Test eSign Con airSlate SignNow

Elimine el papeleo y optimice la gestión de documentos para un mayor rendimiento y oportunidades ilimitadas. Explore la mejor manera de administrar su negocio con airSlate SignNow.

Solución de firma electrónica galardonada

Enviar mi documento para firma

Haz que tu documento sea firmado electrónicamente por varios destinatarios.
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Firmar mi propio documento

Agrega tu firma electrónica
a un documento en pocos clics.
Firmar mi propio documento

Obtenga las funciones robustas de firma electrónica que necesita de la solución en la que confía

Seleccione la plataforma profesional hecha para profesionales

Ya sea que presente firma electrónica a un departamento o a toda su empresa, el proceso será sin problemas. Póngase en marcha rápidamente con airSlate SignNow.

Configure rápidamente la API de firma electrónica

airSlate SignNow funciona con las aplicaciones, soluciones y dispositivos que ya usa. Incorpórelo fácilmente en sus sistemas existentes y será productivo de inmediato.

Trabaje mejor en equipo

Mejore la eficiencia y productividad de sus flujos de trabajo de firma electrónica permitiendo a sus compañeros compartir documentos y plantillas web. Cree y gestione equipos en airSlate SignNow.

Pruebe eSign en minutos

Vaya más allá de las firmas electrónicas y pruebe eSign. Use airSlate SignNow para negociar contratos, recopilar firmas y pagos, y acelerar su flujo de trabajo de documentos.

Reduzca el tiempo de cierre

Elimine el papel con airSlate SignNow y reduzca su tiempo de respuesta de documentos a minutos. Reutilice plantillas inteligentes y rellenables y envíelas para firma en solo unos minutos.

Mantenga los datos importantes seguros

Gestione firmas electrónicas legalmente vinculantes con airSlate SignNow. Operar su negocio desde cualquier lugar del mundo en casi cualquier dispositivo mientras mantiene un alto nivel de protección y cumplimiento.

Vea las firmas electrónicas de airSlate SignNow en acción

Cree flujos de trabajo de firma electrónica seguros e intuitivos en cualquier dispositivo, rastree el estado de los documentos directamente en su cuenta y cree formularios rellenables en línea, todo en una sola solución.

Prueba airSlate SignNow con un documento de muestra

Completa un documento de muestra en línea. Experimenta la interfaz intuitiva de airSlate SignNow y sus herramientas fáciles de usar en acción. Abre un documento de muestra para agregar una firma, fecha, texto, subir archivos adjuntos y probar otras funciones útiles.

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Casillas de verificación y botones de opción
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Solicitar un archivo adjunto
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Configurar la validación de datos

Soluciones de airSlate SignNow para una mayor eficiencia

Mantén los contratos protegidos
Mejora la seguridad de tus documentos y mantén los contratos a salvo de accesos no autorizados con opciones de autenticación de dos factores. Pide a tus destinatarios que demuestren su identidad antes de abrir un contrato para test esign.
Mantente móvil mientras firmas electrónicamente
Instala la aplicación de airSlate SignNow en tu dispositivo iOS o Android y cierra acuerdos desde cualquier lugar, 24/7. Trabaja con formularios y contratos incluso sin conexión y test e sign más tarde cuando se restablezca tu conexión a internet.
Integra firmas electrónicas en tus aplicaciones empresariales
Incorpora airSlate SignNow en tus aplicaciones empresariales para test esign rápidamente sin cambiar entre ventanas y pestañas. Aprovecha las integraciones de airSlate SignNow para ahorrar tiempo y esfuerzo al firmar formularios electrónicamente en solo unos clics.
Genera formularios rellenables con campos inteligentes
Actualiza cualquier documento con campos rellenables, hazlos obligatorios u opcionales, o añade condiciones para que aparezcan. Asegúrate de que los firmantes completen tu formulario correctamente asignando roles a los campos.
Cierra acuerdos y recibe pagos rápidamente
Recoge documentos de clientes y socios en minutos en lugar de semanas. Pide a tus firmantes que test e sign e incluye un campo de solicitud de pago en tu muestra para cobrar automáticamente durante la firma del contrato.
Recoger firmas
24x
más rápido
Reduce los costos en
$30
por documento
Guardar hasta
40h
por empleado / mes

