Dependent. Next: Independent Up: Module 8: Introduction to Previous: One Sample Contents 2.1. Dependent Samples t test Dependent Samples t Test First, it goes by many names... Dependent Samples t Test Matched-Pairs t Test Repeated Measures t Test t Test for Dependent Means t Test for Related Samples Essentially, it compares two sample means which are known to be related in some way. Types of Related Samples There are three types of related samples which are appropriate for the Dependent Samples t Test. Natural Pairs: Comparing the scores of two groups of subjects which are related naturally.
Similiar to previous tests, but... Now we are testing a Difference Score. 2.2. NHST Example We are interested in relationship satisfaction of young adults before and after they go off to college/university which separates them from their sweat-heart. Step 1: State the Null and Alternative Hypotheses Define the populations: Relationship Satisfaction = RS Population 1: RS prior to college separation. With. Untitled Document. The final factor that we need to consider is the set of assumptions of the test. All of the statistical tests of means are parametric tests. All parametric tests assume that the populations have specific characteristics and that samples are drawn under certain conditions.
These characteristics and conditions are expressed in the assumptions of the tests. One-Sample Z Test The assumptions of the one-sample Z test focus on sampling, measurement, and distribution. One-Sample t Test The assumptions of the one-sample t-test are identical to those of the one-sample Z test. T-Test for Dependent Means The assumptions of the t-test for dependent means focus on sampling, research design, measurement, and distribution. T-Test for Independent Means The assumptions of the t-test for independent means focus on sampling, research design, measurement, population distributions and population variance. Type II error | OnTestEngineering. Hypothesis Testing is the use of statistics for making rational decisions and I wanted to explore its use in test engineering. In doing so I found something very interesting that helps to support many of the ideas I’ve had.
I should explain that the title of this article is a bit of a play on words as we will find out later. Forming the Hypothesis1 Let’s start at the beginning. H0 = observe samples from a population with no defect or faults. Next we need to form an Alternative Hypothesis which must be measurable and mutually exclusive from H0 so that if one can occur the other cannot. Ha = observe samples from a population with defect or fault. We have generalized a hypothesis in which we wish to prove that items produced by a manufacturing process are defect free (built correctly) and are without fault (working correctly). Table 1 – Null and Alternative Hypotheses in Test Engineering Hypothesis Testing2 Table 2 – 4 Conditional Outcomes of Test Figure 2 – Hypothesis Test of Manufactured Items.
Methods Manual: t-test, hand calculation. Sampling Distribution of Difference Between Means. Sampling Distribution of Difference Between Means Author(s) David M. Lane Prerequisites Sampling Distributions, Sampling Distribution of the Mean, Variance Sum Law I Learning Objectives State the mean and variance of the sampling distribution of the difference between means Compute the standard error of the difference between means Compute the probability of a difference between means being above a specified value The sampling distribution of the difference between means can be thought of as the distribution that would result if we repeated the following three steps over and over again: (1) sample n1 scores from Population 1 and n2 scores from Population 2, (2) compute the means of the two samples (M1 and M2), and (3) compute the difference between means, M1 - M2.
As you might expect, the mean of the sampling distribution of the difference between means is: which says that the mean of the distribution of differences between sample means is equal to the difference between population means. Testing Differences Between Means. Difference between Two Means (Independent Groups) Author(s) David M. Lane Prerequisites Sampling Distribution of Difference between Means, Confidence Intervals, Confidence Interval on the Difference between Means, Logic of Hypothesis Testing, Testing a Single Mean Learning Objectives State the assumptions for testing the difference between two means Estimate the population variance assuming homogeneity of variance Compute the standard error of the difference between means Compute t and p for the difference between means Format data for computer analysis It is much more common for a researcher to be interested in the difference between means than in the specific values of the means themselves.
We take as an example the data from the "Animal Research" case study. Table 1. In order to test whether there is a difference between population means, we are going to make three assumptions: The consequences of violating the first two assumptions are investigated in the simulation in the next section. Difference in Means. This lesson describes how to construct a confidence interval for the difference between two means.
Estimation Requirements The approach described in this lesson is valid whenever the following conditions are met: Both samples are simple random samples. The samples are independent. Each population is at least 20 times larger than its respective sample. The sampling distribution of the difference between means is approximately normally distributed. Generally, the sampling distribution will be approximately normally distributed when the sample size is greater than or equal to 30. The Variability of the Difference Between Sample Means To construct a confidence interval, we need to know the variability of the difference between sample means. Note: In real-world analyses, the standard deviation of the population is seldom known.
Alert Some texts present additional options for calculating standard deviations. Standard deviation. Previously, we described how to construct confidence intervals. StatsCast: What is a t-test? T-tests. The T-Test. The t-test assesses whether the means of two groups are statistically different from each other. This analysis is appropriate whenever you want to compare the means of two groups, and especially appropriate as the analysis for the posttest-only two-group randomized experimental design.
