What is a Paired t Test? A Third type of a Two Sample t-Test is the Paired t Test. This test is used when the two populations are dependent of each other, so each data point from one distribution corresponds to a data point in the other distribution. When using a paired t test, the […]
What is Two Sample T Test? Two sample t test is a hypothesis test to study whether there is a statistically significant difference between the means of two populations. Where: μ1 is the mean of one population and μ2 is the mean of the other population of our interest. Assumptions of Two Sample T Tests Three […]
What is a t Test? In statistics, a t test is a hypothesis test in which the test statistic follows a Student’s t distribution if the null hypothesis is true. We apply a one sample t test when the population variance (σ) is unknown and we use the sample standard deviation (s) instead. A hypothesis […]
What is Central Limit Theorem? The Central Limit Theorem is one of the fundamental theorems of probability theory. It states a condition under which the mean of a large number of independent and identically-distributed random variables, each of which has a finite mean and variance, would be approximately normally distributed. Let us assume Y1, Y2 […]
What is Multi Vari Analysis? Multi Vari analysis is a graphic-driven method to analyze the effects of categorical inputs on a continuous output. It studies how the variation in the output changes across different inputs and helps us quantitatively determine the major source of variability in the output. Multi-Vari charts are used to visualize the […]
What is Process Capability? Process capability measures how well the process performs to meet given specified outcome. It indicates the conformance of a process to meet given requirements or specifications. Capability analysis helps to better understand the performance of the process with respect to meeting customer’s specifications and identify the process improvement opportunities. Process Capability […]
What is the Pareto Principle? The Pareto principle is an observation not a law. Named after Italian economist Vilfredo Pareto, this principle states that for a variety of situations, 80% of consequences come from 20% of the causes, thus the Pareto principle is also known as the 80/20 rule. The 80/20 rule basically reminds us that […]
What is Variable Gage R&R? Whenever something is measured repeatedly or by different people or processes, the results of the measurements will vary. Variation comes from two primary sources: We can use a variable Gage R&R to conduct a measurement system analysis to determine what portion of the variability comes from the parts and what […]
Use Minitab to Implement an Attribute MSA Data File: “Attribute MSA” tab in “Sample Data.xlsx” (an example in the AIAG MSA Reference Manual, 3rd Edition). Steps in Minitab to run an attribute MSA: Step 1: Reorganize the original data into four new columns (i.e., Appraiser, Assessed Result, Part, and Reference). Click Data → Stack → […]
What is a Box Plot? A box plot is a graphical method to summarize a data set by visualizing the minimum value, 25th percentile, median, 75th percentile, the maximum value, and potential outliers. A percentile is the value below which a certain percentage of data fall. For example, if 75% of the observations have values […]
What is a Histogram? A histogram is a graphical tool to present the distribution of the data. The X axis represents the possible values of the variable and the Y axis represents the frequency of the value occurring. This graphical summary consists of adjacent rectangles erected over intervals with heights equal to the frequency density of […]
What is a Scatter Plot? A scatter plot is a diagram to present the relationship between two variables of a data set. A scatter plot consists of a set of data points. On the scatter plot, a single observation is presented by a data point with its horizontal position equal to the value of one […]
What is Mood’s Median Test? Mood’s median test is a statistical test to compare the medians of two or more populations. Null Hypothesis (H0): η1 = … = ηk Alternative Hypothesis (Ha): At least one of the medians is different from the others. The symbol k is the number of groups of our interest and […]
Kruskal–Wallis One-Way Analysis of Variance The Kruskal Wallis one-way analysis of variance is a statistical hypothesis test to compare the medians among more than two groups. Null Hypothesis (H0): η1 = η2 = … = ηk Alternative Hypothesis (Ha): at least one of the medians is different from others. Where: ηi is the median of […]
What is the Mann Whitney Test? The Mann Whitney test (also called Mann–Whitney U test or Wilcoxon rank-sum test) is a statistical hypothesis test to compare the medians of two populations that are not normally distributed. In a non-normal distribution, the median is the better representation of the center of the distribution. Null Hypothesis (H0): […]
What is One Way ANOVA? One way Analysis of Variance is a statistical method to compare means of two or more populations. It is a generalized form of the two sample t-test since a two sample t-test compares two population means and one way ANOVA compares k population means where k ≥ 2. Null Hypothesis (H0): μ_1=μ_2=…=μ_k […]
Paired t Test The third type of a Two Sample t-Test is the Paired t Test. This test is used when the two populations are dependent of each other, so each data point from one distribution corresponds to a data point in the other distribution. When using a paired t test, the test statistic is calculated […]
Two Sample t Test Two sample t test is a hypothesis test to study whether there is a statistically significant difference between the means of two populations. Null Hypothesis (H0): μ1 = μ2 Alternative Hypothesis (Ha): μ1 ≠ μ2 Where: μ1 is the mean of one population and μ2 is the mean of the other […]
What is a One sample t Test? A One sample t test is a hypothesis test to study whether there is a statistically significant difference between a population mean and a specified value. Null Hypothesis (H0): μ = μ0 Alternative Hypothesis (Ha): μ ≠ μ0 Where: μ is the mean of a population of our […]
Central Limit Theorem The Central Limit Theorem is one of the fundamental theorems of probability theory. It states a condition under which the mean of a large number of independent and identically-distributed random variables, each of which has a finite mean and variance, would be approximately normally distributed. Let us assume Y1, Y2 . . […]