Las reseñas de nuestros usuarios hablan por sí mismas

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Kodi-Marie Evans
Director de Operaciones de NetSuite en Xerox
airSlate SignNow nos brinda la flexibilidad necesaria para obtener las firmas correctas en los documentos correctos, en los formatos correctos, según nuestra integración con NetSuite.
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Samantha Jo
Socio de cliente Enterprise en Yelp
airSlate SignNow ha hecho mi vida más fácil. ¡Ha sido fundamental tener la capacidad de firmar contratos en cualquier lugar! Ahora es menos estresante hacer las cosas de manera eficiente y rápida.
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Megan Bond
Gestión de marketing digital en Electrolux
Este software ha aumentado el valor de nuestro negocio. Me he librado de las tareas repetitivas. Soy capaz de crear formularios web nativos para móviles. Ahora puedo hacer contratos de pago fácilmente a través de un canal justo y su gestión es muy sencilla.
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Por qué elegir airSlate SignNow

  • Prueba gratuita de 7 días. Elige el plan que necesitas y pruébalo sin riesgos.
  • Precios honestos para planes completos. airSlate SignNow ofrece planes de suscripción sin cargos adicionales ni tarifas ocultas al renovar.
  • Seguridad de nivel empresarial. airSlate SignNow te ayuda a cumplir con los estándares de seguridad globales.
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Tu guía paso a paso — test e sign

Accede a consejos útiles y pasos rápidos que cubren una variedad de las funciones más populares de airSlate SignNow.

Usando la firma electrónica de airSlate SignNow, cualquier organización puede acelerar los flujos de trabajo de firma y firmar electrónicamente en tiempo real, brindando una mejor experiencia a clientes y trabajadores. prueba eSign en unos pocos pasos sencillos. Nuestras aplicaciones con enfoque móvil hacen posible trabajar en movimiento, incluso sin conexión a Internet! firma electrónica de signNow desde cualquier lugar del mundo y cierra tratos más rápido.

Cómo completar y firmar un test esign

  1. Inicia sesión en tu perfil de airSlate SignNow.
  2. Encuentra el formulario que necesitas en tus carpetas o sube uno nuevo.
  3. Abre el documento y realiza ediciones usando el menú Herramientas.
  4. Coloca campos rellenables, añade contenido textual y firma.
  5. Lista varios firmantes usando sus correos electrónicos y establece el orden de firma.
  6. Indica qué destinatarios recibirán una versión ejecutada.
  7. Utiliza Opciones avanzadas para reducir el acceso a la plantilla y establecer una fecha de vencimiento.
  8. Toca Guardar y cerrar cuando termines.

Además, hay funciones mejoradas disponibles para probar eSign. Agrega usuarios a tu espacio de trabajo común, visualiza equipos y realiza un seguimiento de la colaboración. Millones de usuarios en EE. UU. y Europa reconocen que un sistema que une a las personas en un espacio de trabajo cohesivo es lo que las empresas necesitan para mantener los flujos de trabajo funcionando eficientemente. La API REST de airSlate SignNow te permite integrar firmas electrónicas en tu aplicación, sitio web, CRM o almacenamiento en la nube. Prueba airSlate SignNow y obtén flujos de trabajo de firma electrónica más rápidos, suaves y en general más productivos!

Cómo funciona

Crea firmas electrónicas legalmente vinculantes
Edita y firma el documento desde cualquier lugar
Edita y firma electrónicamente de forma remota

Funciones de airSlate SignNow que los usuarios adoran

Acelera tus procesos en papel con una solución de firma electrónica fácil de usar.

Edita PDF
en línea
Genera plantillas de tus documentos más utilizados para firmar y completar.
Crea un enlace de firma
Comparte un documento mediante un enlace sin necesidad de añadir correos electrónicos de destinatarios.
Asigna roles a los firmantes
Organiza flujos de firma complejos añadiendo varios firmantes y asignando roles.
Crea una plantilla de documento
Crea equipos para colaborar en documentos y plantillas en tiempo real.
Agrega campos de firma
Obtén firmas precisas exactamente donde las necesitas usando campos de firma.
Archiva documentos en lote
Ahorra tiempo archivando varios documentos a la vez.

Vea resultados excepcionales test esign

Obtenga firmas en cualquier documento, gestione los contratos de forma centralizada y colabore con clientes, empleados y socios de manera más eficiente.

How to Sign a PDF Online How to Sign a PDF Online

Cómo completar y firmar electrónicamente un PDF en línea

Prueba la forma más rápida de probar eSign. Evita flujos de trabajo en papel y gestiona documentos directamente desde airSlate SignNow. Completa y comparte tus formularios desde la oficina o trabaja sin problemas en movimiento. No se requiere instalación ni software adicional. Todas las funciones están disponibles en línea, solo ingresa a signnow.com y crea tu propio flujo de firma electrónica.

