diagnostic test
Thus, a positive diagnostic test result is interpreted as rejecting the null hypothesis. If the person actually does not have the disease, then the positive diagnostic test is a false positive.
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Learn about a null versus alternative hypothesis and what they show with examples for each. Also go over the main differences and similarities between them.
In This Article
What is an alternative hypothesis, outcomes of a hypothesis test.
Main Differences Between Null & Alternative Hypothesis
Similarities Between Null & Alternative Hypothesis
Hypothesis Testing & Errors
In statistics, you’ll draw insights or “inferences” about population parameters using data from a sample. This process is called inferential statistics.
To make statistical inferences, you need to determine if you have enough evidence to support a certain hypothesis about the population. This is where null and alternative hypotheses come into play!
In this article, we’ll explain the differences between these two types of hypotheses, and we’ll explain the role they play in hypothesis testing.
Imagine you want to know what percent of Americans are vegetarians. You find a Gallup poll claiming 5% of the population was vegetarian in 2018, but your intuition tells you vegetarianism is on the rise and that far more than 5% of Americans are vegetarian today.
To investigate further, you collect your own sample data by surveying 1,000 randomly selected Americans. You’ll use this random sample to determine whether it’s likely the true population proportion of vegetarians is, in fact, 5% (as the Gallup data suggests) or whether it could be the case that the percentage of vegetarians is now higher.
Notice that your investigation involves two rival hypotheses about the population. One hypothesis is that the proportion of vegetarians is 5%. The other hypothesis is that the proportion of vegetarians is greater than 5%. In statistics, we would call the first hypothesis the null hypothesis, and the second hypothesis the alternative hypothesis. The null hypothesis ( H 0 H_0 H 0 ) represents the status quo or what is assumed to be true about the population at the start of your investigation.
Null Hypothesis
In hypothesis testing, the null hypothesis ( H 0 H_0 H 0 ) is the default hypothesis.
It's what the status quo assumes to be true about the population.
The alternative hypothesis ( H a H_a H a or H 1 H_1 H 1 ) is the hypothesis that stands contrary to the null hypothesis. The alternative hypothesis represents the research hypothesis—what you as the statistician are trying to prove with your data .
In medical studies, where scientists are trying to demonstrate whether a treatment has a significant effect on patient outcomes, the alternative hypothesis represents the hypothesis that the treatment does have an effect, while the null hypothesis represents the assumption that the treatment has no effect.
Alternative Hypothesis
The alternative hypothesis ( H a H_a H a or H 1 H_1 H 1 ) is the hypothesis being proposed in opposition to the null hypothesis.
In a hypothesis test, the null and alternative hypotheses must be mutually exclusive statements, meaning both hypotheses cannot be true at the same time. For example, if the null hypothesis includes an equal sign, the alternative hypothesis must state that the values being mentioned are “not equal” in some way.
Your hypotheses will also depend on the formulation of your test—are you running a one-sample T-test, a two-sample T-test, F-test for ANOVA , or a Chi-squared test? It also matters whether you are conducting a directional one-tailed test or a nondirectional two-tailed test.
Null Hypothesis: The population mean is equal to some number, x. 𝝁 = x
Alternative Hypothesis: The population mean is not equal to x. 𝝁 ≠ x
Null Hypothesis: The population mean is less than or equal to some number, x. 𝝁 ≤ x Alternative Hypothesis: The population mean is greater than x. 𝝁 > x
Null Hypothesis: The population mean is greater than or equal to some number, x. 𝝁 ≥ x
Alternative Hypothesis: The population mean is less than x. 𝝁 < x
By the end of a hypothesis test, you will have reached one of two conclusions.
You will run into either 2 outcomes:
Fail to reject the null hypothesis on the grounds that there's insufficient evidence to move away from the null hypothesis
Reject the null hypothesis in favor of the alternative.
If you’re confused about the outcomes of a hypothesis test, a good analogy is a jury trial. In a jury trial, the defendant is innocent until proven guilty. To reach a verdict of guilt, the jury must find strong evidence (beyond a reasonable doubt) that the defendant committed the crime.
This is analogous to a statistician who must assume the null hypothesis is true unless they can uncover strong evidence ( a p-value less than or equal to the significance level) in support of the alternative hypothesis.
Notice also, that a jury never concludes a defendant is innocent—only that the defendant is guilty or not guilty. This is similar to how we never conclude that the null hypothesis is true. In a hypothesis test, we never conclude that the null hypothesis is true. We can only “reject” the null hypothesis or “fail to reject” it.
In this video, let’s look at the jury example again, the reasoning behind hypothesis testing, and how to form a test. It starts by stating your null and alternative hypotheses.
Here is a summary of the key differences between the null and the alternative hypothesis test.
The null hypothesis represents the status quo; the alternative hypothesis represents an alternative statement about the population.
The null and the alternative are mutually exclusive statements, meaning both statements cannot be true at the same time.
In a medical study, the null hypothesis represents the assumption that a treatment has no statistically significant effect on the outcome being studied. The alternative hypothesis represents the belief that the treatment does have an effect.
The null hypothesis is denoted by H_0 ; the alternative hypothesis is denoted by H_a H_1
You “fail to reject” the null hypothesis when the p-value is larger than the significance level. You “reject” the null hypothesis in favor of the alternative hypothesis when the p-value is less than or equal to your test’s significance level.
The similarities between the null and alternative hypotheses are as follows.
Both the null and the alternative are statements about the same underlying data.
Both statements provide a possible answer to a statistician’s research question.
