Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not. Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:. Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics. Parametric tests make powerful inferences about the population based on sample data.

But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead. A regression models the extent to which changes in a predictor variable results in changes in outcome variable s. Comparison tests usually compare the means of groups. These may be the means of different groups within a sample e. The z and t tests have subtypes based on the number and types of samples and the hypotheses:. The correlation coefficient r tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population. You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population. A t test can also determine how significantly a correlation coefficient differs from zero based on sample size.

Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:. In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level usually 0. Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population. This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores.

Example: Interpret your results correlational study You compare your p value of 0. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables. A large sample size can also strongly influence the statistical significance of a correlation coefficient by making very small correlation coefficients seem significant. In contrast, the effect size indicates the practical significance of your results.

Because your value is between 0. Decision errors Type I and Type II errors are mistakes made in research conclusions. You can aim to minimize the risk of these errors by selecting an optimal significance level and ensuring high power. Traditionally, frequentist statistics emphasizes null hypothesis significance testing and always starts with the assumption of a true null hypothesis. However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations. Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

Have a language expert improve your writing. Proofreading Services. Run a free plagiarism check in 10 minutes. Plagiarism Checker. Generate accurate citations for free. Citation Generator. Home Knowledge Base Statistics. Example: Causal research question Can meditation improve exam performance in teenagers? Example: Correlational research question Is there a relationship between parental income and college grade point average GPA? Experimental Correlational Example: Experimental research design You design a within-subjects experiment to study whether a 5-minute meditation exercise can improve math test scores.

Your study takes repeated measures from one group of participants. Experimental Correlational Example: Variables experiment You can perform many calculations with quantitative age or test score data, whereas categorical variables can be used to decide groupings for comparison tests. Variable Type of data Age Quantitative ratio Gender Categorical nominal Race or ethnicity Categorical nominal Baseline test scores Quantitative interval Final test scores Quantitative interval. A parametric correlation test can be used for quantitative data, while a non-parametric correlation test should be used if one of the variables is ordinal. Variable Type of data Parental income Quantitative ratio GPA Quantitative interval. You contact three private schools and seven public schools in various districts of the city to see if you can administer your experiment to students in the 11th grade.

Prevent plagiarism, run a free check. Try for free. Experimental Correlational Example: Descriptive statistics experiment After collecting pretest and posttest data from 30 students across the city, you calculate descriptive statistics. Because you have normal distributed data on an interval scale, you tabulate the mean, standard deviation, variance and range. Pretest scores Posttest scores Mean Parental income USD GPA Mean 62, 3. Experimental Correlational Example: Paired t test for experimental research Because your research design is a within-subjects experiment, both pretest and posttest measurements come from the same group, so you require a dependent paired t test.

Since you predict a change in a specific direction an improvement in test scores , you need a one-tailed test. The test gives you: a t value test statistic of 3. The t test gives you: a t value of 3. Experimental Correlational Example: Interpret your results experiment You compare your p value of 0. Since your p value is lower, you decide to reject the null hypothesis, and you consider your results statistically significant. Is this article helpful? Other students also liked. Descriptive Statistics Definitions, Types, Examples Descriptive statistics summarize the characteristics of a data set. There are three types: distribution, central tendency, and variability. What is Effect Size and Why Does It Matter? Examples What Is Kurtosis?

How to Calculate Guide with Examples What is the geometric mean? Following is a list of statistical techniques that are involved in data analysis. Start Your Free Data Science Course. It is the process of collecting and grouping the data for statistical analysis purposes. It has two categories. Random variables are a special type of the variable used in Statistical Techniques that quantify the outcomes which are generated through random processes. The Random variables are generally noted using upper case letters such as X or E X or Y. It is related to the Probability of the process outcomes.

There is another important concept known as skewness, This process determines the coefficient of the skewness of the random variable. It also includes checking the symmetry of data distribution. Also, there are two terms regularly used for data analysis for analyzing data distribution or identifying the distance of data points from the mean. These are also known as measures of data spread. Probability is the process of determining the likelihood of an event that will occur in the future. It works using Numerical values relevant to the process outcomes of the event. Set theory mathematics is the basic fundamentals for probability determinations. The Sample Space contains the elements which equally likely in nature. The Probability of an event can be denoted as P Event. If we assume the event A with sample spaces then P A will be the,.

It is an important statistical technique for data analysis. Hypothesis testing is an efficient validator of data analysis. A statistical hypothesis is mostly driven by certain assumptions about the data.

Statistical analysis means investigating trends, patterns, and relationships using quantitative data. It is an important research tool used by scientists, governments, businesses, and other organizations. To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process. You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure. After collecting data from your sample, you can organize and summarize the data using descriptive statistics.

Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalize your findings. This article is a practical introduction to statistical analysis for students and researchers. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables. Table of contents Step 1: Write your hypotheses and plan your research design Step 2: Collect data from a sample Step 3: Summarize your data with descriptive statistics Step 4: Test hypotheses or make estimates with inferential statistics Step 5: Interpret your results.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design. The goal of research is often to investigate a relationship between variables within a population. You start with a prediction, and use statistical analysis to test that prediction. A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data. While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship. A research design is your overall strategy for data collection and analysis.

It determines the statistical tests you can use to test your hypothesis later on. First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables. Then, your participants will undergo a 5-minute meditation exercise. In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention.

Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. There are no dependent or independent variables in this study, because you only want to measure variables without influencing them in any way. Measuring variables When planning a research design, you should operationalize your variables and decide exactly how you will measure them. Many variables can be measured at different levels of precision. For example, age data can be quantitative 8 years old or categorical young. If a variable is coded numerically e. Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures. You should aim for a sample that is representative of the population. In theory, for highly generalizable findings, you should use a probability sampling method. Random selection reduces sampling bias and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling. While non-probability samples are more likely to be biased, they are much easier to recruit and collect data from.

Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population. Keep in mind that external validity means that you can only generalize your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialized, Rich and Democratic samples e. If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalized in your discussion section. Your participants are self-selected by their schools.

Example: Sampling correlational study Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area. Your participants volunteer for the survey, making this a non-probability sample. Calculate sufficient sample size Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be e.

As a rule of thumb, a minimum of 30 units or more per subgroup is necessary. By visualizing your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data. A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends. In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values. Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:. However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all. Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:. Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics.

The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions. Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test. From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population.

Example: Descriptive statistics correlational study After collecting data from students, you tabulate descriptive statistics for annual parental income and GPA. Next, we can compute a correlation coefficient and perform a statistical test to understand the significance of the relationship between the variables in the population. Step 4: Test hypotheses or make estimates with inferential statistics A number that describes a sample is called a statistic , while a number describing a population is called a parameter. Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample e. Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not. Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:. Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead. A regression models the extent to which changes in a predictor variable results in changes in outcome variable s. Comparison tests usually compare the means of groups. These may be the means of different groups within a sample e. The z and t tests have subtypes based on the number and types of samples and the hypotheses:.

The correlation coefficient r tells you the strength of a linear relationship between two quantitative variables. However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population. You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:. In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level usually 0. Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population. This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results correlational study You compare your p value of 0.

Other students also liked. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions. It determines the statistical tests you can use to test your hypothesis later on. A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends. For example, you can calculate a mean score with quantitative data, but not with categorical data. Using data from a sample, you can test hypotheses about relationships between variables in the population.

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