{"id":378453,"date":"2022-05-06T11:00:53","date_gmt":"2022-05-06T09:00:53","guid":{"rendered":"https:\/\/www.scribbr.nl\/?p=378453"},"modified":"2022-09-14T18:28:29","modified_gmt":"2022-09-14T16:28:29","slug":"null-and-alternative-hypotheses","status":"publish","type":"post","link":"https:\/\/www.scribbr.com\/statistics\/null-and-alternative-hypotheses\/","title":{"rendered":"Null and Alternative Hypotheses | Definitions &#038; Examples"},"content":{"rendered":"<p>The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a <a href=_-11.html>statistical test<\/a>:<\/p>\n<ul>\n<li aria-level=\"1\"><strong>Null hypothesis (<em>H<\/em><\/strong><strong><sub>0<sub><\/sub><\/sub><\/strong><strong>): <\/strong>There\u2019s <strong>no effect<\/strong> in the <a href=_-12.html>population<\/a>.<\/li>\n<li aria-level=\"1\"><strong>Alternative hypothesis (<em>H<\/em><\/strong><strong><sub>a <\/sub><\/strong><strong>or <em>H<\/em><\/strong><strong><sub>1<\/sub><\/strong><strong>)<\/strong><strong>: <\/strong>There\u2019s an <strong>effect<\/strong> in the population.<\/li>\n<\/ul>\n<p>The effect is usually the effect of the <a href=index-2906.html#independent\">independent variable<\/a> on the<a href=index-2906.html#dependent\"> dependent variable<\/a>.<br \/>\n<!--more--><\/p>\n<h2 id=\"answering\">Answering your research question with hypotheses<\/h2>\n<p>The null and alternative hypotheses offer competing answers to your <a href=_-8.html>research question<\/a>. When the research question asks \u201cDoes the independent variable affect the dependent variable?\u201d:<\/p>\n<ul>\n<li>The null hypothesis (<em>H<\/em><sub>0<\/sub>) answers \u201cNo, there\u2019s no effect in the population.\u201d<\/li>\n<li>The alternative hypothesis (<em>H<\/em><sub>a<\/sub>) answers &#8220;Yes, there is an effect in the population.&#8221;<\/li>\n<\/ul>\n<p>The null and alternative are always claims about the population. That\u2019s because the goal of <a href=_-13.html>hypothesis testing<\/a> is to make <a href=_-14.html>inferences<\/a> about a population based on a <a href=_-15.html>sample<\/a>. Often, we infer whether there\u2019s an effect in the population by looking at differences between groups or relationships between variables in the sample. It&#8217;s critical for your research to <a href=_-16.html>write strong hypotheses<\/a>.<\/p>\n<p>You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.<\/p>\n<h2 id=\"definition\">What is a null hypothesis?<\/h2>\n<p>The null hypothesis is the claim that there\u2019s no effect in the population.<\/p>\n<p>If the sample provides enough evidence against the claim that there\u2019s no effect in the population (<em>p<\/em> \u2264 \u03b1), then we can <a href=index-2907.html#step-4-decide-whether-to-reject-or-fail-to-reject-your-null-hypothesis\">reject the null hypothesis<\/a>. Otherwise, we fail to reject the null hypothesis.<\/p>\n<p>Although \u201cfail to reject\u201d may sound awkward, it\u2019s the only wording that statisticians accept. Be careful not to say you \u201cprove\u201d or \u201caccept\u201d the null hypothesis.<\/p>\n<figure class=\"kb-textbox border-left blue\"><figcaption>Example: Population on trial<\/figcaption>Think of a statistical test as being like a legal trial. The population is accused of the \u201ccrime\u201d of having an effect, and the sample is the criminal evidence. In the United States and many other countries, a person accused of a crime is assumed to be innocent until proven guilty. Similarly, we start by assuming the population is \u201cinnocent\u201d of having an effect.<\/p>\n<p>In other words, the null hypothesis (i.e., that there is no effect) is assumed to be true until the sample provides enough evidence to reject it.<\/figure>\n<p>Null hypotheses often include phrases such as \u201cno effect,\u201d \u201cno difference,\u201d or \u201cno relationship.\u201d When written in mathematical terms, they always include an equality (usually =, but sometimes \u2265 or \u2264).