The same hypothesis test will provide evidence for or against the null and alternative hypotheses.
Always remember that statistical inference provides you with inferences based on probability rather than hard truths. Anytime you conduct a hypothesis test, there is a chance that you’ll reach the wrong conclusion about your data.
In statistics, we categorize these wrong conclusions into two types of errors:
Type I Errors
Type II Errors
A Type I error occurs when you reject the null hypothesis when, in fact, the null hypothesis is true. This is sometimes called a false positive and is analogous to a jury that falsely convicts an innocent defendant. The probability of making this type of error is represented by alpha, ɑ.
A Type II error occurs when you fail to reject the null hypothesis when, in fact, the null hypothesis is false. This is sometimes called a false negative and is analogous to a jury that reaches a verdict of “not guilty,” when, in fact, the defendant has committed the crime. The probability of making this type of error is represented by beta, ꞵ.
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Genetics and Statistical Analysis
Once you have performed an experiment, how can you tell if your results are significant? For example, say that you are performing a genetic cross in which you know the genotypes of the parents. In this situation, you might hypothesize that the cross will result in a certain ratio of phenotypes in the offspring . But what if your observed results do not exactly match your expectations? How can you tell whether this deviation was due to chance? The key to answering these questions is the use of statistics , which allows you to determine whether your data are consistent with your hypothesis.
The first thing any scientist does before performing an experiment is to form a hypothesis about the experiment's outcome. This often takes the form of a null hypothesis , which is a statistical hypothesis that states there will be no difference between observed and expected data. The null hypothesis is proposed by a scientist before completing an experiment, and it can be either supported by data or disproved in favor of an alternate hypothesis.
Let's consider some examples of the use of the null hypothesis in a genetics experiment. Remember that Mendelian inheritance deals with traits that show discontinuous variation, which means that the phenotypes fall into distinct categories. As a consequence, in a Mendelian genetic cross, the null hypothesis is usually an extrinsic hypothesis ; in other words, the expected proportions can be predicted and calculated before the experiment starts. Then an experiment can be designed to determine whether the data confirm or reject the hypothesis. On the other hand, in another experiment, you might hypothesize that two genes are linked. This is called an intrinsic hypothesis , which is a hypothesis in which the expected proportions are calculated after the experiment is done using some information from the experimental data (McDonald, 2008).
But how did mathematics and genetics come to be linked through the use of hypotheses and statistical analysis? The key figure in this process was Karl Pearson, a turn-of-the-century mathematician who was fascinated with biology. When asked what his first memory was, Pearson responded by saying, "Well, I do not know how old I was, but I was sitting in a high chair and I was sucking my thumb. Someone told me to stop sucking it and said that if I did so, the thumb would wither away. I put my two thumbs together and looked at them a long time. ‘They look alike to me,' I said to myself, ‘I can't see that the thumb I suck is any smaller than the other. I wonder if she could be lying to me'" (Walker, 1958). As this anecdote illustrates, Pearson was perhaps born to be a scientist. He was a sharp observer and intent on interpreting his own data. During his career, Pearson developed statistical theories and applied them to the exploration of biological data. His innovations were not well received, however, and he faced an arduous struggle in convincing other scientists to accept the idea that mathematics should be applied to biology. For instance, during Pearson's time, the Royal Society, which is the United Kingdom's academy of science, would accept papers that concerned either mathematics or biology, but it refused to accept papers than concerned both subjects (Walker, 1958). In response, Pearson, along with Francis Galton and W. F. R. Weldon, founded a new journal called Biometrika in 1901 to promote the statistical analysis of data on heredity. Pearson's persistence paid off. Today, statistical tests are essential for examining biological data.
One of Pearson's most significant achievements occurred in 1900, when he developed a statistical test called Pearson's chi-square (Χ 2 ) test, also known as the chi-square test for goodness-of-fit (Pearson, 1900). Pearson's chi-square test is used to examine the role of chance in producing deviations between observed and expected values. The test depends on an extrinsic hypothesis, because it requires theoretical expected values to be calculated. The test indicates the probability that chance alone produced the deviation between the expected and the observed values (Pierce, 2005). When the probability calculated from Pearson's chi-square test is high, it is assumed that chance alone produced the difference. Conversely, when the probability is low, it is assumed that a significant factor other than chance produced the deviation.
In 1912, J. Arthur Harris applied Pearson's chi-square test to examine Mendelian ratios (Harris, 1912). It is important to note that when Gregor Mendel studied inheritance, he did not use statistics, and neither did Bateson, Saunders, Punnett, and Morgan during their experiments that discovered genetic linkage . Thus, until Pearson's statistical tests were applied to biological data, scientists judged the goodness of fit between theoretical and observed experimental results simply by inspecting the data and drawing conclusions (Harris, 1912). Although this method can work perfectly if one's data exactly matches one's predictions, scientific experiments often have variability associated with them, and this makes statistical tests very useful.
The chi-square value is calculated using the following formula:
Using this formula, the difference between the observed and expected frequencies is calculated for each experimental outcome category. The difference is then squared and divided by the expected frequency . Finally, the chi-square values for each outcome are summed together, as represented by the summation sign (Σ).
Pearson's chi-square test works well with genetic data as long as there are enough expected values in each group. In the case of small samples (less than 10 in any category) that have 1 degree of freedom, the test is not reliable. (Degrees of freedom, or df, will be explained in full later in this article.) However, in such cases, the test can be corrected by using the Yates correction for continuity, which reduces the absolute value of each difference between observed and expected frequencies by 0.5 before squaring. Additionally, it is important to remember that the chi-square test can only be applied to numbers of progeny , not to proportions or percentages.