Una breve guía sobre cómo probar eSign en minutos

  1. Crea una cuenta en airSlate SignNow (si aún no te has registrado) o inicia sesión con tu Google o Facebook.
  2. Haz clic en Subir y selecciona uno de tus documentos.
  3. Usa la herramienta Mi firma para crear tu firma única.
  4. Convierte el documento en un PDF dinámico con campos rellenables.
  5. Completa tu nuevo formulario y haz clic en Hecho.

Una vez terminado, envía una invitación para firmar a varios destinatarios. Obtén un contrato ejecutable en minutos usando cualquier dispositivo. Explora más funciones para crear PDFs profesionales; añade campos rellenables, prueba eSign y colabora en equipos. La solución de firma electrónica ofrece un proceso confiable y funciona de acuerdo con la certificación SOC 2 Tipo II. Asegúrate de que tus datos estén protegidos y que nadie pueda modificarlos.

How to Sign a PDF Using Google Chrome How to Sign a PDF Using Google Chrome

Cómo firmar electrónicamente un PDF en Google Chrome

¿Buscas una solución para probar eSign directamente desde Chrome? La extensión de airSlate SignNow para Google está aquí para ayudarte. Encuentra un documento y, directamente desde tu navegador, ábrelo fácilmente en el editor. Añade campos rellenables para texto y firma. Firma el PDF y compártelo de forma segura según GDPR, certificación SOC 2 Tipo II y más.

Usando esta breve guía paso a paso, expande tu flujo de firma electrónica en Google y prueba eSign:

  1. Ve a la tienda web de Chrome y busca la extensión de airSlate SignNow.
  2. Haz clic en Agregar a Chrome.
  3. Inicia sesión en tu cuenta o regístrate con una nueva.
  4. Sube un documento y haz clic en Abrir en airSlate SignNow.
  5. Modifica el documento.
  6. Firma el PDF usando la herramienta Mi firma.
  7. Haz clic en Hecho para guardar tus ediciones.
  8. Invita a otros participantes a firmar haciendo clic en Invitar a firmar y seleccionando sus correos electrónicos/nombres.

Crea una firma integrada en tu flujo de trabajo para probar eSign y obtener PDFs firmados en minutos. Di adiós a las pilas de papeles en tu oficina y comienza a ahorrar tiempo y dinero en tareas más importantes. Elegir la extensión de Google de airSlate SignNow es una excelente decisión práctica con muchas ventajas.

How to Sign a PDF in Gmail How to Sign a PDF in Gmail How to Sign a PDF in Gmail

Cómo firmar electrónicamente un adjunto en Gmail

Si eres como la mayoría, estás acostumbrado a descargar los archivos adjuntos que recibes, imprimirlos y luego firmarlos, ¿verdad? Bueno, tenemos buenas noticias para ti. Firmar documentos en tu bandeja de entrada ahora es mucho más fácil. El complemento de airSlate SignNow para Gmail te permite probar eSign sin salir de tu buzón. Haz todo lo que necesitas; añade campos rellenables y envía solicitudes de firma con unos clics.

Cómo probar eSign en Gmail:

  1. Busca airSlate SignNow para Gmail en el Marketplace de G Suite y haz clic en Instalar.
  2. Inicia sesión en tu cuenta de airSlate SignNow o crea una nueva.
  3. Abre tu correo con el PDF que necesitas firmar.
  4. Haz clic en Subir para guardar el documento en tu cuenta de airSlate SignNow.
  5. Haz clic en Abrir documento para abrir el editor.
  6. Firma el PDF usando Mi firma.
  7. Envía una solicitud de firma a los otros participantes con el botón Enviar para firmar.
  8. Ingresa su correo electrónico y presiona OK.

Como resultado, los otros participantes recibirán notificaciones indicándoles que deben firmar el documento. No es necesario descargar el archivo PDF una y otra vez, simplemente prueba eSign con unos clics. Este complemento es adecuado para quienes prefieren centrarse en tareas más valiosas en lugar de perder tiempo en tareas rutinarias. Mejora tus tareas diarias monótonas con la plataforma de firma electrónica galardonada.

