Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 where 0 indicates impossibility and 1 indicates certainty. Alternative hypothesis H 1 and H a denotes that a statement between the variables is expected to be true.
The P value or the calculated probability is the probability of the event occurring by chance if the null hypothesis is true.
The P value is a numerical between 0 and 1 and is interpreted by researchers in deciding whether to reject or retain the null hypothesis [ Table 3 ]. However, if null hypotheses H0 is incorrectly rejected, this is known as a Type I error. Numerical data quantitative variables that are normally distributed are analysed with parametric tests. The assumption of normality which specifies that the means of the sample group are normally distributed.
The assumption of equal variance which specifies that the variances of the samples and of their corresponding population are equal. However, if the distribution of the sample is skewed towards one side or the distribution is unknown due to the small sample size, non-parametric[ 14 ] statistical techniques are used. Non-parametric tests are used to analyse ordinal and categorical data.
The parametric tests assume that the data are on a quantitative numerical scale, with a normal distribution of the underlying population. The samples have the same variance homogeneity of variances. The samples are randomly drawn from the population, and the observations within a group are independent of each other.
Student's t -test is used to test the null hypothesis that there is no difference between the means of the two groups. It is used in three circumstances:. To test if a sample mean as an estimate of a population mean differs significantly from a given population mean this is a one-sample t -test. The formula for one sample t -test is. To test if the population means estimated by two independent samples differ significantly the unpaired t -test. The formula for unpaired t -test is:. To test if the population means estimated by two dependent samples differ significantly the paired t -test.
A usual setting for paired t -test is when measurements are made on the same subjects before and after a treatment. The group variances can be compared using the F -test. If F differs significantly from 1. The Student's t -test cannot be used for comparison of three or more groups. The purpose of ANOVA is to test if there is any significant difference between the means of two or more groups. The within-group variability error variance is the variation that cannot be accounted for in the study design.
It is based on random differences present in our samples. However, the between-group or effect variance is the result of our treatment. These two estimates of variances are compared using the F-test.
However, a repeated measure ANOVA is used when all variables of a sample are measured under different conditions or at different points in time. As the variables are measured from a sample at different points of time, the measurement of the dependent variable is repeated. When the assumptions of normality are not met, and the sample means are not normally, distributed parametric tests can lead to erroneous results.
Non-parametric tests distribution-free test are used in such situation as they do not require the normality assumption. That is, they usually have less power.
As is done for the parametric tests, the test statistic is compared with known values for the sampling distribution of that statistic and the null hypothesis is accepted or rejected. The types of non-parametric analysis techniques and the corresponding parametric analysis techniques are delineated in Table 5. Median test for one sample: The sign test and Wilcoxon's signed rank test.
The sign test and Wilcoxon's signed rank test are used for median tests of one sample. These tests examine whether one instance of sample data is greater or smaller than the median reference value. Therefore, it is useful when it is difficult to measure the values. Wilcoxon's rank sum test ranks all data points in order, calculates the rank sum of each sample and compares the difference in the rank sums.
It is used to test the null hypothesis that two samples have the same median or, alternatively, whether observations in one sample tend to be larger than observations in the other. The two-sample Kolmogorov-Smirnov KS test was designed as a generic method to test whether two random samples are drawn from the same distribution.
The null hypothesis of the KS test is that both distributions are identical. The statistic of the KS test is a distance between the two empirical distributions, computed as the maximum absolute difference between their cumulative curves. The Kruskal—Wallis test is a non-parametric test to analyse the variance. The data values are ranked in an increasing order, and the rank sums calculated followed by calculation of the test statistic.
In contrast to Kruskal—Wallis test, in Jonckheere test, there is an a priori ordering that gives it a more statistical power than the Kruskal—Wallis test. The Friedman test is a non-parametric test for testing the difference between several related samples. The Friedman test is an alternative for repeated measures ANOVAs which is used when the same parameter has been measured under different conditions on the same subjects.
Chi-square test, Fischer's exact test and McNemar's test are used to analyse the categorical or nominal variables. The Chi-square test compares the frequencies and tests whether the observed data differ significantly from that of the expected data if there were no differences between groups i. It is calculated by the sum of the squared difference between observed O and the expected E data or the deviation, d divided by the expected data by the following formula:.
A Yates correction factor is used when the sample size is small. Fischer's exact test is used to determine if there are non-random associations between two categorical variables. It does not assume random sampling, and instead of referring a calculated statistic to a sampling distribution, it calculates an exact probability.
McNemar's test is used for paired nominal data. The null hypothesis is that the paired proportions are equal. The Mantel-Haenszel Chi-square test is a multivariate test as it analyses multiple grouping variables. It stratifies according to the nominated confounding variables and identifies any that affects the primary outcome variable.