Now that you know the rules for using the test, it's time to consider an example of how to calculate Pearson's chi-square. Recall that when Mendel crossed his pea plants, he learned that tall (T) was dominant to short (t). You want to confirm that this is correct, so you start by formulating the following null hypothesis: In a cross between two heterozygote (Tt) plants, the offspring should occur in a 3:1 ratio of tall plants to short plants. Next, you cross the plants, and after the cross, you measure the characteristics of 400 offspring. You note that there are 305 tall pea plants and 95 short pea plants; these are your observed values. Meanwhile, you expect that there will be 300 tall plants and 100 short plants from the Mendelian ratio.
You are now ready to perform statistical analysis of your results, but first, you have to choose a critical value at which to reject your null hypothesis. You opt for a critical value probability of 0.01 (1%) that the deviation between the observed and expected values is due to chance. This means that if the probability is less than 0.01, then the deviation is significant and not due to chance, and you will reject your null hypothesis. However, if the deviation is greater than 0.01, then the deviation is not significant and you will not reject the null hypothesis.
So, should you reject your null hypothesis or not? Here's a summary of your observed and expected data:
300 | 100 | |
305 | 95 |
Now, let's calculate Pearson's chi-square:
Next, you determine the probability that is associated with your calculated chi-square value. To do this, you compare your calculated chi-square value with theoretical values in a chi-square table that has the same number of degrees of freedom. Degrees of freedom represent the number of ways in which the observed outcome categories are free to vary. For Pearson's chi-square test, the degrees of freedom are equal to n - 1, where n represents the number of different expected phenotypes (Pierce, 2005). In your experiment, there are two expected outcome phenotypes (tall and short), so n = 2 categories, and the degrees of freedom equal 2 - 1 = 1. Thus, with your calculated chi-square value (0.33) and the associated degrees of freedom (1), you can determine the probability by using a chi-square table (Table 1).
Table 1: Chi-Square Table
| ||||||||||
0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 | |
1 | --- | --- | 0.001 | 0.004 | 0.016 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 |
2 | 0.010 | 0.020 | 0.051 | 0.103 | 0.211 | 4.605 | 5.991 | 7.378 | 9.210 | 10.597 |
3 | 0.072 | 0.115 | 0.216 | 0.352 | 0.584 | 6.251 | 7.815 | 9.348 | 11.345 | 12.838 |
4 | 0.207 | 0.297 | 0.484 | 0.711 | 1.064 | 7.779 | 9.488 | 11.143 | 13.277 | 14.860 |
5 | 0.412 | 0.554 | 0.831 | 1.145 | 1.610 | 9.236 | 11.070 | 12.833 | 15.086 | 16.750 |
6 | 0.676 | 0.872 | 1.237 | 1.635 | 2.204 | 10.645 | 12.592 | 14.449 | 16.812 | 18.548 |
7 | 0.989 | 1.239 | 1.690 | 2.167 | 2.833 | 12.017 | 14.067 | 16.013 | 18.475 | 20.278 |
8 | 1.344 | 1.646 | 2.180 | 2.733 | 3.490 | 13.362 | 15.507 | 17.535 | 20.090 | 21.955 |
9 | 1.735 | 2.088 | 2.700 | 3.325 | 4.168 | 14.684 | 16.919 | 19.023 | 21.666 | 23.589 |
10 | 2.156 | 2.558 | 3.247 | 3.940 | 4.865 | 15.987 | 18.307 | 20.483 | 23.209 | 25.188 |
11 | 2.603 | 3.053 | 3.816 | 4.575 | 5.578 | 17.275 | 19.675 | 21.920 | 24.725 | 26.757 |
12 | 3.074 | 3.571 | 4.404 | 5.226 | 6.304 | 18.549 | 21.026 | 23.337 | 26.217 | 28.300 |
13 | 3.565 | 4.107 | 5.009 | 5.892 | 7.042 | 19.812 | 22.362 | 24.736 | 27.688 | 29.819 |
14 | 4.075 | 4.660 | 5.629 | 6.571 | 7.790 | 21.064 | 23.685 | 26.119 | 29.141 | 31.319 |
15 | 4.601 | 5.229 | 6.262 | 7.261 | 8.547 | 22.307 | 24.996 | 27.488 | 30.578 | 32.801 |
16 | 5.142 | 5.812 | 6.908 | 7.962 | 9.312 | 23.542 | 26.296 | 28.845 | 32.000 | 34.267 |
17 | 5.697 | 6.408 | 7.564 | 8.672 | 10.085 | 24.769 | 27.587 | 30.191 | 33.409 | 35.718 |
18 | 6.265 | 7.015 | 8.231 | 9.390 | 10.865 | 25.989 | 28.869 | 31.526 | 34.805 | 37.156 |
19 | 6.844 | 7.633 | 8.907 | 10.117 | 11.651 | 27.204 | 30.144 | 32.852 | 36.191 | 38.582 |
20 | 7.434 | 8.260 | 9.591 | 10.851 | 12.443 | 28.412 | 31.410 | 34.170 | 37.566 | 39.997 |
21 | 8.034 | 8.897 | 10.283 | 11.591 | 13.240 | 29.615 | 32.671 | 35.479 | 38.932 | 41.401 |
22 | 8.643 | 9.542 | 10.982 | 12.338 | 14.041 | 30.813 | 33.924 | 36.781 | 40.289 | 42.796 |
23 | 9.260 | 10.196 | 11.689 | 13.091 | 14.848 | 32.007 | 35.172 | 38.076 | 41.638 | 44.181 |
24 | 9.886 | 10.856 | 12.401 | 13.848 | 15.659 | 33.196 | 36.415 | 39.364 | 42.980 | 45.559 |
25 | 10.520 | 11.524 | 13.120 | 14.611 | 16.473 | 34.382 | 37.652 | 40.646 | 44.314 | 46.928 |
26 | 11.160 | 12.198 | 13.844 | 15.379 | 17.292 | 35.563 | 38.885 | 41.923 | 45.642 | 48.290 |
27 | 11.808 | 12.879 | 14.573 | 16.151 | 18.114 | 36.741 | 40.113 | 43.195 | 46.963 | 49.645 |
