Other links. Discrete and continuous variables Daniel's text distinguishes between discrete and continuous variables. These are technical distinctions that will not be all that important to us in this class.
According to the text, discrete variables are variables in which there are no intermediate values possible. For instance, the number of phone calls you receive per day. You cannot receive 6. Continuous variables are everything else; any variable that can theoretically have values in between points e.
It turns out that this is not all that useful of a distinction for our purposes. What is really more important for statistical considerations is the level of measurement used. When I say it is more important, I've really understated this. Understanding the level of measurement of a variable or scale or measure is the first and most important distinction one must make about a variable when doing statistics!
Levels of measurement Statisticians often refer to the "levels of measurement" of a variable, a measure, or a scale to distinguish between measured variables that have different properties.
There are four basic levels: nominal, ordinal, interval, and ratio. Nominal A variable measured on a "nominal" scale is a variable that does not really have any evaluative distinction. One value is really not any greater than another.
A good example of a nominal variable is sex or gender. Information in a data set on sex is usually coded as 0 or 1, 1 indicating male and 0 indicating female or the other way around for male, 1 for female. There is only a nominal difference between 0 and 1.
With nominal variables, there is a qualitative difference between values, not a quantitative one. Ordinal Something measured on an "ordinal" scale does have an evaluative connotation. One value is greater or larger or better than the other. Product A is preferred over product B, and therefore A receives a value of 1 and B receives a value of 2.
Another example might be rating your job satisfaction on a scale from 1 to 10, with 10 representing complete satisfaction. With ordinal scales, we only know that 2 is better than 1 or 10 is better than 9; we do not know by how much.
It may vary. The distance between 1 and 2 maybe shorter than between 9 and In some cases, the measurement scale for data is ordinal, but the variable is treated as continuous. For example, a Likert scale that contains five values - strongly agree, agree, neither agree nor disagree, disagree, and strongly disagree - is ordinal. However, where a Likert scale contains seven or more value - strongly agree, moderately agree, agree, neither agree nor disagree, disagree, moderately disagree, and strongly disagree - the underlying scale is sometimes treated as continuous although where you should do this is a cause of great dispute.
It is worth noting that how we categorise variables is somewhat of a choice. Whilst we categorised gender as a dichotomous variable you are either male or female , social scientists may disagree with this, arguing that gender is a more complex variable involving more than two distinctions, but also including measurement levels like genderqueer, intersex and transgender.
At the same time, some researchers would argue that a Likert scale, even with seven values, should never be treated as a continuous variable. Types of Variable All experiments examine some kind of variable s.
Dependent and Independent Variables 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. The dependent and independent variables for the study are: Dependent Variable: Test Mark measured from 0 to Independent Variables: Revision time measured in hours Intelligence measured using IQ score The dependent variable is simply that, a variable that is dependent on an independent variable s.
Join the 10,s of students, academics and professionals who rely on Laerd Statistics. Experimental and Non-Experimental Research Experimental research : In experimental research, the aim is to manipulate an independent variable s and then examine the effect that this change has on a dependent variable s. Since it is possible to manipulate the independent variable s , experimental research has the advantage of enabling a researcher to identify a cause and effect between variables.
For example, take our example of students completing a maths exam where the dependent variable was the exam mark measured from 0 to , and the independent variables were revision time measured in hours and intelligence measured using IQ score. Here, it would be possible to use an experimental design and manipulate the revision time of the students. The tutor could divide the students into two groups, each made up of 50 students.
In "group one", the tutor could ask the students not to do any revision. Alternately, "group two" could be asked to do 20 hours of revision in the two weeks prior to the test. The tutor could then compare the marks that the students achieved.
Non-experimental research : In non-experimental research, the researcher does not manipulate the independent variable s. This is not to say that it is impossible to do so, but it will either be impractical or unethical to do so. For example, a researcher may be interested in the effect of illegal, recreational drug use the independent variable s on certain types of behaviour the dependent variable s.
However, whilst possible, it would be unethical to ask individuals to take illegal drugs in order to study what effect this had on certain behaviours. As such, a researcher could ask both drug and non-drug users to complete a questionnaire that had been constructed to indicate the extent to which they exhibited certain behaviours.
Whilst it is not possible to identify the cause and effect between the variables, we can still examine the association or relationship between them. The research methods you use depend on the type of data you need to answer your research question. In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question.