<\/p>\n<p>You can never know with complete certainty whether there is an effect in the population. Some percentage of the time, your inference about the population will be incorrect. When you incorrectly reject the null hypothesis, it&#8217;s called a <a href=_-17.html>type I error<\/a>. When you incorrectly fail to reject it, it&#8217;s a type II error.<\/p>\n<h3 id=\"examples-null\">Examples of null hypotheses<\/h3>\n<p>The table below gives examples of <a href=_-8.html>research questions<\/a> and null hypotheses. There\u2019s always more than one way to answer a research question, but these null hypotheses can help you get started.<\/p>\n<table class=\"kb-table bordered vertical-borders\">\n<tbody>\n<tr>\n<td rowspan=\"2\"><strong>Research question<\/strong><\/td>\n<td colspan=\"2\"><strong><strong>Null hypothesis <\/strong>(<em>H<\/em><sub style=\"font-family: inherit;\">0<\/sub>)<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>General<\/strong><\/td>\n<td><strong>Test-specific<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Does tooth flossing affect the number of cavities?<\/td>\n<td>Tooth flossing has <strong>no effect<\/strong> on the number of cavities.<\/td>\n<td><strong><a href=_-18.html><em>t <\/em>test<\/a>:<\/strong><\/p>\n<p>The mean number of cavities per person does not differ between the flossing group (\u00b5<sub>1<\/sub>) and the non-flossing group (\u00b5<sub>2<\/sub>) in the population; \u00b5<sub>1<\/sub> = \u00b5<sub>2<\/sub>.<\/td>\n<\/tr>\n<tr>\n<td>Does the amount of text highlighted in the textbook affect exam scores?<\/td>\n<td>The amount of text highlighted in the textbook has <strong>no effect<\/strong> on exam scores.<\/td>\n<td><strong><a href=_-19.html>Linear regression<\/a>:<\/strong><\/p>\n<p>There is no relationship between the amount of text highlighted and exam scores in the population; \u03b2<sub>1<\/sub> = 0.<\/td>\n<\/tr>\n<tr>\n<td>Does daily meditation decrease the incidence of depression?<\/td>\n<td>Daily meditation <strong>does not decrease <\/strong>the incidence of depression.*<\/td>\n<td><strong>Two-proportions <em>z <\/em>test:<\/strong><\/p>\n<p>The proportion of people with depression in the daily-meditation group (<em>p<\/em><sub>1<\/sub>) is greater than or equal to the no-meditation group (<em>p<\/em><sub>2<\/sub>) in the population; <em>p<\/em><sub>1<\/sub> \u2265 <em>p<\/em><sub>2<\/sub>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><small>*Note that some researchers prefer to always write the null hypothesis in terms of \u201cno effect\u201d and \u201c=\u201d. It would be fine to say that daily meditation has <strong>no effect <\/strong>on the incidence of depression and <em>p<\/em><sub>1<\/sub> = <em>p<\/em><sub>2<\/sub>.<small><\/small><\/small><\/p>\n<h2 id=\"alternative\">What is an alternative hypothesis?<\/h2>\n<p>The alternative hypothesis (<em>H<\/em><sub>a<\/sub>) is the other answer to your <a href=_-8.html>research question<\/a>. It claims that there\u2019s an effect in the population.<\/p>\n<p>Often, your alternative hypothesis is the same as your research hypothesis. In other words, it\u2019s the claim that you expect or hope will be true.<\/p>\n<p>The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.<\/p>\n<figure class=\"kb-textbox border-left green\"><figcaption>Tip<\/figcaption>Be careful with your words when you <a href=index-2907.html#step-5-present-your-findings\">report the results of a statistical test<\/a> in a <a href=_-20.html>research paper<\/a> or <a href=_-21.html>thesis<\/a>. If you <a href=index-2907.html#step-4-decide-whether-to-reject-or-fail-to-reject-your-null-hypothesis\"><strong>reject<\/strong> the null hypothesis<\/a>, you can say that the alternative hypothesis is <strong>supported<\/strong>. On the other hand, if you<strong> fail to reject<\/strong> the null hypothesis, then you can say that the alternative hypothesis is <strong>not supported<\/strong>. Never say that you\u2019ve proven or disproven a hypothesis.<\/figure>\n<p>Alternative hypotheses often include phrases such as \u201can effect,\u201d \u201ca difference,\u201d or \u201ca relationship.