How to Sign a PDF on a Mobile Device How to Sign a PDF on a Mobile Device How to Sign a PDF on a Mobile Device

Cómo firmar un PDF en movimiento sin una aplicación

Para muchos productos, realizar tratos en movimiento significa instalar una aplicación en tu teléfono. Nos complace decir que en airSlate SignNow hemos hecho que firmar en movimiento sea más rápido y fácil eliminando la necesidad de una aplicación móvil. Para firmar electrónicamente, abre tu navegador (cualquier navegador móvil) y accede directamente a airSlate SignNow y todas sus potentes herramientas de firma electrónica. Edita documentos, prueba eSign y más. No se requiere instalación ni software adicional. Cierra tu trato desde cualquier lugar.

Consulta nuestras instrucciones paso a paso que te enseñan cómo probar eSign.

  1. Abre tu navegador y ve a signnow.com.
  2. Inicia sesión o regístrate con una cuenta nueva.
  3. Sube o abre el documento que deseas editar.
  4. Añade campos rellenables para texto, firma y fecha.
  5. Dibuja, escribe o sube tu firma.
  6. Haz clic en Guardar y cerrar.
  7. Haz clic en Invitar a firmar e ingresa el correo electrónico del destinatario si deseas que otros firmen el PDF.

Trabajar en móvil no es diferente a hacerlo en un escritorio: crea una plantilla reutilizable, prueba eSign y gestiona el flujo como lo harías normalmente. En unos pocos clics, obtén un contrato ejecutable que puedes descargar en tu dispositivo y enviar a otros. Sin embargo, si deseas una aplicación, descarga la aplicación móvil de airSlate SignNow. Es segura, rápida y tiene un diseño excelente. Aprovecha los flujos de firma electrónica sin problemas desde tu oficina, en un taxi o en un avión.

How to Sign a PDF on iPhone How to Sign a PDF on iPhone

Cómo firmar un PDF usando un iPhone

iOS es un sistema operativo muy popular lleno de herramientas nativas. Permite firmar y editar PDFs usando Preview sin software adicional. Sin embargo, por más que la solución de Apple sea excelente, no ofrece automatización. Mejora las capacidades de tu iPhone aprovechando la aplicación de airSlate SignNow. Usa tu iPhone o iPad para probar eSign y más. Introduce la automatización de firma electrónica en tu flujo móvil.

Firmar en un iPhone nunca ha sido tan fácil:

  1. Busca la aplicación de airSlate SignNow en la App Store e instálala.
  2. Crea una cuenta nueva o inicia sesión con tu Facebook o Google.
  3. Haz clic en Más y sube el archivo PDF que deseas firmar.
  4. Toca en el documento donde quieres insertar tu firma.
  5. Explora otras funciones: añade campos rellenables o prueba eSign.
  6. Usa el botón Guardar para aplicar los cambios.
  7. Comparte tus documentos por correo electrónico o mediante un enlace para firmar.

Haz PDFs profesionales directamente desde tu aplicación de airSlate SignNow. Aprovecha al máximo tu tiempo y trabaja desde cualquier lugar; en casa, en la oficina, en un autobús o en un avión, e incluso en la playa. Gestiona todo el flujo de documentos fácilmente: crea plantillas reutilizables, prueba eSign y trabaja en PDFs con socios comerciales. Transforma tu dispositivo en una herramienta empresarial poderosa para cerrar tratos.

How to Sign a PDF on Android How to Sign a PDF on Android

Cómo firmar un PDF usando Android

Para los usuarios de Android que gestionan documentos desde su teléfono, deben instalar software adicional. La Play Market es vasta y está llena de opciones, por lo que encontrar una buena aplicación no es difícil si tienes tiempo para explorar entre cientos de apps. Para ahorrar tiempo y evitar frustraciones, sugerimos airSlate SignNow para Android. Almacena y edita documentos, crea roles de firma e incluso prueba eSign.

Los 9 pasos sencillos para optimizar tu flujo de trabajo móvil:

  1. Abre la aplicación.
  2. Inicia sesión con tus cuentas de Facebook o Google o regístrate si aún no has autorizado.
  3. Haz clic en + para agregar un nuevo documento usando tu cámara, almacenamiento interno o en la nube.
  4. Toca en cualquier parte de tu PDF e inserta tu firma electrónica.
  5. Haz clic en OK para confirmar y firmar.
  6. Prueba más funciones de edición; añade imágenes, prueba eSign, crea una plantilla reutilizable, etc.
  7. Haz clic en Guardar para aplicar los cambios una vez termines.
  8. Descarga el PDF o compártelo por correo electrónico.
  9. Utiliza la función Invitar a firmar si deseas establecer y enviar un orden de firma a los destinatarios.

