# Assumptions and conditions for using statistical

## Statistical assumptions examples

Normal models are continuous and theoretically extend forever in both directions. Inference for the Difference of Two Proportions When we have proportions from two groups, the same assumptions and conditions apply to each. Remember, students need to check this condition using the information given in the problem. Make checking them a requirement for every statistical procedure you do. Equality of variance is usually examined when assessing for mean differences on an independent grouping variable e. The T-Test The t-test was developed by a chemist working for the Guinness brewing company as a simple way to measure the consistent quality of stout. Homoscedasticity homogeneity of variances — When you graph the residuals against any of the independent variables, you should see a random pattern. Linearity is typically assessed in Pearson correlation analyses and regression analyses. The null hypothesis is the default assumption that no relationship exists between two different measured phenomena. Many students observed that this amount of rainfall was about one standard deviation below average and then called upon the Linearity — You have two independent variables and so you should create two scatter charts: 1 independent variable 1 with the dependent variable and 2 independent variable 2 with the dependent variable.

Start Early Inference is a difficult topic for students. It was further developed and adapted, and now refers to any test of a statistical hypothesis in which the statistic being tested for is expected to correspond to a t-distribution if the null hypothesis is supported.

Normality can be examined by several methods, two of which are the Kolmogorov Smirnov KS test and the examination of skew and kurtosis.

## Assumptions for t confidence interval

Unless assumption 7 is violated you will be able to build a linear regression model, but you may not be able to gain some of the advantages of the model if some of these other assumptions are not met. Normal models are continuous and theoretically extend forever in both directions. If those assumptions are violated, the method may fail. Normality is typically assessed in the examination of mean differences e. Homoscedasticity homogeneity of variances — When you graph the residuals against any of the independent variables, you should see a random pattern. By this we mean that all the Normal models of errors at the different values of x have the same standard deviation. Regression Models Least squares regression and correlation are based on the If the problem specifically tells them that a Normal model applies, fine. You can reduce the impact of multicollinearity by using Ridge regression or some other similar method. Looking at the paired differences gives us just one set of data, so we apply our one-sample t-procedures. Students should have recognized that a Normal model did not apply.

Independence Assumption: The errors are independent. Independent Groups Assumption: The two groups and hence the two sample proportions are independent. After all, binomial distributions are discrete and have a limited range of from 0 to n successes. They check the Random Condition a random sample or random allocation to treatment groups and the 10 Percent Condition for samples for both groups.

We already know the appropriate assumptions and conditions. If the problem specifically tells them that a Normal model applies, fine. Nearly Normal Residuals Condition: A histogram of the residuals looks roughly unimodal and symmetric.

Straight Enough Condition: The pattern in the scatterplot looks fairly straight. Sample-to-sample variation in slopes can be described by a t-model, provided several assumptions are met. The assumptions are about populations and models, things that are unknown and usually unknowable.

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