\u201d When null hypotheses are written in mathematical terms, they always include an inequality (usually \u2260, but sometimes &lt; or &gt;). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.<\/p>\n<h3 id=\"examples-alternative\">Examples of alternative hypotheses<\/h3>\n<p>The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.<\/p>\n<table class=\"kb-table bordered vertical-borders\">\n<tbody>\n<tr>\n<td rowspan=\"2\"><strong>Research question<\/strong><\/td>\n<td colspan=\"2\"><strong>Alternative hypothesis (<em>H<\/em><sub>a<\/sub><\/strong><strong>)<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>General<\/strong><\/td>\n<td><strong>Test-specific<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Does tooth flossing affect the number of cavities?<\/td>\n<td>Tooth flossing has an<strong> effect<\/strong> on the number of cavities.<\/td>\n<td><strong><a href=_-18.html><em>t <\/em>test<\/a>:<\/strong><\/p>\n<p>The mean number of cavities per person differs between the flossing group (\u00b5<sub>1<\/sub>) and the non-flossing group (\u00b5<sub>2<\/sub>) in the population; \u00b5<sub>1<\/sub> \u2260 \u00b5<sub>2<\/sub>.<\/td>\n<\/tr>\n<tr>\n<td>Does the amount of text highlighted in a textbook affect exam scores?<\/td>\n<td>The amount of text highlighted in the textbook has an<strong> effect<\/strong> on exam scores.<\/td>\n<td><strong><a href=_-19.html>Linear regression<\/a>:<\/strong><\/p>\n<p>There is a relationship between the amount of text highlighted and exam scores in the population; \u03b2<sub>1<\/sub> \u2260 0.<\/td>\n<\/tr>\n<tr>\n<td>Does daily meditation decrease the incidence of depression?<\/td>\n<td>Daily meditation <strong>decreases <\/strong>the incidence of depression.<\/td>\n<td><strong>Two-proportions <em>z <\/em>test:<\/strong><\/p>\n<p>The proportion of people with depression in the daily-meditation group (<em>p<\/em><sub>1<\/sub>) is less than the no-meditation group (<em>p<\/em><sub>2<\/sub>) in the population; <em>p<\/em><sub>1<\/sub> &lt; <em>p<\/em><sub>2<\/sub>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"similarities-differences\">Similarities and differences between null and alternative hypotheses<\/h2>\n<p>Null and alternative hypotheses are similar in some ways:<\/p>\n<ul class=\"kb-checklist\">\n<li aria-level=\"1\">They\u2019re both answers to the research question.<\/li>\n<li aria-level=\"1\">They both make claims about the population.<\/li>\n<li aria-level=\"1\">They\u2019re both evaluated by statistical tests.<\/li>\n<\/ul>\n<p>However, there are important differences between the two types of hypotheses, summarized in the following table.<\/p>\n<table class=\"kb-table vertical-borders\">\n<tbody>\n<tr>\n<td><\/td>\n<td><strong>Null hypotheses (<em>H<\/em><sub style=\"font-family: inherit;\">0<\/sub><\/strong><strong>)<\/strong><\/td>\n<td><strong>Alternative hypotheses (<em>H<\/em><sub>a<\/sub><\/strong><strong>)<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Definition<\/strong><\/td>\n<td>A claim that there is <strong>no effect<\/strong> in the population.<\/td>\n<td>A claim that there is <strong>an effect<\/strong> in the population.<\/td>\n<\/tr>\n<tr>\n<td><strong>Also known as<\/strong><\/td>\n<td><em>H<\/em><sub style=\"font-family: inherit;\">0<\/sub><\/td>\n<td><em>H<\/em><sub>a<\/sub><\/p>\n<p><em>H<\/em><sub>1<\/sub><\/td>\n<\/tr>\n<tr>\n<td><strong>Typical phrases used<\/strong><\/td>\n<td>\n<ul>\n<li aria-level=\"1\">No effect<\/li>\n<li aria-level=\"1\">No difference<\/li>\n<li aria-level=\"1\">No relationship<\/li>\n<li aria-level=\"1\">No change<\/li>\n<li aria-level=\"1\">Does not increase<\/li>\n<li aria-level=\"1\">Does not decrease<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li aria-level=\"1\">An effect<\/li>\n<li aria-level=\"1\">A difference<\/li>\n<li aria-level=\"1\">A relationship<\/li>\n<li aria-level=\"1\">A change<\/li>\n<li aria-level=\"1\">Increases<\/li>\n<li aria-level=\"1\">Decreases<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td><strong>Symbols used<\/strong><\/td>\n<td>Equality symbol (=, \u2265, or \u2264)<\/td>\n<td>Inequality symbol (\u2260, &lt;, or &gt;)<\/td>\n<\/tr>\n<tr>\n<td><strong><em>p <\/em><\/strong><strong>\u2264 \u03b1<\/strong><\/td>\n<td>Rejected<\/td>\n<td>Supported<\/td>\n<\/tr>\n<tr>\n<td><strong><em>p <\/em><\/strong><strong>&gt; \u03b1<\/strong><\/td>\n<td>Failed to reject<\/td>\n<td>Not supported<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"how-to\">How to write null and alternative hypotheses<\/h2>\n<p>To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you\u2019re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.