**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Student's t-test

Summary

A t-test is a type of statistical analysis used to compare the averages of two groups and determine if the differences between them are more likely to arise from random chance. It is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known (typically, the scaling term is unknown and therefore a nuisance parameter). When the scaling term is estimated based on the data, the test statistic—under certain conditions—follows a Student's t distribution. The t-test's most common application is to test whether the means of two populations are different.
History
The term "t-statistic" is abbreviated from "hypothesis test statistic". In statistics, the t-distribution was first derived as a posterior distribution in 1876 by Helmert and Lüroth. The t-distribution also appea

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related publications (17)

Loading

Loading

Loading

Related people (1)

Related units (1)

Related courses (33)

BIO-449: Understanding statistics and experimental design

This course is neither an introduction to the mathematics of statistics nor an introduction to a statistics program such as R. The aim of the course is to understand statistics from its experimental design and to avoid common pitfalls of statistical reasoning. There is space to discuss ongoing work.

MICRO-110: Design of experiments

This course provides an introduction to experimental statistics, including use of population statistics to characterize experimental results, use of comparison statistics and hypothesis testing to evaluate validity of experiments, and design, application, and analysis of multifactorial experiments

MATH-233: Probability and statistics

The course gives an introduction to probability and statistics for physicists.

Related concepts (25)

Statistics

Statistics (from German: Statistik, "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and present

Effect size

In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a

Analysis of variance

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among m

This thesis focuses on the analysis of the trajectories of a mobile agent. It presents different techniques to acquire a quantitative measure of the difference between two trajectories or two trajectory datasets. A novel approach is presented here, based on the Point Distribution Model (PDM). This model was developed by computer vision scientists to compare deformable shapes. This thesis presents the mathematical reformulation of the PDM to fit spatiotemporal data, such as trajectory information. The behavior of a mobile agent can rarely be represented by a unique trajectory, as its stochastic component will not be taken into account. Thus, the PDM focuses on the comparison of trajectory datasets. If the difference between datasets is greater than the variation within each dataset, it will be observable in the first few dimensions of the PDM. Moreover, this difference can also be quantified using the inter-cluster distance defined in this thesis. The resulting measure is much more efficient than visual comparisons of trajectories, as are often made in existing scientific literature. This thesis also compares the PDM with standard techniques, such as statistical tests, Hidden Markov Models (HMMs) or Correlated Random Walk (CRW) models. As a PDM is a linear transformation of space, it is much simpler to comprehend. Moreover, spatial representations of the deformation modes can easily be constructed in order to make the model more intuitive. This thesis also presents the limits of the PDM and offers other solutions when it is not adequate. From the different results obtained, it can be pointed out that no universal solution exists for the analysis of trajectories, however, solutions were found and described for all of the problems presented in this thesis. As the PDM requires that all the trajectories consist of the same number of points, techniques of resampling were studied. The main solution was developed for trajectories generated on a track, such as the trajectory of a car on a road or the trajectory of a pedestrian in a hallway. The different resampling techniques presented in this thesis provide solutions to all the experimental setups studied, and can easily be modified to fit other scenarios. It is however very important to understand how they work and to tune their parameters according to the characteristics of the experimental setup. The main principle of this thesis is that analysis techniques and data representations must be appropriately selected with respect to the fundamental goal. Even a simple tool such as the t-test can occasionally be sufficient to measure trajectory differences. However, if no dissimilarity can be observed, it does not necessarily mean that the trajectories are equal – it merely indicates that the analyzed feature is similar. Alternatively, other more complex methods could be used to highlight differences. Ultimately, two trajectories are equal if and only if they consist of the exact same sequence of points. Otherwise, a difference can always be found. Thus, it is important to know which trajectory features have to be compared. Finally, the diverse techniques used in this thesis offer a complete methodology to analyze trajectories.

Mathews Jacob, Pascal Steiner, Michaël Unser

Background: For the investigation of the molecular mechanisms involved in neurite outgrowth and differentiation, accurate and reproducible segmentation and quantification of neuronal processes are a prerequisite. To facilitate this task, we developed a semiautomatic neurite tracing technique. This article describes the design and validation of the technique. Methods: The technique was compared to fully manual delineation. Four observers repeatedly traced selected neurites in 20 fluorescence microscopy images of cells in culture, using both methods. Accuracy and reproducibility were determined by comparing the tracings to high-resolution reference tracings, using two error measures. Labor intensiveness was measured in numbers of mouse clicks required. The significance of the results was determined by a Student t-test and by analysis of variance. Results: Both methods slightly underestimated the true neurite length, but the differences were not unanimously significant. The average deviation from the true neurite centerline was a factor 2.6 smaller with the developed technique compared to fully manual tracing. Intraobserver variability in the respective measures was reduced by a factor 6.0 and 23.2. Interobserver variability was reduced by a factor 2.4 and 8.8, respectively, and labor intensiveness by a factor 3.3. Conclusions: Providing similar accuracy in measuring neurite length, significantly improved accuracy in neurite centerline extraction, and significantly improved reproducibility and reduced labor intensiveness, the developed technique may replace fully manual tracing methods.

Kamiar Aminian, Farzin Dadashi, Vincent Gremeaux, Mahdi Hamidi Rad, Fabien Massé

Swimming coaches provide regular timed and technical feedback to swimmers and guide them efficiently in training sessions. Due to the complexity of swimmers' performance, which is not visible in qualitative observation, quantitative and objective performance evaluation can better assist the coach in this regard. Inertial measurement units (IMUs) are used in swimming for objective performance evaluation. In this study, we propose a new performance evaluation feedback (SmartSwim) using IMU and investigate its effects on the swimmer's weekly progress. Measurements were conducted each week with 15 competitive swimmers for 10 weeks using a Sacrum IMU. The SmartSwim report included a comprehensive representation of performance based on goal metrics of each phase extracted from the IMU signals. The swimmers were divided into two groups: the experimental and control groups. The SmartSwim report for each swimmer in the experimental group was given to the coach, who used it to adjust the training accordingly. The results showed that the experimental group outperformed the control group when comparing each swimmer, each session and the whole sessions. At the level of each individual, more members of the experimental group showed significant downward trend of average lap time (Mann-Kendall trend test, 95% confidence level). While comparing the sessions, the experimental group showed significantly lower lap time than the control group from the sixth session onwards (p-value < 0.05 from t-test). Considering all sessions, the experimental group showed significantly higher progress, lower average lap time, and more consistent records (Mann-Whitney U test at 95% confidence level) than the control group. This study demonstrated that SmartSwim can assist coaching by quantitatively assessing swimmers' performance, leading to more efficient training.

Related lectures (87)