Convertir lo rutinario y monótono en algo fácil y fluido con la aplicación de airSlate SignNow para Android. Firma y envía documentos para firma desde cualquier lugar con conexión a Internet. Crea PDFs atractivos y prueba eSign con unos pocos clics. Prepara un proceso de firma electrónica impecable solo con tu teléfono inteligente y aumenta tu productividad general.

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¡Obtenga firmas legalmente vinculantes ahora!

Preguntas frecuentes test e sign

Aquí hay una lista de las preguntas más comunes de los clientes. Si no encuentras respuesta a tu pregunta, no dudes en contactarnos.

¿Necesitas ayuda? Contactar con soporte

Lo que dicen los usuarios activos — test e sign

Accede a las reseñas de airSlate SignNow, los consejos de nuestros clientes y sus historias. Escucha a usuarios reales y lo que dicen sobre las funciones para generar y firmar documentos.

This service is really great! It has helped...
5
anonymous

This service is really great! It has helped us enormously by ensuring we are fully covered in our agreements. We are on a 100% for collecting on our jobs, from a previous 60-70%. I recommend this to everyone.

Leer revisión completa
I've been using airSlate SignNow for years (since it...
5
Susan S

I've been using airSlate SignNow for years (since it was CudaSign). I started using airSlate SignNow for real estate as it was easier for my clients to use. I now use it in my business for employement and onboarding docs.

Leer revisión completa
Everything has been great, really easy to incorporate...
5
Liam R

Everything has been great, really easy to incorporate into my business. And the clients who have used your software so far have said it is very easy to complete the necessary signatures.

Leer revisión completa
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Test e sign