28 | 12.461 | 13.565 | 15.308 | 16.928 | 18.939 | 37.916 | 41.337 | 44.461 | 48.278 | 50.993 |
29 | 13.121 | 14.256 | 16.047 | 17.708 | 19.768 | 39.087 | 42.557 | 45.722 | 49.588 | 52.336 |
30 | 13.787 | 14.953 | 16.791 | 18.493 | 20.599 | 40.256 | 43.773 | 46.979 | 50.892 | 53.672 |
40 | 20.707 | 22.164 | 24.433 | 26.509 | 29.051 | 51.805 | 55.758 | 59.342 | 63.691 | 66.766 |
50 | 27.991 | 29.707 | 32.357 | 34.764 | 37.689 | 63.167 | 67.505 | 71.420 | 76.154 | 79.490 |
60 | 35.534 | 37.485 | 40.482 | 43.188 | 46.459 | 74.397 | 79.082 | 83.298 | 88.379 | 91.952 |
70 | 43.275 | 45.442 | 48.758 | 51.739 | 55.329 | 85.527 | 90.531 | 95.023 | 100.425 | 104.215 |
80 | 51.172 | 53.540 | 57.153 | 60.391 | 64.278 | 96.578 | 101.879 | 106.629 | 112.329 | 116.321 |
90 | 59.196 | 61.754 | 65.647 | 69.126 | 73.291 | 107.565 | 113.145 | 118.136 | 124.116 | 128.299 |
100 | 67.328 | 70.065 | 74.222 | 77.929 | 82.358 | 118.498 | 124.342 | 129.561 | 135.807 | 140.169 |
& |
|
(Table adapted from Jones, 2008)
Note that the chi-square table is organized with degrees of freedom (df) in the left column and probabilities (P) at the top. The chi-square values associated with the probabilities are in the center of the table. To determine the probability, first locate the row for the degrees of freedom for your experiment, then determine where the calculated chi-square value would be placed among the theoretical values in the corresponding row.
At the beginning of your experiment, you decided that if the probability was less than 0.01, you would reject your null hypothesis because the deviation would be significant and not due to chance. Now, looking at the row that corresponds to 1 degree of freedom, you see that your calculated chi-square value of 0.33 falls between 0.016, which is associated with a probability of 0.9, and 2.706, which is associated with a probability of 0.10. Therefore, there is between a 10% and 90% probability that the deviation you observed between your expected and the observed numbers of tall and short plants is due to chance. In other words, the probability associated with your chi-square value is much greater than the critical value of 0.01. This means that we will not reject our null hypothesis, and the deviation between the observed and expected results is not significant.
Determining whether to accept or reject a hypothesis is decided by the experimenter, who is the person who chooses the "level of significance" or confidence. Scientists commonly use the 0.05, 0.01, or 0.001 probability levels as cut-off values. For instance, in the example experiment, you used the 0.01 probability. Thus, P ≥ 0.01 can be interpreted to mean that chance likely caused the deviation between the observed and the expected values (i.e. there is a greater than 1% probability that chance explains the data). If instead we had observed that P ≤ 0.01, this would mean that there is less than a 1% probability that our data can be explained by chance. There is a significant difference between our expected and observed results, so the deviation must be caused by something other than chance.
Harris, J. A. A simple test of the goodness of fit of Mendelian ratios. American Naturalist 46 , 741–745 (1912)
Jones, J. "Table: Chi-Square Probabilities." http://people.richland.edu/james/lecture/m170/tbl-chi.html (2008) (accessed July 7, 2008)
McDonald, J. H. Chi-square test for goodness-of-fit. From The Handbook of Biological Statistics . http://udel.edu/~mcdonald/statchigof.html (2008) (accessed June 9, 2008)
Pearson, K. On the criterion that a given system of deviations from the probable in the case of correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine 50 , 157–175 (1900)
Pierce, B. Genetics: A Conceptual Approach (New York, Freeman, 2005)
Walker, H. M. The contributions of Karl Pearson. Journal of the American Statistical Association 53 , 11–22 (1958)
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Null hypothesis
Null hypothesis n., plural: null hypotheses [nʌl haɪˈpɒθɪsɪs] Definition: a hypothesis that is valid or presumed true until invalidated by a statistical test
Table of Contents
Null hypothesis is defined as “the commonly accepted fact (such as the sky is blue) and researcher aim to reject or nullify this fact”.
More formally, we can define a null hypothesis as “a statistical theory suggesting that no statistical relationship exists between given observed variables” .
In biology , the null hypothesis is used to nullify or reject a common belief. The researcher carries out the research which is aimed at rejecting the commonly accepted belief.
A hypothesis is defined as a theory or an assumption that is based on inadequate evidence. It needs and requires more experiments and testing for confirmation. There are two possibilities that by doing more experiments and testing, a hypothesis can be false or true. It means it can either prove wrong or true (Blackwelder, 1982).