Figure 1 shows the distributions for the treated (blue) and control (green) groups in a study. Actually, the figure shows the idealized distribution – the actual distribution would usually be depicted with a histogram or bar graph. The figure indicates where the control and treatment group means are located. The question the t-test addresses is whether the means are statistically different. What does it mean to say that the averages for two groups are statistically different?
This leads us to a very important conclusion: when we are looking at the differences between scores for two groups, we have to judge the difference between their means relative to the spread or variability of their scores. One-Sample T-Test - QMSS. It is perhaps easiest to demonstrate the ideas and methods of the one-sample t-test by working through an example. To reiterate, the one-sample t-test compares the mean score of a sample to a known value, usually the population mean (the average for the outcome of some population of interest).
The basic idea of the test is a comparison of the average of the sample (observed average) and the population (expected average), with an adjustment for the number of cases in the sample and the standard deviation of the average. Working through an example can help to highlight the issues involved and demonstrate how to conduct a t-test using actual data. Example - Prenatal Care and Birthweight One of the best indicators of the health of a baby is his/her weight at birth. Birthweight is an outcome that is sensitive to the conditions in which mothers experienced pregnancy, particularly to issues of deprivation and poor diet, which are tied to lower birthweight. 1. In this case: 2. 3. Summary 3. T Test. We are called on many times to determine if the mean performance of two groups are significantly different.
Those two groups might be students, cattle, plants, or other objects. When attempting to determine if the difference between two means is greater than that expected from chance, the "t" test may be the needed statistical technique. If the data is from a normal population and at least ordinal in nature, then we are surer that this is the technique to use. If you wish to generalize to a population, then the samples must be representative. "t" is the difference between two sample means measured in terms of the standard error of those means, or "t" is a comparison between two groups means which takes into account the differences in group variation and group size of the two groups. Separate variance formula Use the separate variance formula if: Pooled Variance Formula Use the pooled variance formula if: Correlated Data Formula. Independent Groups t-test: Chapter 10. Independent Groups t-test: Chapter 10 Strength of the Relationship (10.3) - For the example we computed in class, we found a statistically significant difference – there is a “statistically significant relationship” between test-taking strategy (fake v. honest) and personality test scores. - Our next question is: since a relationship exists, how strong is this relationship?
- Question addresses the issue of “practical significance” or “real-world significance” - One way to address question is to try to interpret the difference between means directly. - We know our best estimate of this difference is 5.300, in raw-score units. - May be o.k. when have implicit knowledge of distribution (e.g., income) of DV - Problem with most DVs – we are not informed of distribution - What is the meaning of a 5.3 unit difference in personality scores? - Another way of judging how strongly the IV and DV are associated, or related, to one another is to compute “eta-squared” (eta2 or where df = n1 + n2 – 2 to. Dependent t-test. Dependent t-tests are a special brand of t-tests used when your two "groups" to be compared are actually just one group measured on two occasions. For example, you could use a dependent t-test to compare a group's score on the GRE before and after they have completed a test preparation course.
It's important to use the dependent t-test instead of the regular old independent t-test because the independent t-test makes the assumption of independent observations. If you've got more than one data point per person, then those data points are not independent; they are dependent. Thus the dependent t-test. The dependent t-test is also more powerful (more likely to produce a significant result) than the independent t-test because it is a within-subjects test. Imagine a test-preparation course for the GRE. Look at the scores in the "pre" column and compare them with the scores in the "post" column. Plotting Your Data the Between-Subjects (Wrong) Way Plotting Repeated-Measures Data (the Right Way)
Paired t-test. When to use it You use the paired t-test when there is one measurement variable and two nominal variables. One of the nominal variables has only two values. The most common design is that one nominal variable represents different individuals, while the other is "before" and "after" some treatment. Sometimes the pairs are spatial rather than temporal, such as left vs. right, injured limb vs. uninjured limb, above a dam vs. below a dam, etc. An example would be the performance of undergraduates on a test of manual dexterity before and after drinking a cup of tea. For each student, there would be two observations, one before the tea and one after. I would expect the students to vary widely in their performance, so if the tea decreased their mean performance by 5 percent, it would take a very large sample size to detect this difference if the data were analyzed using a Student's t-test. Null hypothesis The null hypothesis is that the mean difference between paired observations is zero.
Paired T-test. Standard Error. The standard error of the mean. Standard Error of Sample-Mean Differences. T-table. Chapter 9. Objectives By the end of this lesson, you will be able to... state properties of Student’s t-distribution determine t-values construct and interpret a confidence interval for a population mean find the sample size needed to estimate the population mean within a given margin of error Similar to confidence intervals about proportions from Section 9.1, we can also find confidence intervals about population means. Using the same general set-up, we should have something like this: point estimate ± margin of error What's our point estimate for the population mean?
If you recall, we discussed the distribution of in Chapter 8: The Central Limit Theorem Regardless of the distribution shape of the population, the sampling distribution of becomes approximately normal as the sample size n increases (conservatively n≥30). The Sampling Distribution of If a simple random sample of size n is drawn from a large population with mean μ and standard deviation σ, the sampling distribution of where Source: Wikipedia. The t table. Dependent t Test & Effect Size.