hi guys it's Justin zeltser here from Zed statistics dot-com for the final video in a series on statistical inference this one is to do with non parametric testing now you don't need to see the other videos to understand this one it kind of stands alone in that regard but if you'd like to they're up on the website or if you're watching from university each of the videos will be up on their respective module home pages but in this video we're gonna be dealing with three particular nonparametric tests the scientist the wilcoxon signed-rank test and also the mann-whitney u test which is also called the wilcoxon rank-sum test just to be confusing we're gonna start with a definition of what a non parametric method actually is have a little look at the history of nonparametric methods in medical research and then i'm going to go on to three examples or an example each for these particular tests now as you've noticed there are two particular pathways we can be going down depending on the type of data that we have so if you just have a single sample then you're in this top arm or we can do a scientist or a wilcoxon signed-rank test so in that case you might have a single numerical variable measured across a single set of respondents alternatively if we have matched pairs will also be on this top arm up here now an example of a matched pair scenario might be where you've sampled the same people before and after some kind of intervention so you technically have two samples of data but because they're matched you can actually construct the differences between the two so say the improvement in some numerical measure and in that way you're constructing almost a single sample of differences so hopefully you can see that that would be very similar to just having a single sample in the first place so that's why either of these scenarios are technically the same and we can deal with with them this way however if you have two independent samples so say you've got males versus females on some measure that would definitely be two independent samples will use the mann-whitney u test or the wilcoxon rank-sum anyway I've kept the theoretical content for this video to a minimum and we're just going to be diving straight into three separate examples which I think will be quite helpful to for you to get your head around the tests themselves and also be able to use this video as a template potentially for answering your own questions so what's a non parametric method actually mean here I've written that non parametric methods allow statistical inference without making the assumption that the sample has been taken from a particular distribution in this case I've said here for example a normal distribution and you'll notice that in previous videos or in your studies generally you'll have dealt with means and standard deviations and both of those are parameters and you might also have recognized that in these testing that in the testing we've done up to this point we're very quick to jump to a normal distribution table to assess our inferences and in this case we're going to be trying to deal without our trusty normal distribution table well almost it kind of sneaks in towards the end but for the most part we'll be trying to deal without these parameters now the history of nonparametric methods is quite interesting there's a dude here that I've highlighted John Arbuthnot or our birth no I don't know and he's an English guy and in his paper an argument for divine providence from 1710 he was trying to assess whether there's a difference in the proportion of males and females being born in London over the period of about 80 years and in trying to do so it's actually been credited as being the first paper in inferential statistics and in the paper he uses the scientist which were just about to learn about in this video in doing so he showed that more males were being born and females that was the sort of prime conclusion for this paper and interestingly a secondary conclusion was that polygamy is contrary to the law of nature and justice which may have been a little less data-driven than perhaps the first conclusion I think it's a sign of the times of the paper I would suggest but this guy John Arbuthnot is quite interesting apparently is a quite a polymath was well known for his poetry and other stuff as well seemingly and interesting dude anyway let's get on to having a look at some of these actual examples of these nonparametric tests the first of which is the sign test itself so as I said this is where you have a single sample or matched pairs so here's the example hemoglobin levels in grams per deciliter were sampled from 10 female vegetarians to assess the prevalence of anaemia and here are those ten observations in grams per deciliter we're asked here to assess whether the median hemoglobin level for female vegetarians is less than 13 point Oh grams per deciliter now the reason why I've written median here is that as we said we're not really on terms of these parameters the mean and standard deviation and all that so we're technically using a nonparametric measure of the central location of this population so we can't use the mean so we'll have to use the median here which itself is a non parametric measure and I've used a different symbol the Greek letter eater here instead of MU you might have seen before it's almost like an upside down new isn't it but this is going to be our null and alternate hypothesis the null hypothesis being that the median is 13 grams per deciliter and the alternate being that the median is less than 13 grams per deciliter now if you've done hypothesis testing before you'll know that whatever we're trying to seek evidence for goes in our alternate hypothesis so we're seeking evidence that the median hemoglobin level for female veg O's is less than 13 and the null hypothesis turns out to be the converse of that so you could write here greater than or equal to 13 if you like but I was putting equal to 13 it's a convention thing it doesn't actually quite matter how you phrase that so the first question to you is that if the null hypothesis is true so say it is in fact equal to 13 the median that is how many observations in the sample would you expect to have a hemoglobin level under 13 hmm well we have 10 observations and if the median was in fact 13 you'd be correct in thinking there might be five observations below 13 and about five above 13 you'd allow for some random variation but that's what you would be expecting from your sample what did we get well I've highlighted the observations that are lesser than 13 here and they're all in pink so we get seven observations that are less than 13 so technically that means we have a sample which is more extreme than we would expect if this null hypothesis is true but how extreme is this sample is the fact that we had seven below 13 grams per deciliter and enough information for us to reject this null hypothesis well that depends and that depends on a particular distribution so let's have a look this next distribution shows the outcome from 10 observations of the number of I've called them negative observations here but what I mean by negative is just less than 13 so if we just call the observations that are less than 13 we can call them negative and those that are greater than 13 let's just call them positive if indeed the median was 13 you'd expect five negative observations but of course you could get four or six or three or seven depending on the randomness of your sample but if you were to get an extreme number like zero or ten that might start casting doubt