For example, Susie assumes that mineral water helps in the better growth and nourishment of plants over distilled water. To prove this hypothesis, she performs this experiment for almost a month. She watered some plants with mineral water and some with distilled water.
In a hypothesis when there are no statistically significant relationships among the two variables, the hypothesis is said to be a null hypothesis. The investigator is trying to disprove such a hypothesis. In the above example of plants, the null hypothesis is:
There are no statistical relationships among the forms of water that are given to plants for growth and nourishment.
Usually, an investigator tries to prove the null hypothesis wrong and tries to explain a relation and association between the two variables.
An opposite and reverse of the null hypothesis are known as the alternate hypothesis . In the example of plants the alternate hypothesis is:
There are statistical relationships among the forms of water that are given to plants for growth and nourishment.
The example below shows the difference between null vs alternative hypotheses:
Alternate Hypothesis: The world is round Null Hypothesis: The world is not round.
Copernicus and many other scientists try to prove the null hypothesis wrong and false. By their experiments and testing, they make people believe that alternate hypotheses are correct and true. If they do not prove the null hypothesis experimentally wrong then people will not believe them and never consider the alternative hypothesis true and correct.
The alternative and null hypothesis for Susie’s assumption is:
The null hypothesis suggests that there is no significant or statistical relationship. The relation can either be in a single set of variables or among two sets of variables.
Most people consider the null hypothesis true and correct. Scientists work and perform different experiments and do a variety of research so that they can prove the null hypothesis wrong or nullify it. For this purpose, they design an alternate hypothesis that they think is correct or true. The null hypothesis symbol is H 0 (it is read as H null or H zero ).
Why is it named the “Null”?
The name null is given to this hypothesis to clarify and explain that the scientists are working to prove it false i.e. to nullify the hypothesis. Sometimes it confuses the readers; they might misunderstand it and think that statement has nothing. It is blank but, actually, it is not. It is more appropriate and suitable to call it a nullifiable hypothesis instead of the null hypothesis.
Why do we need to assess it? Why not just verify an alternate one?
In science, the scientific method is used. It involves a series of different steps. Scientists perform these steps so that a hypothesis can be proved false or true. Scientists do this to confirm that there will be any limitation or inadequacy in the new hypothesis. Experiments are done by considering both alternative and null hypotheses, which makes the research safe. It gives a negative as well as a bad impact on research if a null hypothesis is not included or a part of the study. It seems like you are not taking your research seriously and not concerned about it and just want to impose your results as correct and true if the null hypothesis is not a part of the study.
In statistics, firstly it is necessary to design alternate and null hypotheses from the given problem. Splitting the problem into small steps makes the pathway towards the solution easier and less challenging. how to write a null hypothesis?
Writing a null hypothesis consists of two steps:
In other words, assume in such a way that the treatment does not have any effect.
Questions | Null Hypothesis |
---|---|
Are adults doing better at mathematics than teenagers? | Mathematical ability does not depend on age. |
Does the risk of a heart attack reduce by daily intake of aspirin? | A heart attack is not affected by the daily dose of aspirin. |
Are teenagers using cell phones to access the internet more than elders? | Age does not affect the usage of cell phones for internet access. |
Are cats concerned about their food color? | Cats do not prefer food based on color. |
Does pain relieve by chewing willow bark? | Pain is not relieved by chewing willow bark. |
The usual recovery duration after knee surgery is considered almost 8 weeks.
A researcher thinks that the recovery period may get elongated if patients go to a physiotherapist for rehabilitation twice per week, instead of thrice per week, i.e. recovery duration reduces if the patient goes three times for rehabilitation instead of two times.
Step 1: Look for the problem in the hypothesis. The hypothesis either be a word or can be a statement. In the above example the hypothesis is:
“The expected recovery period in knee rehabilitation is more than 8 weeks”
Step 2: Make a mathematical statement from the hypothesis. Averages can also be represented as μ, thus the null hypothesis formula will be.
In the above equation, the hypothesis is equivalent to H1, the average is denoted by μ and > that the average is greater than eight.
Step 3: Explain what will come up if the hypothesis does not come right i.e., the rehabilitation period may not proceed more than 08 weeks.
There are two options: either the recovery will be less than or equal to 8 weeks.
H 0 : μ ≤ 8
In the above equation, the null hypothesis is equivalent to H 0 , the average is denoted by μ and ≤ represents that the average is less than or equal to eight.
What will happen if the scientist does not have any knowledge about the outcome?
Problem: An investigator investigates the post-operative impact and influence of radical exercise on patients who have operative procedures of the knee. The chances are either the exercise will improve the recovery or will make it worse. The usual time for recovery is 8 weeks.
Step 1: Make a null hypothesis i.e. the exercise does not show any effect and the recovery time remains almost 8 weeks.
H 0 : μ = 8
In the above equation, the null hypothesis is equivalent to H 0 , the average is denoted by μ, and the equal sign (=) shows that the average is equal to eight.
Step 2: Make the alternate hypothesis which is the reverse of the null hypothesis. Particularly what will happen if treatment (exercise) makes an impact?
In the above equation, the alternate hypothesis is equivalent to H1, the average is denoted by μ and not equal sign (≠) represents that the average is not equal to eight.
To get a reasonable and probable clarification of statistics (data), a significance test is performed. The null hypothesis does not have data. It is a piece of information or statement which contains numerical figures about the population. The data can be in different forms like in means or proportions. It can either be the difference of proportions and means or any odd ratio.