If the outcome variable is dichotomous, then logistic regression is used. Numerous statistical software systems are available currently.
There are a number of web resources which are related to statistical power analyses. A few are:. It gives an output of a complete report on the computer screen which can be cut and paste into another document. It is important that a researcher knows the concepts of the basic statistical methods used for conduct of a research study. This will help to conduct an appropriately well-designed study leading to valid and reliable results.
Inappropriate use of statistical techniques may lead to faulty conclusions, inducing errors and undermining the significance of the article. Bad statistics may lead to bad research, and bad research may lead to unethical practice. Hence, an adequate knowledge of statistics and the appropriate use of statistical tests are important. An appropriate knowledge about the basic statistical methods will go a long way in improving the research designs and producing quality medical research which can be utilised for formulating the evidence-based guidelines.
We use cookies to track how our visitors are browsing and engaging with our website in order to understand and improve the user experience. Review our Privacy Policy to learn more. Support Login. Probability Sampling vs. Non-Probability Sampling In statistics, sampling is when researchers determine a representative segment of a larger population that is then used to conduct a study. Sampling comes in two forms — probability sampling and non-probability sampling.
Probability sampling uses random sampling techniques to create a sample. Probability Sampling For a sampling method to be considered probability sampling, it must utilize some form of random selection. The Methods of Probability Sampling There are several types of probability sampling.
Simple Random Sampling Simple random sampling is considered the easiest method of probability sampling. Stratified Random Sampling Stratified random sampling is also referred to as proportional random sampling. Systematic Random Sampling Systematic random sampling is often compared to an arithmetic progression in which the difference between any two consecutive numbers is of the same value.
Cluster Area Random Sampling Cluster random sampling is conducted when the size of a population is too large to perform simple random sampling.
Multi-Stage Sampling Multi-stage sampling involves a combination of two or more of the probability sampling methods outlined above. Get started with Alchemer today. Start making smarter decisions Contact sales Start a free trial.
Contact Sales. By accessing and using this page, you agree to the Terms of Use. As stated above, this is the unit where the two versions of the course differ. In the Probability and Statistics course the unit is a classical treatment of probability and includes basic probability principles, conditional probability, discrete random variables including the Binomial distribution and continuous random variables with emphasis on the normal distribution.
Both probability units culminate in a discussion of sampling distributions that is grounded in simulation. This unit introduces students to the logic as well as the technical side of the main forms of inference: point estimation, interval estimation and hypothesis testing. The unit covers inferential methods for the population mean and population proportion, Inferential methods for comparing the means of two groups and of more than two groups ANOVA , the Chi-Square test for independence and linear regression.
The unit reinforces the framework that the students were introduced to in the Exploratory Data Analysis for choosing the appropriate, in this case, inferential method in various data analysis scenarios. By the end of this course, students will have gained an appreciation for the diverse applications of statistics and its relevance to their lives and fields of study. They will learn to:.
OLI system requirements, regardless of course :. Some courses include exercises with exceptions to these requirements, such as technology that cannot be used on mobile devices. Watch the video to see how easily students can register with a Course Key. Statistics presented with a full treatment of probability Free for independent learners.
Unit 1 Exploratory Data Analysis. Unit 2 Producing Data. This unit is organized into two modules — Sampling and Study Design. Unit 3 Probability. Unit 4 Inference. What students will learn By the end of this course, students will have gained an appreciation for the diverse applications of statistics and its relevance to their lives and fields of study. Compare and contrast distributions of quantitative data from two or more groups, and produce a brief summary, interpreting your findings in context.
Generate and interpret several different graphical displays of the distribution of a quantitative variable histogram, stemplot, boxplot. Relate measures of center and spread to the shape of the distribution, and choose the appropriate measures in different contexts. Summarize and describe the distribution of a categorical variable in context.
Summarize and describe the distribution of a quantitative variable in context: a describe the overall pattern, b describe striking deviations from the pattern. Graphically display the relationship between two quantitative variables and describe: a the overall pattern, and b striking deviations from the pattern. In the special case of linear relationship, use the least squares regression line as a summary of the overall pattern, and use it to make predictions.
Interpret the value of the correlation coefficient, and be aware of its limitations as a numerical measure of the association between two quantitative variables. Produce a two-way table, and interpret the information stored in it about the association between two categorical variables by comparing conditional percentages. Recognize the distinction between association and causation, and identify potential lurking variables for explaining an observed relationship.
Unit 3: Producing Data Module 6: Sampling Critically evaluate the reliability and validity of results published in mainstream media. Identify the sampling method used in a study and discuss its implications and potential limitations. Module 7: Designing Studies Determine how the features of a survey impact the collected data and the accuracy of the data.
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