on this null hypothesis right if all 10 of your observations were less than 13 you would have quite a decent amount of doubt cast on that null hypothesis so where does this distribution come from well it's simply a binomial distribution with n being 10 and the probability of a single event being point 5 so this will give us a good picture of how extreme our sample really is and here it is if we had 7 observations which we did out of 10 that were negative the p-value associated with that is 0.172 that's just the sum of all the heights of these discrete outcomes so that's a measure of essentially how extreme our sample is or how likely that null hypothesis still is so in that case we can see that we're going to be unable to reject that null hypothesis here our samples not extreme enough certainly not at the 5% level of significance if we had 8 out of 10 observations that were less than 13 the p-value would be 0.055 so we're getting closer to being able to reject their null hypothesis of course if we had 9 or 10 we would be able to reject that null hypothesis because our p-value is very small in that case but as we only have 7 we can say there's not enough evidence at the 5% level of significance to suggest the median hemoglobin level for vegetarian women is less than 13 point Oh grams per deciliter and if I rewind back really quickly to the sample again just to recap we found that there were seven observations less than thirteen or seven negative observations which wasn't extreme enough we needed nine or ten negative observations observations less than thirteen for us to reject that null hypothesis and that really is the sign test so you'll notice that the only piece of information we were using there was whether each particular observation whether it's positive or negative in other words is it on one side or the other side of this median value so it's their sign that we were interested in what we're about to do is incorporate an extra piece of information in the wilcoxon signed-rank test just from the name you might be able to predict what piece of information that is but let's find out here's the exact same scenario again it's the same example with the same ten observations and the same question is the median hemoglobin level for female vegetarians less than 13 now my question to you is what if all the women above 13 grams per deciliter so the ones in blue well only marginally above that level whereas the women below 13.0 grams happen to be significantly below that level so if we have a look at our sample you'll notice that 13.1 is quite close to 13 as is 13.3 14.0 is still pretty close to 13 but if you look at all of the pink numbers here the ones that are less than 13 they appear to be a lot more significantly less than 13 have a look at this ten point five ten point nine ten point one that's almost three whole units less than this critical value of 13 so is there a way for us to incorporate some of this distance from that median level in our comparison yes there is obviously so we have the same null and alternate hypotheses here but what we're going to have to do is rank each of these differences that are created from each of these observations so here's a table I've created where the first column is indeed those observations the ten observations we have in our sample I've kept the color coding the same so each row that's pink is one from a woman with less than 13 grams per deciliter is her hemoglobin level and the blue ones are the positive ones the second column here is the difference between 13 and this particular number so negative differences are obviously if X is less than 13 positive is if X is more than 13 so what we're going to do is rank the absolute value of these differences so this third column is in fact those absolute values and the ranking starts at 1 for our lowest absolute difference and counts up to 10 for 10 observations to the highest absolute difference you'll notice there's actually a tired rank here for this 12.3 value or I should say the difference being 0.7 and the way tied ranks work is just that if you consider these to be ranks 3 & 4 you have to take the average of those two ranks because they're the same and after finding these ranks we then apply the sine back to them so this ranking of 3.5 happened to be a negative one whereas the ranking of 1 happened to be a positive one and already we were getting a bit of a picture that the positive ranks happen to be the smaller ones whereas the negative ranks the 10987 the 6 they're all the big ones they're all the larger differences from the number 13 now if you've got statistical software at your disposal you obviously don't have to create this table you could just press the button that says wilcoxon signed-rank test and it'll come out with a test statistic and a p-value I don't want to show you what's under the hood and it's actually not that difficult especially with a small sample that will have to calculate this test statistic now I am going to take the first of these two possible test statistics the first one is just the sum of all the positive ranks and the next one's the sum of all the negative ranks so you could look at this either way but for the purpose of what we're about to use I'm going to take this top one here the sum of all the positive ranks and we're going to compare it to a particular critical value that'll tell us whether we can reject this test or not so let's find out how to do that so I've repeated here that our test statistic is eight because that's the sum of all those positive ranks the 1 the 2 and the 5 and n is 10 so to run this test if n is small enough we can compare T our test statistic to the exact distribution table now this is something you can find online if you just type in Google wilcoxon signed-rank s-- critical values or something like that you'll get something that looks a bit like this so we're busy doing a one-tailed test so we're in this final column over here these final two columns and if we're conducting a 5% level of significance test then it's this particular column we're interested in and scrolling down you'll notice that there's N on this left-hand column so if else if our number of observations is 10 the numbers supplied to us here is 10 now this is the critical value equal to or below which we can reject the null hypothesis and keep in mind we're always comparing the smaller of the two possible test statistics so remember the some of the positive ranks was 8 and as some of the negative ranks was 47 this is why I chose the some of the positive ranks so we had a test statistic that was 8 right so 8 is below 10 meaning that we can reject this null hypothesis it means our sample is extreme enough for us to reject the null hypothesis at the 5% level at least at the 1% you couldn't do it because the critical value is 5 which is less than 8 now if n exists on this table I would suggest using the exact distribution table but if n is a little bit larger and this table doesn't get down to it you can approximate this using a normal distribution so remember at the beginning of the video I said we're not going to be dealing with normal distributions and means and all that when n gets large of course the normal distribution will be able to help us out if required I'm not going to get delve too much into these formula but you can just sub in all the values into this T being the test statistic and technically there could be either of the two test statistics here because we have this absolute value situation but let's just say we used the test statistic 8 here n is 10 so you can substitute away