The following table will explain the symbols:
P-value | |
Probability of success | |
Size of sample | |
Null Hypothesis | |
Alternate Hypothesis |
P-value is the chief statistical final result of the significance test of the null hypothesis.
The first stage of Null Hypothesis Significance Testing (NHST) is to form an alternate and null hypothesis. By this, the research question can be briefly explained.
Null Hypothesis = no effect of treatment, no difference, no association Alternative Hypothesis = effective treatment, difference, association
When to reject the null hypothesis?
Researchers will reject the null hypothesis if it is proven wrong after experimentation. Researchers accept null hypothesis to be true and correct until it is proven wrong or false. On the other hand, the researchers try to strengthen the alternate hypothesis. The binomial test is performed on a sample and after that, a series of tests were performed (Frick, 1995).
Step 1: Evaluate and read the research question carefully and consciously and make a null hypothesis. Verify the sample that supports the binomial proportion. If there is no difference then find out the value of the binomial parameter.
Show the null hypothesis as:
H 0 :p= the value of p if H 0 is true
To find out how much it varies from the proposed data and the value of the null hypothesis, calculate the sample proportion.
Step 2: In test statistics, find the binomial test that comes under the null hypothesis. The test must be based on precise and thorough probabilities. Also make a list of pmf that apply, when the null hypothesis proves true and correct.
When H 0 is true, X~b(n, p)
N = size of the sample
P = assume value if H 0 proves true.
Step 3: Find out the value of P. P-value is the probability of data that is under observation.
Rise or increase in the P value = Pr(X ≥ x)
X = observed number of successes
P value = Pr(X ≤ x).
Step 4: Demonstrate the findings or outcomes in a descriptive detailed way.
Variable or model selection and less information in some cases are the chief important issues that affect the testing of the null hypothesis. Statistical tests of the null hypothesis are reasonably not strong. There is randomization about significance. (Gill, 1999) The main issue with the testing of the null hypothesis is that they all are wrong or false on a ground basis.
There is another problem with the a-level . This is an ignored but also a well-known problem. The value of a-level is without a theoretical basis and thus there is randomization in conventional values, most commonly 0.q, 0.5, or 0.01. If a fixed value of a is used, it will result in the formation of two categories (significant and non-significant) The issue of a randomized rejection or non-rejection is also present when there is a practical matter which is the strong point of the evidence related to a scientific matter.
The P-value has the foremost importance in the testing of null hypothesis but as an inferential tool and for interpretation, it has a problem. The P-value is the probability of getting a test statistic at least as extreme as the observed one.
The main point about the definition is: Observed results are not based on a-value
Moreover, the evidence against the null hypothesis was overstated due to unobserved results. A-value has importance more than just being a statement. It is a precise statement about the evidence from the observed results or data. Similarly, researchers found that P-values are objectionable. They do not prefer null hypotheses in testing. It is also clear that the P-value is strictly dependent on the null hypothesis. It is computer-based statistics. In some precise experiments, the null hypothesis statistics and actual sampling distribution are closely related but this does not become possible in observational studies.
Some researchers pointed out that the P-value is depending on the sample size. If the true and exact difference is small, a null hypothesis even of a large sample may get rejected. This shows the difference between biological importance and statistical significance. (Killeen, 2005)
Another issue is the fix a-level, i.e., 0.1. On the basis, if a-level a null hypothesis of a large sample may get accepted or rejected. If the size of simple is infinity and the null hypothesis is proved true there are still chances of Type I error. That is the reason this approach or method is not considered consistent and reliable. There is also another problem that the exact information about the precision and size of the estimated effect cannot be known. The only solution is to state the size of the effect and its precision.
Here are some examples:
Among all the population of humans, almost 10% of people prefer to do their task with their left hand i.e. left-handed. Let suppose, a researcher in the Penn States says that the population of students at the College of Arts and Architecture is mostly left-handed as compared to the general population of humans in general public society. In this case, there is only a sample and there is a comparison among the known population values to the population proportion of sample value.
A generic brand of antihistamine Diphenhydramine making medicine in the form of a capsule, having a 50mg dose. The maker of the medicines is concerned that the machine has come out of calibration and is not making more capsules with the suitable and appropriate dose.
Several people choose vegetarian meals on a daily basis. Typically, the researcher thought that females like vegetarian meals more than males.
Nowadays obesity and being overweight is one of the major and dangerous health issues. Research is performed to confirm that a low carbohydrates diet leads to faster weight loss than a low-fat diet.
A case-control study was performed. The study contains nonsmokers, stroke patients, and controls. The subjects are of the same occupation and age and the question was asked if someone at their home or close surrounding smokes?
A financial expert observes that there is somehow a positive and effective relationship between the variation in stock rate price and the quantity of stock bought by non-management employees
Try to answer the quiz below to check what you have learned so far about the null hypothesis.
Choose the best answer.
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Last updated on June 16th, 2022
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In a scientific experiment, the null hypothesis is the proposition that there is no effect or no relationship between phenomena or populations. If the null hypothesis is true, any observed difference in phenomena or populations would be due to sampling error (random chance) or experimental error. The null hypothesis is useful because it can be tested and found to be false, which then implies that there is a relationship between the observed data. It may be easier to think of it as a nullifiable hypothesis or one that the researcher seeks to nullify. The null hypothesis is also known as the H 0, or no-difference hypothesis.
The alternate hypothesis, H A or H 1 , proposes that observations are influenced by a non-random factor. In an experiment, the alternate hypothesis suggests that the experimental or independent variable has an effect on the dependent variable .
