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# statistics how to tell whether x and y are independent or not Mathematics Stack Exchange

As another example, say you want to know whether or not eating breakfast affects student test scores. The factor under the experimenter’s control is the presence or absence of breakfast, so you know it is the independent six reasons why organic growth is so important variable. The experiment measures test scores of students who ate breakfast versus those who did not. Theoretically, the test results depend on breakfast, so the test results are the dependent variable.

• If you’re serious about the question, eventually you’ll want to learn the implicit function theorem which sorts out this question in considerable generality.
• The convention is to use the independent variable as the x-axis and the dependent variable as the y-axis.
• How the moth reacts to the different light levels (distance to light source) would be the dependent variable.
• The results showed that inclusion of the covariate allowed improved estimates of the trend against time to be obtained, compared to analyses which omitted the covariate.

It is a variable; the researcher has control over its selection and manipulation, i.e. the levels can be changed, or it changes on its own due to circumstances. The slope tells us how the dependent variable (\(y\)) changes for every one unit increase in the independent (\(x\)) variable, on average. The \(y\)-intercept is used to describe the dependent variable when the independent variable equals zero. A variable may be thought to alter the dependent or independent variables, but may not actually be the focus of the experiment. So that the variable will be kept constant or monitored to try to minimize its effect on the experiment.

If you didn’t have any constant variables, you wouldn’t be able to tell if the independent variable was what was really affecting the dependent variable. Here, as before, the independent variable is tooth-brushing, but now it is the comparison of groups of children in each category (#times brushed per day). The dependent (outcome measure) variable, is still the number of caries. In both math and science, dependent and independent variables can be plotted on the x and y axes of a graph. It is called the “dependent” variable because we are trying to figure out whether its value depends on the value of the independent variable. If there is a direct link between the two types of variables (independent and dependent) then you may be uncovering a cause and effect relationship.

Note that test scores are the dependent variable, even if it turns out there is no relationship between scores and breakfast. The independent and dependent variables are key to any scientific experiment, but how do you tell them apart? Here are the definitions of independent and dependent variables, examples of each type, and tips for telling them apart and graphing them. An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study. It is common to give the control group a placebo, which is some substance that is designed to have no therapeutic value.

## Independent vs. Dependent Variables Definition & Examples

The two main variables in an experiment are the independent and dependent variable. If y is an
independent variable and you’re talking about the derivative with
respect to x, it would be 1/y. A dependent variable is a consequence of an independent variable i.e. it is variable that measures the effect of the independent variable on the test units. When we create a graph, the independent variable will go on the x-axis and the dependent variable will go on the y-axis. Changing the plant growth rate affects the value of the amount of water. Changing the amount of water affects the value of the plant growth rate.

Such variables may be designated as either a “controlled variable”, “control variable”, or “fixed variable”. For another experiment, a scientist wants to determine whether one drug is more effective than another at controlling high blood pressure. The independent variable is the drug, while patient blood pressure is the dependent variable.

Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable. As you can see, this is a graph showing how the number of hours a student studies affects the score she got on an exam. From the graph, it looks like studying up to six hours helped her raise her score, but as she studied more than that her score dropped slightly. It can be a lot easier to understand the differences between these two variables with examples, so let’s look at some sample experiments below. Based on your findings, you can estimate the degree to which your independent variable variation drives changes in your dependent variable. You can also predict how much your dependent variable will change as a result of variation in the independent variable.

You can apply just two levels in order to find out if an independent variable has an effect at all. You vary the room temperature by making it cooler for half the participants, and warmer for the other half. The variable x is the independent variable, and y is the dependent variable. A independent variable is “the input” and the dependent variable is the “output”, atleast thats how it was explained to us.

• It’s not possible to randomly assign these to participants, since these are characteristics of already existing groups.
• If you’re studying how people feel about different television shows, the variables in that experiment are television shows and feelings.
• A variable is said to be independent, whose change influence another variable, while if the variable is dependent, it will change in response to the change in some other variable.
• You find some and conclude that gender identity influences brain responses to infant cries.

Our new student and parent forum, at ExpertHub.PrepScholar.com, allow you to interact with your peers and the PrepScholar staff. See how other students and parents are navigating high school, college, and the college admissions process. Scoring well on standardized tests is an important part of having a strong college application. You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment.

## 1: Linear Equations

Sometimes a model comes with some idea of cause and effect which is not reversible. You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Independent and dependent variables are generally used in experimental and quasi-experimental research. A dependent variable from one study can be the independent variable in another study, so it’s important to pay attention to research design. A dependent variable is the variable that changes as a result of the independent variable manipulation. It’s the outcome you’re interested in measuring, and it “depends” on your independent variable.

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Changing (independent variable) affects the value of (dependent variable). For example, a researcher might change the amount of water they provide to a certain plant to observe how it affects the growth rate of the plant. The independent variable (\(x\)) is the number of hours Ethan works each visit. The dependent variable (\(y\)) is the amount, in dollars, Ethan earns for each visit.

## How to Tell the Variables Apart

Emma’s Extreme Sports hires hang-gliding instructors and pays them a fee of \$50 per class as well as \$20 per student in the class. The total cost Emma pays depends on the number of students in a class. Find the equation that expresses the total cost in terms of the number of students in a class. Find the equation that expresses the total cost in terms of the number of hoursrequired to complete the job. In research, variables are any characteristics that can take on different values, such as height, age, temperature, or test scores. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

Thus, we know that we must have the independent and dependent variables switched around. In an experiment, an experimenter is interested in seeing how the dependent variable changes as a result of the independent being changed or manipulated in some way. Equations, some functions, it is the case that several variables can be used as the independent variable. If you’re serious about the question, eventually you’ll want to learn the implicit function theorem which sorts out this question in considerable generality. To ensure the internal validity of an experiment, you should only change one independent variable at a time. To inspect your data, you place your independent variable of treatment level on the x-axis and the dependent variable of blood pressure on the y-axis.

## Independent Variable

Changes to each of these independent variables cause the dependent variables to change in the experiments. The independent variable (sometimes known as the manipulated variable) is the variable whose change isn’t affected by any other variable in the experiment. Either the scientist has to change the independent variable herself or it changes on its own; nothing else in the experiment affects or changes it. There’s nothing you or anything else can do to speed up or slow down time or increase or decrease age. Of the two, it is always the dependent variable whose variation is being studied, by altering inputs, also known as regressors in a statistical context. In an experiment, any variable that can be attributed a value without attributing a value to any other variable is called an independent variable.

## Does the equation x plus y equals 41 define y as a function of x?

For experimental data, you analyze your results by generating descriptive statistics and visualizing your findings. Then, you select an appropriate statistical test to test your hypothesis. A doctor changes the dose of a particular medicine to see how it affects the blood pressure of a patient. Based on your results, you note that the placebo and low-dose groups show little difference in blood pressure, while the high-dose group sees substantial improvements. It’s not possible to randomly assign these to participants, since these are characteristics of already existing groups.

The independent variables are the administration of the drug – the dosage and the timing. The dependent variable (sometimes known as the responding variable) is what is being studied and measured in the experiment. It’s what changes as a result of the changes to the independent variable. The independent variable (sometimes known as the manipulated variable) is the variable whose change isn’t affected by any other variable in the experiment. There’s nothing you or anything else can do to speed up or slow down time or increase or decrease age. The slope of a line is a value that describes the rate of change between the independent and dependent variables.

In high school she scored in the 99th percentile on the SAT and was named a National Merit Finalist. Yes, but including more than one of either type requires multiple research questions. You’ll often use t tests or ANOVAs to analyze your data and answer your research questions.