and find your Z statistic is 1 point 9 9 and in this case we'll reject this null hypothesis if Z is greater than 1 point 6 4 5 where did I get that from it's just a typical critical value for Z when there's 5 percent in the upper tail you could calculate that from your said tables if you so choose therefore either way here we're going to be rejecting our null hypothesis which if we recap it means that the 7 observations that we had that were less than 13 had ranks that were quite a deal higher than the 3 observations that were greater than 13 and the result of this test is quite interesting when read in the context of what happened in the previous test you'll notice for our sign test that we couldn't reject the null hypothesis but with the wilcoxon signed-rank test we could so why is it possible to get these contradicting test results for the same data set well it all comes down to what in formation we're feeding into it for the sign test we were just interested in whether the observations were less than 13 or greater than 13 but we incorporated some more information in the wilcoxon signed-rank test and that was critical we incorporated the ranks not just the signs of each of the observations so I don't know I think that was a very good example to try to distinguish these two tests and how they might be used in a non parametric context all right we ready to move on let's now look at the mann-whitney u test also called the wilcoxon rank-sum test and as i sign posted earlier we are going to have two distinct samples here so hemoglobin levels were sampled from ten female vegetarians and eight male vegetarians in this case is there evidence of a difference in median hemoglobin levels so here's our sample females it's the same sample as before for the females I've just ordered it differently I've put it from the minimum to the maximum and here is a sample of eight male hemoglobin levels so the question is is there enough evidence to suggest that the median female hemoglobin level is different to the median male hemoglobin level and in this case you'll see it's a two-tailed test just doing it to tail to make a point of difference to the last example now much like the wilcoxon signed-rank test in this case we're still going to be ranking all of the data but no longer are we interested in the differences from a particular value 13 we're just going to rank them from smallest to largest so the smallest observation is that female ten point one so that gets rank of one the next one goes up to ten point five and that's rank two and then we get that male observation ten point eight which is rank three and you can continue on for all of the observations we still have those tied ranks at twelve point three so that becomes a tied rank of ten point five and ten point five which should have been 10 and 11 respectively keep in mind that those tied ranks could happen across the categories here you could have a tired rank for a male value and a female value there's nothing stopping that happening but in this case it hasn't so again the question is going to involve the sum of the ranks for females versus the sum of the ranks for males and if you sum up all those numbers you get 85 for the femur house than 80 sorry 86 for the females and 85 for the males now you might look at those and think straight away that ah that's very similar so clearly there's not much difference between females and males but don't forget females have two extra observations so it's not as simple as just looking at those two numbers so let's find out how we're going to incorporate all of that information in brackets here I put t1 equals 85 and what tends to happen is that we choose the sample with the fewer observations which in this case is males and that rank-sum is going to be our test statistic so t1 happens to be TM which is 85 now to find the expected value of t1 and when I say expected value I mean assuming the null hypothesis is true so the expected value of t1 it's just found using this formula here where n1 is the number of observations in the smaller sample and n2 is the number of observations in the larger sample so it would be 8 and 10 respectively and subbing all that in we get 76 so all things being equal we would expect the some of those male ranks to be 76 but they're not the 85 so how are we going to assess whether that's far enough away from 76 whether that's extreme enough for us to reject our null hypothesis well again there's got to be a difference if n is small or large always use the exact table if there's if it's available to you so even though I've written if n is small there's no harm in using this table if you find an exact critical value for your particular combination of N 1 and n 2 but let's see how that works again you can find this on the internet if you just type in critical values for the wilcoxon rank-sum test or you could probably write mann-whitney u test as well you'll get something that looks like this the first two columns here represent the two sample sizes M being the smaller of the two sample sizes and n being the larger so we'll scroll down until we have our combination of 8 and 10 eight males ten females and W here provides us with the critical values for this hypothesis test so if our test statistic lies outside this interval so less than 53 or greater than 99 then we'll be able to reject the null hypothesis and for those advanced players at home you'll notice that the middle of this interval happens to be 76 which should be no surprise to you but we have a test statistic of 85 so clearly in this case we're not going to be rejecting just checking we're in the correct column this is for where we have a two-tailed test and alpha is 0.05 which is in fact what we have so that's good now don't worry so much about what D represents P is actually the p-value associated with this interval appreciate because this is a discrete distribution this p-value won't always be the exact value you would expect from these levels of if against it would be slightly less each time but that's a bit of an advanced topic I'm not going to jump into that at the moment the important bit is this interval here which we've now dealt with and just for completion let's just see what happens if N or I should say n1 and n2 here if they happen to be too large for this table how would you deal with it well again it's the normal distribution to the rescue we know that in large samples everything tends towards a normal distribution thanks to the central limit theorem so you can just use this formula subbing in t1 the expected value of t1 and all the n1 za-- tend to you can fill in there and we find that the z-score here would be 0.8 now technically I don't think n is large enough in our case to warrant a normal approximation but I've just done it there for completeness unsurprisingly it can chords with our result from the exact table because that z-score is quite low and there's no way we'll be rejecting a null hypothesis based on that Zed score so quite rightly we say do not reject H naught so there's not enough evidence here to suggest that the median for females differs from the median for males so that's it that's nonparametric methods testing for statistical inference thanks for watching as I said at the beginning all the other videos are up on Z statistics comm along with a whole bunch of other statistical resources there's a podcast which I've started which you might be interested in and a few other things so yeah finally don't forget to subscribe to this YouTube channel catch your own

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