There are two ways to state a null hypothesis. One is to state it as a declarative sentence, and the other is to present it as a mathematical statement.
For example, say a researcher suspects that exercise is correlated to weight loss, assuming diet remains unchanged. The average length of time to achieve a certain amount of weight loss is six weeks when a person works out five times a week. The researcher wants to test whether weight loss takes longer to occur if the number of workouts is reduced to three times a week.
The first step to writing the null hypothesis is to find the (alternate) hypothesis. In a word problem like this, you're looking for what you expect to be the outcome of the experiment. In this case, the hypothesis is "I expect weight loss to take longer than six weeks."
This can be written mathematically as: H 1 : μ > 6
In this example, μ is the average.
Now, the null hypothesis is what you expect if this hypothesis does not happen. In this case, if weight loss isn't achieved in greater than six weeks, then it must occur at a time equal to or less than six weeks. This can be written mathematically as:
H 0 : μ ≤ 6
The other way to state the null hypothesis is to make no assumption about the outcome of the experiment. In this case, the null hypothesis is simply that the treatment or change will have no effect on the outcome of the experiment. For this example, it would be that reducing the number of workouts would not affect the time needed to achieve weight loss:
H 0 : μ = 6
"Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a null hypothesis.
Another example of a null hypothesis is "Plant growth rate is unaffected by the presence of cadmium in the soil ." A researcher could test the hypothesis by measuring the growth rate of plants grown in a medium lacking cadmium, compared with the growth rate of plants grown in mediums containing different amounts of cadmium. Disproving the null hypothesis would set the groundwork for further research into the effects of different concentrations of the element in soil.
You may be wondering why you would want to test a hypothesis just to find it false. Why not just test an alternate hypothesis and find it true? The short answer is that it is part of the scientific method. In science, propositions are not explicitly "proven." Rather, science uses math to determine the probability that a statement is true or false. It turns out it's much easier to disprove a hypothesis than to positively prove one. Also, while the null hypothesis may be simply stated, there's a good chance the alternate hypothesis is incorrect.
For example, if your null hypothesis is that plant growth is unaffected by duration of sunlight, you could state the alternate hypothesis in several different ways. Some of these statements might be incorrect. You could say plants are harmed by more than 12 hours of sunlight or that plants need at least three hours of sunlight, etc. There are clear exceptions to those alternate hypotheses, so if you test the wrong plants, you could reach the wrong conclusion. The null hypothesis is a general statement that can be used to develop an alternate hypothesis, which may or may not be correct.
The null hypothesis (H 0 ) is the hypothesis that states there is no statistical difference between two sample sets. In other words, it assumes the independent variable does not have an effect on the dependent variable in a scientific experiment .
The null hypothesis is the most powerful type of hypothesis in the scientific method because it’s the easiest one to test with a high confidence level using statistics. If the null hypothesis is accepted, then it’s evidence any observed differences between two experiment groups are due to random chance. If the null hypothesis is rejected, then it’s strong evidence there is a true difference between test sets or that the independent variable affects the dependent variable.
The null hypothesis is written as H 0 , which is read as H-zero, H-nought, or H-null. It is associated with another hypothesis, called the alternate or alternative hypothesis H A or H 1 . When the null hypothesis and alternate hypothesis are written mathematically, they cover all possible outcomes of an experiment.
An experimenter tests the null hypothesis with a statistical analysis called a significance test. The significance test determines the likelihood that the results of the test are not due to chance. Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01). But, even if the confidence in the test is high, there is always a small chance the outcome is incorrect. This means you can’t prove a null hypothesis. It’s also a good reason why it’s important to repeat experiments.
The most common type of null hypothesis assumes no difference between two samples or groups or no measurable effect of a treatment. This is the exact hypothesis . If you’re asked to state a null hypothesis for a science class, this is the one to write. It is the easiest type of hypothesis to test and is the only one accepted for certain types of analysis. Examples include:
There is no difference between two groups H 0 : μ 1 = μ 2 (where H 0 = the null hypothesis, μ 1 = the mean of population 1, and μ 2 = the mean of population 2)
Both groups have value of 100 (or any number or quality) H 0 : μ = 100
However, sometimes a researcher may test an inexact hypothesis . This type of hypothesis specifies ranges or intervals. Examples include:
Recovery time from a treatment is the same or worse than a placebo: H 0 : μ ≥ placebo time
There is a 5% or less difference between two groups: H 0 : 95 ≤ μ ≤ 105
An inexact hypothesis offers “directionality” about a phenomenon. For example, an exact hypothesis can indicate whether or not a treatment has an effect, while an inexact hypothesis can tell whether an effect is positive of negative. However, an inexact hypothesis may be harder to test and some scientists and statisticians disagree about whether it’s a true null hypothesis .
To state the null hypothesis, first state what you expect the experiment to show. Then, rephrase the statement in a form that assumes there is no relationship between the variables or that a treatment has no effect.
Example: A researcher tests whether a new drug speeds recovery time from a certain disease. The average recovery time without treatment is 3 weeks.
This null hypothesis (inexact hypothesis) covers both the scenario in which the drug has no effect and the one in which the drugs makes the recovery time longer. The alternate hypothesis is that average recovery time will be less than three weeks:
H A : μ < 3
Of course, the researcher could test the no-effect hypothesis (exact null hypothesis): H 0 : μ = 3
The danger of testing this hypothesis is that rejecting it only implies the drug affected recovery time (not whether it made it better or worse). This is because the alternate hypothesis is:
H A : μ ≠ 3 (which includes μ <3 and μ >3)
Even though the no-effect null hypothesis yields less information, it’s used because it’s easier to test using statistics. Basically, testing whether something is unchanged/changed is easier than trying to quantify the nature of the change.