<\/p>\n<h3 id=\"general\">General template sentences<\/h3>\n<p>The only thing you need to know to use these general template sentences are your <a href=index-2906.html#dependent\">dependent<\/a> and <a href=index-2906.html#independent\">independent<\/a> variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:<\/p>\n<p>Does <span class=\"highlight-purple\">independent variable<\/span> affect <span class=\"highlight-blue\">dependent variable<\/span>?<\/p>\n<ul>\n<li aria-level=\"1\">Null hypothesis (<em>H<\/em><sub style=\"font-family: inherit;\">0<\/sub>): <span class=\"highlight-purple\">Independent variable<\/span> does not affect <span class=\"highlight-blue\">dependent variable.<\/span><\/li>\n<li aria-level=\"1\">Alternative hypothesis (<em>H<\/em><sub>a<\/sub>): <span class=\"highlight-purple\">Independent variable<\/span> affects <span class=\"highlight-blue\">dependent variable.<\/span><\/li>\n<\/ul>\n<h3 id=\"test-specific\">Test-specific template sentences<\/h3>\n<p>Once you know the <a href=_-11.html>statistical test<\/a> you\u2019ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.<\/p>\n<table class=\"kb-table bordered vertical-borders\">\n<tbody>\n<tr>\n<td><strong>Statistical test<\/strong><\/td>\n<td><strong><strong>Null hypothesis <\/strong>(<em>H<\/em><sub style=\"font-family: inherit;\">0<\/sub>)<\/strong><\/td>\n<td><strong>Alternative hypothesis (<em>H<\/em><sub>a<\/sub><\/strong><strong>)<\/strong><\/td>\n<\/tr>\n<tr>\n<td><a href=_-18.html>Two-sample <em>t <\/em>test\u00a0<\/a><\/p>\n<p><em>or<\/em><\/p>\n<p><a href=_-22.html>One-way ANOVA <\/a>with two groups<\/td>\n<td>The mean <span class=\"highlight-blue\">dependent variable<\/span> does not differ between <span class=\"highlight-purple\">group 1<\/span> (\u00b5<sub>1<\/sub>) and <span class=\"highlight-purple\">group 2<\/span> (\u00b5<sub>2<\/sub>) in the population; \u00b5<sub>1<\/sub> = \u00b5<sub>2<\/sub>.<\/td>\n<td>The mean <span class=\"highlight-blue\">dependent variable<\/span> differs between <span class=\"highlight-purple\">group 1<\/span> (\u00b5<sub>1<\/sub>), <span class=\"highlight-purple\">group 2<\/span> (\u00b5<sub>2<\/sub>) in the population; \u00b5<sub>1<\/sub> \u2260 \u00b5<sub>2<\/sub>.<\/td>\n<\/tr>\n<tr>\n<td><a href=_-22.html>One-way ANOVA <\/a>with three groups<\/td>\n<td>The mean <span class=\"highlight-blue\">dependent variable<\/span> does not differ between <span class=\"highlight-purple\">group 1<\/span> (\u00b5<sub>1<\/sub>), <span class=\"highlight-purple\">group 2<\/span> (\u00b5<sub>2<\/sub>), and <span class=\"highlight-purple\">group 3<\/span> (\u00b5<sub>3<\/sub>) in the population; \u00b5<sub>1<\/sub> = \u00b5<sub>2<\/sub> = \u00b5<sub>3<\/sub>.<\/td>\n<td>The mean <span class=\"highlight-blue\">dependent variable<\/span> of <span class=\"highlight-purple\">group 1<\/span> (\u00b5<sub>1<\/sub>), <span class=\"highlight-purple\">group 2<\/span> (\u00b5<sub>2<\/sub>), and <span class=\"highlight-purple\">group 3<\/span> (\u00b5<sub>3<\/sub>) are not all equal in the population.<\/td>\n<\/tr>\n<tr>\n<td><a href=_-23.html>Pearson correlation<\/a><\/td>\n<td>There is no correlation between <span class=\"highlight-purple\">independent variable<\/span> and <span class=\"highlight-blue\">dependent variable<\/span>\u00a0in the population; \u03c1 = 0.<\/td>\n<td>There is a correlation between <span class=\"highlight-purple\">independent variable<\/span> and <span class=\"highlight-blue\">dependent variable<\/span> in the population; \u03c1 \u2260 0.