# Blog Details

## Definition Of Statistical Testing

In epidemiological studies, there are various type of study design like case control, cohort, and cross-sectional study designs. For example, we want to evaluate the effect of a new drug on blood pressure in a group of 10 healthy volunteers. If we compare the values of blood pressure in the same group of 10 individuals, before intervention and after intervention, then this is known as paired or matched design. However, if we want to compare the values of blood pressure in two entirely different groups, then this is known as unpaired or independent study design. Variable or data may be numerical or categorical type.[12,13] Numerical data may be continuous or discrete. Significance testing is used as a substitute for the traditional comparison of predicted value and experimental result at the core of the scientific method.

It indicates where a given value is located on the normal curve in terms of the number of standard deviations from the mean. In a hypothesis test, the p value is compared to the significance level to decide whether to reject the null hypothesis. If a result is statistically significant, that means it’s unlikely to be explained solely by chance or random factors. In other words, a statistically significant result has a very low chance of occurring if there were no true effect in a research study. One-sample tests are appropriate when a sample is being compared to the population from a hypothesis.

## Definition: Statistical tests

To determine whether a discovery or relationship is statistically significant, hypothesis testing uses a z-test. It usually checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more, can a z-test be applied. Null and alternative hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship. As shown in Tables 4 and 5, regression models are fit at first for the whole case study area and then the main road and alleyway networks separately.

• The more unlikely your results are under this assumption, the easier it becomes to reject the null hypothesis in favor of an alternative hypothesis.
• Statistical tests further assume the null hypothesis, which states that there are no differences between two populations or classes.
• Remember, the null hypothesis states that there is no significant change in blood pressure if the patient is or is not taking the new medication.
• However, there are important differences between the two types of hypotheses, summarized in the following table.
• Neyman–Pearson theory was proving the optimality of Fisherian methods from its inception.
• However, you may encounter data sets that fail to meet one or more of these assumptions.

One naïve Bayesian approach to hypothesis testing is to base decisions on the posterior probability, but this fails when comparing point and continuous hypotheses. Other approaches to decision making, such as Bayesian decision theory, attempt to balance the consequences of incorrect decisions across all possibilities, rather than concentrating on a single null hypothesis. A number of other approaches to reaching a decision based on data are available via decision theory and optimal decisions, some of which have desirable properties. Hypothesis testing, though, is a dominant approach to data analysis in many fields of science.

## What are the Four Key Steps Involved in Hypothesis Testing?

It is used to estimate the relationship between 2 statistical variables. When reporting statistical significance, include relevant descriptive statistics about your data (e.g., means and standard deviations) as well as the test statistic and p value. An important property of a test statistic is that its sampling distribution under the null hypothesis must be calculable, either exactly or approximately, which allows p-values to be calculated. A test statistic shares some of the same qualities of a descriptive statistic, and many statistics can be used as both test statistics and descriptive statistics.

As you can see, the lower the p-value, the chances of the alternate hypothesis being true increases, which means that the new advertising campaign causes an increase or decrease in sales. If the sample falls within this range, the alternate hypothesis will be accepted, and the null hypothesis will be rejected. Another straightforward example to understand this concept is determining whether or not a coin is fair and balanced. The null hypothesis states that the probability of a show of heads is equal to the likelihood of a show of tails. In contrast, the alternate theory states that the probability of a show of heads and tails would be very different. The Alternate Hypothesis is the logical opposite of the null hypothesis.

## Hypothesis testing

That’s why APA guidelines advise reporting not only p values but also effect sizes and confidence intervals wherever possible to show the real world implications of a research outcome. An extremely low p value indicates high statistical significance, while a high p value means low or no statistical significance. F-tests (analysis of variance, ANOVA) are commonly used when deciding whether groupings of data by category are meaningful. If the variance of test scores of the left-handed in a class is much smaller than the variance of the whole class, then it may be useful to study lefties as a group. The null hypothesis is that two variances are the same – so the proposed grouping is not meaningful. If the homogeneity of a region is rejected, even after checking the discordant sites, then in principle no unique bivariate distribution can be selected to model the flood (or other events) response in that region. Consequently, one of the options is to divide the region with appropriate clustering method into smaller subregions provided that at least they contain enough number of sites. In the newly obtained subregions, the discordancy of the sites is tested again and the statistic H is evaluated as well. In the case one or more subregions remain heterogenous, then the clustering procedure can be repeated by considering different variables or number of clusters. The latter should be flexible and general, to include most distributions commonly used in hydrology, in order to avoid subjective selection of that distribution. Recall that a multivariate distribution is composed of margins and a copula (see Chapter 5).

Hypothesis testing always starts with the assumption that the null hypothesis is true. Using this procedure, you can assess the likelihood (probability) of obtaining your results under this assumption. Based on the outcome of the test, you can reject static testing definition or retain the null hypothesis. Correlation tests determine the relationship between two variables without proposing a cause-effect relationship. They can be used in multiple regression to test if there is autocorrelation between two variables. The researcher must then settle for some level of confidence or the significance level for which they do want to be correct. The significance level is given the Greek letter alpha and specified as the probability the researcher is willing to be incorrect. Our researcher wants to be correct about their outcome 95% of the time, or the researcher is willing to be incorrect 5% of the time. Probabilities are stated as decimals, with 1.0 being completely positive (100%) and 0 being completely negative (0%).

Cart

No products in the cart.

Select the fields to be shown. Others will be hidden. Drag and drop to rearrange the order.
• Image
• SKU
• Rating
• Price
• Stock
• Availability