Remember, a researcher hopes to reject the null hypothesis because this supports the alternate hypothesis. Also, be sure the null and alternate hypothesis cover all outcomes. Finally, remember a simple true/false, equal/unequal, yes/no exact hypothesis is easier to test than a more complex inexact hypothesis.
Does chewing willow bark relieve pain? | Pain relief is the same compared with a . (exact) Pain relief after chewing willow bark is the same or worse versus taking a placebo. (inexact) | Pain relief is different compared with a placebo. (exact) Pain relief is better compared to a placebo. (inexact) |
Do cats care about the shape of their food? | Cats show no food preference based on shape. (exact) | Cat show a food preference based on shape. (exact) |
Do teens use mobile devices more than adults? | Teens and adults use mobile devices the same amount. (exact) Teens use mobile devices less than or equal to adults. (inexact) | Teens and adults used mobile devices different amounts. (exact) Teens use mobile devices more than adults. (inexact) |
Does the color of light influence plant growth? | The color of light has no effect on plant growth. (exact) | The color of light affects plant growth. (exact) |
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The null hypothesis (H0) answers "No, there's no effect in the population.". The alternative hypothesis (Ha) answers "Yes, there is an effect in the population.". The null and alternative are always claims about the population. That's because the goal of hypothesis testing is to make inferences about a population based on a sample.
The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups. An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study. Symbol. It is denoted by H 0.
The alternative hypothesis and null hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making judgments on the basis of data. In statistical hypothesis testing, the null hypothesis and alternative hypothesis are two mutually exclusive statements. "The statement being tested in a test of statistical significance is called the null ...
The null hypothesis implies that the presumed factor being tested has no effect (i.e., "null"). The alternative hypothesis states that the presumed relevant factor has the effect embodied in the explanation of what was observed. The Test: Grow two plants (or better, two replicate groups of plants) in pots close by each other so that they ...
Biology is the science that studies living organisms and their interactions with one another and with their environment. The process of science attempts to describe and understand the nature of the universe by rational means. ... Alternative hypothesis includes that toaster wasn't turned on. The original hypothesis is correct. The coffee ...
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0, the —null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
These kinds of null hypotheses are the subject of Chapters 8 through 12. The Null hypothesis (H O) is a statement about the comparisons, e.g., between a sample statistic and the population, or between two treatment groups. The former is referred to as a one tailed test whereas the latter is called a two-tailed test.
Most technical papers rely on just the first formulation, even though you may see some of the others in a statistics textbook. Null hypothesis: " x is equal to y.". Alternative hypothesis " x is not equal to y.". Null hypothesis: " x is at least y.". Alternative hypothesis " x is less than y.". Null hypothesis: " x is at most ...
The alternative hypothesis (H a H_a H a or H 1 H_1 H 1 ) is the hypothesis being proposed in opposition to the null hypothesis. Examples of Null and Alternative Hypotheses In a hypothesis test, the null and alternative hypotheses must be mutually exclusive statements, meaning both hypotheses cannot be true at the same time.
Biological vs. Statistical Null Hypotheses. It is important to distinguish between biological null and alternative hypotheses and statistical null and alternative hypotheses. "Sexual selection by females has caused male chickens to evolve bigger feet than females" is a biological alternative hypothesis; it says something about biological processes, in this case sexual selection.
Biology definition: A hypothesis is a supposition or tentative explanation for (a group of) phenomena, (a set of) facts, or a scientific inquiry that may be tested, verified or answered by further investigation or methodological experiment. It is like a scientific guess. It's an idea or prediction that scientists make before they do ...
An alternative hypothesis is a hypothesis that there is a relationship between variables. This includes any hypothesis that predicts positive correlation, negative correlation, non-directional correlation or causation.The only hypothesis that isn't an alternative hypothesis is a null hypothesis that predicts no relationship between independent and dependent variables.
The null hypothesis is proposed by a scientist before completing an experiment, and it can be either supported by data or disproved in favor of an alternate hypothesis.
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. \(H_0\): The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.
The alternative hypothesis is a hypothesis used in significance testing which contains a strict inequality. A test of significance will result in either rejecting the null hypothesis (indicating ...
How is Null hypothesis different from Alternative Hypothesis? Please subscribe using the link: https://bit.ly/3kG2kKfAn explanation with a simple example " E...
Biology definition: A null hypothesis is an assumption or proposition where an observed difference between two samples of a statistical population is purely accidental and not due to systematic causes. It is the hypothesis to be investigated through statistical hypothesis testing so that when refuted indicates that the alternative hypothesis is true. . Thus, a null hypothesis is a hypothesis ...
Null Hypothesis Examples. "Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a ...
The null hypothesis is written as H 0, which is read as H-zero, H-nought, or H-null. It is associated with another hypothesis, called the alternate or alternative hypothesis H A or H 1. When the null hypothesis and alternate hypothesis are written mathematically, they cover all possible outcomes of an experiment.
The alternative hypothesis is a statement used in statistical inference experiment. It is contradictory to the null hypothesis and denoted by H a or H 1. We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing.
For example, engineered microbes now produce many of the protein-rich supplements used in animal feed and the stain-removing enzymes in laundry detergents. "We talk about synthetic biology as what's next," says Tom Brennan, a partner at McKinsey & Company, a consulting firm. "But it's here." And there's room to grow, analysts say.