<\/td>\n<\/tr>\n<tr>\n<td><a href=_-19.html>Simple linear regression<\/a><\/td>\n<td>There is no relationship between <span class=\"highlight-purple\">independent variable<\/span> and <span class=\"highlight-blue\">dependent variable<\/span> in the population; \u03b2<sub>1<\/sub> = 0.<\/td>\n<td>There is a relationship between <span class=\"highlight-purple\">independent variable<\/span> and <span class=\"highlight-blue\">dependent variable<\/span> in the population; \u03b2<sub>1<\/sub> \u2260 0.<\/td>\n<\/tr>\n<tr>\n<td>Two-proportions <em>z <\/em>test<\/td>\n<td>The <span class=\"highlight-blue\">dependent variable<\/span> expressed as a proportion does not differ between <span class=\"highlight-purple\">group 1<\/span> (<em>p<\/em><sub>1<\/sub>) and <span class=\"highlight-purple\">group 2<\/span> (<em>p<\/em><sub>2<\/sub>) in the population; <em>p<\/em><sub>1<\/sub> = <em>p<\/em><sub>2<\/sub>.<\/td>\n<td>The <span class=\"highlight-blue\">dependent variable<\/span> expressed as a proportion differs between <span class=\"highlight-purple\">group 1<\/span> (<em>p<\/em><sub>1<\/sub>) and <span class=\"highlight-purple\">group 2<\/span> (<em>p<\/em><sub>2<\/sub>) in the population; <em>p<\/em><sub>1<\/sub> \u2260 <em>p<\/em><sub>2<\/sub>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><small><strong>Note:<\/strong> The template sentences above assume that you\u2019re performing <a href=index-2908.html#how\">one-tailed tests<\/a>. One-tailed tests are appropriate for most studies.<small><\/small><\/small><\/p>\n    <h2>Frequently asked questions<\/h2>\n<dl class=\"faq-list faq-list--arrows w-100 my-5\" itemscope itemtype=\"https:\/\/schema.org\/FAQPage\">\n            <div itemscope itemprop=\"mainEntity\" itemtype=\"https:\/\/schema.org\/Question\">\n            <dt id=\"what-is-hypothesis-testing\" class=\"faq-list__title\">\n                <a href=_-24.html class=\"faq-list__link qa-faq-anchor\">\n                    <span itemprop=\"name\">\n                        What is hypothesis testing?\n                    <\/span>\n                <\/a>\n            <\/dt>\n            <dd id=\"what-is-hypothesis-testing-answer\" class=\"faq-list__answer qa-faq-answer kb-article-styles\" itemscope itemprop=\"acceptedAnswer\" itemtype=\"https:\/\/schema.org\/Answer\">\n                <div itemprop=\"text\">\n                                        <p><a href=_-13.html>Hypothesis testing<\/a> is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called <a href=_-16.html>hypotheses<\/a>, by calculating how likely it is that a pattern or relationship between <a href=_-25.html>variables<\/a> could have arisen by chance.<\/p>\n\n                <\/div>\n            <\/dd>\n        <\/div>\n            <div itemscope itemprop=\"mainEntity\" itemtype=\"https:\/\/schema.org\/Question\">\n            <dt id=\"null-vs-alternative-hypothesis\" class=\"faq-list__title\">\n                <a href=_-26.html class=\"faq-list__link qa-faq-anchor\">\n                    <span itemprop=\"name\">\n                        What are null and alternative hypotheses?\n                    <\/span>\n                <\/a>\n            <\/dt>\n            <dd id=\"null-vs-alternative-hypothesis-answer\" class=\"faq-list__answer qa-faq-answer kb-article-styles\" itemscope itemprop=\"acceptedAnswer\" itemtype=\"https:\/\/schema.org\/Answer\">\n                <div itemprop=\"text\">\n                                        <p><a href=_-27.html>Null and alternative hypotheses<\/a> are used in statistical <a href=_-13.html>hypothesis testing<\/a>. The <strong>null hypothesis<\/strong> of a test always predicts no effect or no relationship between variables, while the <strong>alternative hypothesis<\/strong> states your research prediction of an effect or relationship.<\/p>\n\n                <\/div>\n            <\/dd>\n        <\/div>\n            <div itemscope itemprop=\"mainEntity\" itemtype=\"https:\/\/schema.org\/Question\">\n            <dt id=\"symbols-used-for-null-hypotheses\" class=\"faq-list__title\">\n                <a href=_-28.html class=\"faq-list__link qa-faq-anchor\">\n                    <span itemprop=\"name\">\n                        What symbols are used to represent null hypotheses?