Excellent Hypothesis testing

Hypothesis testing is a process of validating or disproving a hypothesis through experimentation. The first step in the process is to construct an educated guess about what you think may be happening. Next, you must create and test your experiment with the goal of proving your hypothesis correct or providing evidence for its validity. Finally, it is important to analyze and interpret data from the experiment by communicating results as compellingly as possible–to convince others that there is enough information to support your conclusion. Are you looking for an excellent hypothesis testing help? Worry no more! We got you covered!

Excellent Hypothesis testing
Excellent Hypothesis testing

Hypothesis testing

Hypothesis testing is a process of validating or disproving a hypothesis through experimentation. The first step in the process is to construct an educated guess about what you think may be happening. Next, you must create and test your experiment with the goal of proving your hypothesis correct or providing evidence for its validity. Finally, it is important to analyze and interpret data from the experiment by communicating results as compellingly as possible–to convince others that there is enough information to support your conclusion.

Null and Alternative Hypotheses

The null hypothesis (H0) is generally what you want to prove false; it’s the opposite of your research question or hypothesis. For example, if you want to know if watching violent video games increases aggressive behavior among children, your null hypothesis would be that the violent video games do not influence children’s aggression. The alternative hypothesis (Ha) is what you’re looking for; it might include game play causes aggression or game play does not cause aggression.

Statistically Significant Result

In research, when a hypothesis has been tested and the results are analyzed, if the sample data produce a p-value that is less than or equal to your predetermined alpha level (usually .05), then this indicates that could not have occurred by chance; thus, it is considered statistically significant. A common misinterpretation of the term statistically significant is that a result with a p-value of less than or equal to .05 has been proven true. This is not the case; only from a statistical standpoint can a researcher say that results null hypothesis could have occurred by chance at a 5% level of significance, rather than assuming it’s true.

Type I and Type II errors

A p-value of less than or equal to .05 indicates that the result could not have occurred by chance. An alpha level is selected before data are collected, so there is always some chance that results will be statistically significant when they should not be. This is called a Type I error, or a false positive result. A Type II error occurs when data are not statistically significant and the null hypothesis of no difference between groups is actually true–a false negative result.

 Significance Level

The significance level (also known as alpha or α) is the probability of a Type I error, or false positive. In other words, it’s the chance that results will be statistically significant when they should not be. For example, if your alpha level is set at .05, then there is a 5% chance that the “null hypothesis” will be falsely rejected and an alternative hypothesis will erroneously be accepted as true.

 Margin of Error

In statistics, margin of error (MOE) refers to an amount by which a reported statistic may vary from its true value due to the random variation in measurements. For example, a survey result with a 5% margin of error means that if the same procedures were used 100 times, the resulting statistic would be within 5 percent of the true value 95 times.

 Confidence Interval

A confidence interval (CI) expresses the precision of a sample statistic. By its very nature, estimation introduces some amount of error. Therefore, CI allows us to create bounds on the population parameter such that there is a specified probability (e.g., 95%) of including the true value, should we repeat our estimation process many times.

 Hypothesis Test

A hypothesis test for a population proportion is done by determining if the sample data could have occurred by chance. Therefore, we reject H0 and conclude that there is sufficient evidence to suggest that p > 0.5 (1 − p) = 1 − 0.5 = 0.5

For example, let’s say that it is believed that the percentage of people in the U.S. over the age of 65 who receive Social Security benefits is 30%. In other words, we believe that \ (\frac {30}{100} = 0.3\). Then we would use this information to test our hypothesis, testing the following: \ (H_0: \; \frac {30}{100} \leq 0.5\) versus \ (H_a:\; \frac {30}{100} > 0.5\)

We would then look at a sample of people over the age of 65 and determine what percentage of them receive Social Security benefits. If the sample percentage is .34, for example, this indicates that 29.6% of people over the age of 65 receive Social Security benefits. In other words, we would not be able to reject the null hypothesis that p ≤ 0.5 because it’s possible that this could have occurred by chance (see assumptions below).

However, if a different sample were taken and the percentage was .58, then we would reject the null hypothesis that p ≤ 0.5 because it’s highly unlikely that this sample could have occurred by chance. The probability of a Type I error is equal to alpha (.05), which means there is a 5% chance of rejecting a true null hypothesis.

In general, the assumptions of a hypothesis test for a population proportion include: the population is normally distributed, the random variable follows a binomial distribution with n = sample size and p = hypothesized probability.

The null hypothesis is rejected if it is more likely that the sample results could have occurred by chance. However, this does not mean that the alternative hypothesis is automatically accepted. We must also evaluate whether the results are congruent with our expectations for the study. If these expectations are not met, then we cannot assume that p > 0.5.

 

 Standard Deviation

The standard deviation (SD) is most often used as the measure of spread for continuous data. It indicates how far, on average, individual data values are from the mean. The larger the standard deviation, the more spread out numbers are in a set of data. For example, if you have test scores with a mean of 80 and a standard deviation of 10, then most people scored between 70 and 90 (80 ± 10). But if your test scores had a mean of 80 and a standard deviation of 30, most people would have scored between 50 and 130 (80 ± 30)

Hypothesis Testing Application

Hypothesis tests and confidence intervals, like the ones we covered in this article, are important procedures for assessing your data. However, there are some cases where they simply aren’t appropriate. For example:

  1. When you need to make a decision based on whether or not an observed difference is greater than zero (e.g., the performance of a drug)
  2. When you’re comparing group averages (e.g., weight differences between men and women)
  3. When the distributions in your sample are extremely asymmetrical or skewed (i.e., outliers aren’t adequately represented by your results).

Example of what happens when you don’t use a good experiment design or analysis plan:  An experimenter hypothesized that obese individuals walk slower than individuals of average weight. A random sample was taken from two populations, obese and non-obese. However, there was no variability in the dependent variable (walking speed).

Obese participants had an average walking speed of 1.3 m/s while non-obese participants had an average walking speed of 1.6 m/s. The experimenter rejected the null hypothesis that there was no difference in walking speed between obese and non-obese participants, but the evidence does not support this conclusion since there is little variance in walking speed across both groups.

What are some other examples where you can’t use a hypothesis test?  The average number of visits in a medical practice is 10 per patient, and the standard deviation is 2. A researcher hypothesized that this mean is less than 10; however, when tested, the difference was not statistically significant (p = 0.27). Thus, the null hypothesis cannot be rejected.

Conclusion

If you’re trying to improve your hypothesis testing, there are a few things you should keep in mind. In order for any experiment to be valid, it must have two independent variables and one dependent variable. Without this structure, the results of your test may not provide accurate data about what is happening during that time period or situation. The more rigorous an experiment is structured according to these standards, the better chance it will reflect reality accurately.

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Excellent Hypothesis testing
Excellent Hypothesis testing