A more realistic depiction can be found on p. In the curve with the "small size samples," notice that there are fewer samples with means around the middle value, and more samples with means out at the extremes.
Both the right and left tails of the distribution are "fatter. The differences in the curves represent differences in the standard deviation of the sampling distribution--smaller samples tend to have larger standard errors and larger samples tend to have smaller standard errors. This point about standard errors can be illustrated a different way.
One statistical test is designed to see if a single sample mean is different from a population mean. A version of this test is the t-test for a single mean. The purpose of this t-test is to see if there is a significant difference between the sample mean and the population mean.
The t-test formula looks like this:. The t-test formula also found on p. First, it takes into account how large the difference between the sample and the population mean is by finding the difference between them. When the sample mean is far from the population mean, the difference will be large.
Second, t-test formula divides this quantity by the standard error symbolized by. By dividing by the standard error, we are taking into account sampling variability. Only if the difference between the sample and population means is large relative to the amount of sampling variability will we consider the difference to be "statistically significant".
When sampling variability is high i. Ratio of the distance from the population mean relative to the sampling variability. 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. Overall Likert scale scores are sometimes treated as interval data.
These scores are considered to have directionality and even spacing between them. The type of data determines what statistical tests you should use to analyze your data. 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. With random error, multiple measurements will tend to cluster around the true value.
Systematic errors are much more problematic because they can skew your data away from the true value. Random error is almost always present in scientific studies, even in highly controlled settings. You can avoid systematic error through careful design of your sampling , data collection , and analysis procedures. For example, use triangulation to measure your variables using multiple methods; regularly calibrate instruments or procedures; use random sampling and random assignment ; and apply masking blinding where possible.
A correlational research design investigates relationships between two variables or more without the researcher controlling or manipulating any of them. A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables. Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions.
A correlation is usually tested for two variables at a time, but you can test correlations between three or more variables. Controlled experiments establish causality, whereas correlational studies only show associations between variables. In general, correlational research is high in external validity while experimental research is high in internal validity.
Correlation describes an association between variables: when one variable changes, so does the other. A correlation is a statistical indicator of the relationship between variables. Causation means that changes in one variable brings about changes in the other; there is a cause-and-effect relationship between variables.
The third variable problem means that a confounding variable affects both variables to make them seem causally related when they are not. A questionnaire is a data collection tool or instrument, while a survey is an overarching research method that involves collecting and analyzing data from people using questionnaires.
Closed-ended, or restricted-choice, questions offer respondents a fixed set of choices to select from. These questions are easier to answer quickly. Open-ended or long-form questions allow respondents to answer in their own words. Because there are no restrictions on their choices, respondents can answer in ways that researchers may not have otherwise considered.
You can organize the questions logically, with a clear progression from simple to complex, or randomly between respondents. A logical flow helps respondents process the questionnaire easier and quicker, but it may lead to bias.
Randomization can minimize the bias from order effects. But what about cases where knowing the ratio of men to women that passed a test after studying for less than 40 hours is important? Here, a stratified random sample would be preferable to a simple random sample. This type of sampling, also referred to as proportional random sampling or quota random sampling, divides the overall population into smaller groups.
These are known as strata. People within the strata share similar characteristics. What if age was an important factor that researchers would like to include in their data? Using the stratified random sampling technique, they could create layers or strata for each age group. The selection from each stratum would have to be random so that everyone in the bracket has a likely chance of being included in the sample.
For example, two participants, Alex and David, are 22 and 24 years old, respectively. The sample selection cannot pick one over the other based on some preferential mechanism. They both should have an equal chance of being selected from their age group. The strata could look something like this:. From the table, the population has been divided into age groups. For example, 30, people within the age range of 20 to 24 years old took the CFA exam in Alex or David—or both or neither—may be included among the random exam participants of the sample.
There are many more strata that could be compiled when deciding on a sample size. Some researchers might populate the job functions, countries, marital status, etc. As of , the population of the world was 7. The total number of people in any given country can also be a population size. The total number of students in a city can be taken as a population, and the total number of dogs in a city is also a population size. Samples can be taken from these populations for research purposes.
Following our CFA exam example, the researchers could take a sample of 1, CFA participants from the total , test-takers—the population—and run the required data on this number. The mean of this sample would be taken to estimate the average of CFA exam takers that passed even though they only studied for less than 40 hours. The sample group taken should not be biased. This means that if the sample mean of the 1, CFA exam participants is 50, the population mean of the , test-takers should also be approximately Often, a population is too large or extensive in order to measure every member and measuring each member would be expensive and time-consuming.
A sample allows for inferences to be made about the population using statistical methods. This sampling method uses respondents or data points that are randomly selected from the larger population. Apart from product and pricing research, Conjoint. Fully-functional online survey tool with various question types, logic, randomisation, and reporting for unlimited number of responses and surveys.
When we sample, the units that we sample — usually people — supply us with one or more responses. In this sense, a response is a specific measurement value that a sampling unit supplies.
In the figure, the person is responding to a survey instrument and gives a response of 4. When we look across the responses that we get for our entire sample, we use a statistic. There are a wide variety of statistics we can use — mean, median, mode, and so on. In this example, we see that the mean or average for the sample is 3. But the reason we sample is so that we might get an estimate for the population we sampled from.
If we could, we would much prefer to measure the entire population. So how do we get from our sample statistic to an estimate of the population parameter? A crucial midway concept you need to understand is the sampling distribution.
In order to understand it, you have to be able and willing to do a thought experiment. Imagine that instead of just taking a single sample like we do in a typical study, you took three independent samples of the same population. And furthermore, imagine that for each of your three samples, you collected a single response and computed a single statistic, say, the mean of the response. But you would expect that all three samples would yield a similar statistical estimate because they were drawn from the same population.
Now, for the leap of imagination! Imagine that you did an infinite number of samples from the same population and computed the average for each one. If you plotted them on a histogram or bar graph you should find that most of them converge on the same central value and that you get fewer and fewer samples that have averages farther away up or down from that central value.
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