\n                    <\/span>\n                <\/a>\n            <\/dt>\n            <dd id=\"symbols-used-for-null-hypotheses-answer\" class=\"faq-list__answer qa-faq-answer kb-article-styles\" itemscope itemprop=\"acceptedAnswer\" itemtype=\"https:\/\/schema.org\/Answer\">\n                <div itemprop=\"text\">\n                                        <p>The <a href=_-27.html>null hypothesis<\/a> is often abbreviated as <em>H<\/em><sub>0<\/sub>. When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes \u2265 or \u2264).<\/p>\n\n                <\/div>\n            <\/dd>\n        <\/div>\n            <div itemscope itemprop=\"mainEntity\" itemtype=\"https:\/\/schema.org\/Question\">\n            <dt id=\"symbols-used-for-alternative-hypotheses\" class=\"faq-list__title\">\n                <a href=_-29.html class=\"faq-list__link qa-faq-anchor\">\n                    <span itemprop=\"name\">\n                        What symbols are used to represent alternative hypotheses?\n                    <\/span>\n                <\/a>\n            <\/dt>\n            <dd id=\"symbols-used-for-alternative-hypotheses-answer\" class=\"faq-list__answer qa-faq-answer kb-article-styles\" itemscope itemprop=\"acceptedAnswer\" itemtype=\"https:\/\/schema.org\/Answer\">\n                <div itemprop=\"text\">\n                                        <p>The <a href=_-27.html>alternative hypothesis<\/a> is often abbreviated as <em>H<\/em><sub>a<\/sub> or <em>H<\/em><sub>1<\/sub>. When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually \u2260, but sometimes &lt; or &gt;).<\/p>\n\n                <\/div>\n            <\/dd>\n        <\/div>\n            <div itemscope itemprop=\"mainEntity\" itemtype=\"https:\/\/schema.org\/Question\">\n            <dt id=\"difference-between-research-and-statistical-hypotheses\" class=\"faq-list__title\">\n                <a href=_-30.html class=\"faq-list__link qa-faq-anchor\">\n                    <span itemprop=\"name\">\n                        What\u2019s the difference between a research hypothesis and a statistical hypothesis?\n                    <\/span>\n                <\/a>\n            <\/dt>\n            <dd id=\"difference-between-research-and-statistical-hypotheses-answer\" class=\"faq-list__answer qa-faq-answer kb-article-styles\" itemscope itemprop=\"acceptedAnswer\" itemtype=\"https:\/\/schema.org\/Answer\">\n                <div itemprop=\"text\">\n                                        <p>A <strong><a href=_-16.html>research hypothesis<\/a><\/strong> is your proposed answer to your research question. The research hypothesis usually includes an explanation (\u201c<em>x<\/em> affects <em>y<\/em> because \u2026\u201d).<\/p>\n<p>A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the <a href=_-27.html>null and alternative hypotheses<\/a>. In a <a href=_-8.html>well-designed study<\/a>, the statistical hypotheses correspond logically to the research hypothesis.<\/p>\n\n                <\/div>\n            <\/dd>\n        <\/div>\n    <\/dl>\n","protected":false},"excerpt":{"rendered":"<p>The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There\u2019s no effect in the population. Alternative hypothesis (Ha or H1): There\u2019s an effect in the population. The effect is usually the effect of the independent variable on the dependent variable.<\/p>\n","protected":false},"author":151,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":""},"categories":[39099],"tags":[],"acf":[],"yoast_head":"<title>Null &amp; Alternative Hypotheses | Definitions, Templates &amp; Examples<\/title>\n<meta name=\"description\" content=\"A null hypothesis claims that there is no effect in the population, while an alternative hypothesis claims that there is an effect.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=_-27.html \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Null and Alternative Hypotheses | Definitions &amp; 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