends revising and the higher a student's IQ score may or may not change the test mark that a student achieves, a change in a student's test mark has no bearing on whether a student revises more or is more intelligent this simply doesn't make sense.
Therefore, the aim of the tutor's investigation is to examine whether these independent variables - revision time and IQ - result in a change in the dependent variable, the students' test scores.
However, it is also worth noting that whilst this is the main aim of the experiment, the tutor may also be interested to know if the independent variables - revision time and IQ - are also connected in some way.
In the section on experimental and non-experimental research that follows, we find out a little more about the nature of independent and dependent variables. Categorical variables are also known as discrete or qualitative variables. Categorical variables can be further categorized as either nominal , ordinal or dichotomous.
Continuous variables are also known as quantitative variables. Continuous variables can be further categorized as either interval or ratio variables. Distance in miles is a quantitative variable because it takes on numerical values with meaningful magnitudes and equal intervals. This is a categorical variable. While there is a meaningful order of educational attainment, the differences between each category are not consistent. Because there are not equal intervals, this variable cannot be classified as quantitative.
A survey designed for online instructors asks, "How many online courses have you taught? If the survey had asked, "How many online courses have you taught? Enter a number. Quantitative variables can be classified as discrete or continuous.
Categorical variable Categorical variables contain a finite number of categories or distinct groups. Categorical data might not have a logical order. For example, categorical predictors include gender, material type, and payment method.
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