Internal validity is the extent to which you can be confident that a cause-and-effect relationship established in a study cannot be explained by other factors. There are eight threats to internal validity : history, maturation, instrumentation, testing, selection bias, regression to the mean, social interaction and attrition. Longitudinal studies and cross-sectional studies are two different types of research design.
In a cross-sectional study you collect data from a population at a specific point in time; in a longitudinal study you repeatedly collect data from the same sample over an extended period of time.
Longitudinal studies are better to establish the correct sequence of events, identify changes over time, and provide insight into cause-and-effect relationships, but they also tend to be more expensive and time-consuming than other types of studies. The British Cohort Study , which has collected data on the lives of 17, Brits since their births in , is one well-known example of a longitudinal study. Longitudinal studies can last anywhere from weeks to decades, although they tend to be at least a year long.
Cross-sectional studies are less expensive and time-consuming than many other types of study. Sometimes only cross-sectional data is available for analysis; other times your research question may only require a cross-sectional study to answer it.
Cross-sectional studies cannot establish a cause-and-effect relationship or analyze behavior over a period of time. To investigate cause and effect, you need to do a longitudinal study or an experimental study.
The external validity of a study is the extent to which you can generalize your findings to different groups of people, situations, and measures. The two types of external validity are population validity whether you can generalize to other groups of people and ecological validity whether you can generalize to other situations and settings.
There are seven threats to external validity : selection bias, history, experimenter effect, Hawthorne effect, testing effect, aptitude-treatment and situation effect.
Samples are used to make inferences about populations. Samples are easier to collect data from because they are practical, cost-effective, convenient and manageable. Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.
A statistic refers to measures about the sample , while a parameter refers to measures about the population. A sampling error is the difference between a population parameter and a sample statistic. Sampling bias occurs when some members of a population are systematically more likely to be selected in a sample than others.
Sampling bias is a threat to external validity — it limits the generalizability of your findings to a broader group of people. Some common types of sampling bias include self-selection, non-response, undercoverage, survivorship, pre-screening or advertising, and healthy user bias. Using careful research design and sampling procedures can help you avoid sampling bias.
Oversampling can be used to correct undercoverage bias. Probability sampling means that every member of the target population has a known chance of being included in the sample. Probability sampling methods include simple random sampling , systematic sampling , stratified sampling , and cluster sampling. In non-probability sampling , the sample is selected based on non-random criteria, and not every member of the population has a chance of being included.
Common non-probability sampling methods include convenience sampling, voluntary response sampling, purposive sampling, snowball sampling, and quota sampling.
Determining cause and effect is one of the most important parts of scientific research. You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment.
The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both!
Yes, but including more than one of either type requires multiple research questions. For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question. 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.
Each of these is a separate independent variable. To ensure the internal validity of an experiment , you should only change one independent variable at a time. To ensure the internal validity of your research, you must consider the impact of confounding variables. If you fail to account for them, you might over- or underestimate the causal relationship between your independent and dependent variables , or even find a causal relationship where none exists.
A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the supposed cause , while the dependent variable is the supposed effect.
A confounding variable is a third variable that influences both the independent and dependent variables. Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables. There are several methods you can use to decrease the impact of confounding variables on your research: restriction, matching, statistical control and randomization.
In restriction , you restrict your sample by only including certain subjects that have the same values of potential confounding variables. In matching , you match each of the subjects in your treatment group with a counterpart in the comparison group.
The matched subjects have the same values on any potential confounding variables, and only differ in the independent variable. In statistical control , you include potential confounders as variables in your regression. In randomization , you randomly assign the treatment or independent variable in your study to a sufficiently large number of subjects, which allows you to control for all potential confounding variables.
Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations. However, there are also some drawbacks: data collection can be time-consuming, labor-intensive and expensive.
Operationalization means turning abstract conceptual ideas into measurable observations. Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
There are five common approaches to qualitative research :. There are various approaches to qualitative data analysis , but they all share five steps in common:. The specifics of each step depend on the focus of the analysis. Some common approaches include textual analysis , thematic analysis , and discourse analysis. In scientific research, concepts are the abstract ideas or phenomena that are being studied e.
Variables are properties or characteristics of the concept e. The process of turning abstract concepts into measurable variables and indicators is called operationalization. A Likert scale is a rating scale that quantitatively assesses opinions, attitudes, or behaviors. It is made up of 4 or more questions that measure a single attitude or trait when response scores are combined. To use a Likert scale in a survey , you present participants with Likert-type questions or statements, and a continuum of items, usually with 5 or 7 possible responses, to capture their degree of agreement.
An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not.
They should be identical in all other ways. A true experiment a. However, some experiments use a within-subjects design to test treatments without a control group. Blinding means hiding who is assigned to the treatment group and who is assigned to the control group in an experiment. If participants know whether they are in a control or treatment group , they may adjust their behavior in ways that affect the outcome that researchers are trying to measure.
If the people administering the treatment are aware of group assignment, they may treat participants differently and thus directly or indirectly influence the final results. A quasi-experiment is a type of research design that attempts to establish a cause-and-effect relationship. The main difference with a true experiment is that the groups are not randomly assigned. Quasi-experimental design is most useful in situations where it would be unethical or impractical to run a true experiment.
Quasi-experiments have lower internal validity than true experiments, but they often have higher external validity as they can use real-world interventions instead of artificial laboratory settings. Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected. Data is then collected from as large a percentage as possible of this random subset. The American Community Survey is an example of simple random sampling.
In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3. If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity. However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,. If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.
Cluster sampling is a probability sampling method in which you divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as your sample. There are three types of cluster sampling : single-stage, double-stage and multi-stage clustering. In all three types, you first divide the population into clusters, then randomly select clusters for use in your sample.
Cluster sampling is more time- and cost-efficient than other probability sampling methods , particularly when it comes to large samples spread across a wide geographical area. However, it provides less statistical certainty than other methods, such as simple random sampling , because it is difficult to ensure that your clusters properly represent the population as a whole. In stratified sampling , researchers divide subjects into subgroups called strata based on characteristics that they share e.
Once divided, each subgroup is randomly sampled using another probability sampling method. Using stratified sampling will allow you to obtain more precise with lower variance statistical estimates of whatever you are trying to measure. For example, say you want to investigate how income differs based on educational attainment, but you know that this relationship can vary based on race.
Using stratified sampling, you can ensure you obtain a large enough sample from each racial group, allowing you to draw more precise conclusions.
Yes, you can create a stratified sample using multiple characteristics, but you must ensure that every participant in your study belongs to one and only one subgroup. In this case, you multiply the numbers of subgroups for each characteristic to get the total number of groups.
Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval — for example, by selecting every 15th person on a list of the population. If the population is in a random order, this can imitate the benefits of simple random sampling. There are three key steps in systematic sampling :. A mediator variable explains the process through which two variables are related, while a moderator variable affects the strength and direction of that relationship.
A confounder is a third variable that affects variables of interest and makes them seem related when they are not. In contrast, a mediator is the mechanism of a relationship between two variables: it explains the process by which they are related. Including mediators and moderators in your research helps you go beyond studying a simple relationship between two variables for a fuller picture of the real world. They are important to consider when studying complex correlational or causal relationships.
Mediators are part of the causal pathway of an effect, and they tell you how or why an effect takes place. Moderators usually help you judge the external validity of your study by identifying the limitations of when the relationship between variables holds. Control variables help you establish a correlational or causal relationship between variables by enhancing internal validity. Researchers often model control variable data along with independent and dependent variable data in regression analyses and ANCOVAs.
In experimental research, random assignment is a way of placing participants from your sample into different groups using randomization. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group. In contrast, random assignment is a way of sorting the sample into control and experimental groups. Random sampling enhances the external validity or generalizability of your results, while random assignment improves the internal validity of your study.
Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a dice to randomly assign participants to groups.
Random assignment is used in experiments with a between-groups or independent measures design. Random assignment helps ensure that the groups are comparable. In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.
In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.
In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions. Between-subjects and within-subjects designs can be combined in a single study when you have two or more independent variables a factorial design. In a mixed factorial design, one variable is altered between subjects and another is altered within subjects. While a between-subjects design has fewer threats to internal validity , it also requires more participants for high statistical power than a within-subjects design.
Within-subjects designs have many potential threats to internal validity , but they are also very statistically powerful. In a factorial design, multiple independent variables are tested. If you test two variables, each level of one independent variable is combined with each level of the other independent variable to create different conditions. A confounding variable is a type of extraneous variable that not only affects the dependent variable, but is also related to the independent variable.
There are 4 main types of extraneous variables :. Controlled experiments require:. Depending on your study topic, there are various other methods of controlling variables. The difference between explanatory and response variables is simple:. On graphs, the explanatory variable is conventionally placed on the x-axis, while the response variable is placed on the y-axis. Random and systematic error are two types of measurement error. Random error is a chance difference between the observed and true values of something e.
Systematic error is a consistent or proportional difference between the observed and true values of something e. Systematic error is generally a bigger problem in research.
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