Type I and II Errors: A Deep Dive into Hypothesis Testing and Errors

This presentation transcript and accompanying report delve into the critical concepts of Type I and Type II errors within the context of hypothesis testing in research. The document begins by establishing the importance of hypothesis testing and defines the null and alternative hypotheses, along with the selection of significance levels and the role of p-values. It then proceeds to define and differentiate between Type I errors (false positives) and Type II errors (false negatives), explaining their causes, consequences, and probabilities (alpha and beta). The transcript provides real-world application of these concepts by examining HIV testing, demonstrating how these errors can impact the accuracy of test results and the spread of the virus. The presentation also discusses strategies for mitigating these errors, such as increasing sample sizes and the power of statistical tests. Finally, the transcript emphasizes the correlation between the two types of errors and the importance of considering their implications when interpreting research findings. References from various research papers are included to support the arguments made in the presentation.

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Type I and II error Video Transcript
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TYPE I AND II ERROR
Type I and II error Video Transcript
A primary cause of inaccurate research papers and studies are errors that are made during
the research process. Hypothesis testing is a critical part of the research process and generally
involves first defining a null and alternative hypothesis which is followed by selecting a sample
from the population from which data will be collected (Urbano, Lima, & Hanjalic, 2019). The
null hypothesis is usually common knowledge or the status quo while the alternative hypothesis
relates to the new phenomena which is being tested or observed. The level of significance is then
selected, and the data required for the study is collected. The final step in the process is statistical
calculations to determine whether to accept or reject the null hypothesis. The p-value is then
selected
p-value = P (statistic / H0 . Is true)
When the p-value is less that the level of significance level α we reject our null hypothesis
p-value < α
However, if the if the p-value is greater that or equal to the significance level α we accept the
null hypothesis.
p-value > or = to α
An error may occur during the hypothesis testing stage when if we incorrectly accept or reject
the null hypothesis. As such, these errors are referred to as Type I and II errors.
Type I Error
A type I error (false positive) can be defined as an error that occurs during hypothesis
testing when the null hypothesis is wrongly rejected when it is accurate (Urbano et al., 2019). In
other words, this error occurs when a difference is observed when, in actual fact, there is no
statistically significant difference. Alpha (α) represents the probability of making a type I error. α
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can be defined as the p-value below which you reject the null hypothesis. The probability of
committing a type I error can be reduced by decreasing the p-value. A study with a αof 0.05 can
be reduced to a α of 0.01 and this would decrease the probability of a type I error. However,
decreasing the p-value decreases the likelihood of detecting a statistically significant difference.
Type I errors result from random chance therefore increasing the number of tests would increase
type I errors.
Type II Error
Type II error (false negative) occurs when the null hypothesis is wrongfully accepted
when it is false during hypothesis testing. As such, a type II error is said to have occurred when
there is a failure to observe a statistically significant difference (Chazard, Ficheur, Beuscart, &
Preda, 2017). Beta (β) can be defined as the probability of producing type II errors. β shares the
following relationship with the power of the statistical test
Power = 1- β
The Power of a test can be defined as the probability of rejecting H0 when it is false. The value
β is dependent on a number of factors which include the sample size, variance and the value of α.
The probability of type II errors can be decreased by ensuring that the study has a large sample
size to detect any statistically significant difference or by ensuring that the test has enough
power.
The Power of Test
The power of test can be defined as the probability of rejecting a false null hypothesis. As
such, the power is the ability to detect statistically significant differences by a statistical test or
the ability to avoid type II errors. The power is an important aspect and has to be considered
when the sample size is being determined. In research the power is determined by four main
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factors namely the sample’s characteristics, the type I errors specified, sample size and the aspect
that the research wants to measure (Singh, 2007).
The Relationship Between Type I and II Errors
Type I and type II errors are correlated and an increase in type II errors would lead to a decrease
in type I error’s and vice versa. Similarly, decreasing the level of significance from 0.05 to 00.1
will reduce type I errors but this will also increase type II errors. Another example of the
relationship between type I and type II errors is sample size (Cunningham & Koscik, 2017). In
research the consequences of type I errors are viewed as more serious that that of type II errors.
Type II errors would result in a researcher not receiving the results that were anticipated
resulting and the researcher may choose to redo the study or accept the results. However, in the
case type I errors the researcher receives the results that where expected and this leads to false
reporting.
Mitigating Type I and Type II Errors
Real-world application of the concept of Type I and II errors
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Human immunodeficiency virus (HIV) is a virus that attacks the human body and
weakens its immune system and progresses to Acquired Immune Deficiency Syndrome (AIDS).
HIV is a global pandemic that adversely affects the economies and communities around the
world. HIV has no known cure, and it is managed by encouraging individuals to get tested for
the virus so that they can know their HIV status (Omidikia & Kompany-Zareh, 2016). As such,
this ensures individuals who test positive for the virus receive medical attention and they do not
pass on the virus to other individuals. HIV testing kits also suffer from type I and II errors due to
the fact that they are not 100% accurate. HIV testing kits have a 99.9% accuracy rate when it
comes to detecting negative results and a 99.7% accuracy rate when it comes to testing for
positive results (Figueroa et al., 2018).
Type I Error and Type II Errors in HIV Testing
In the case of HIV testing to conduct a hypothesis test, the null hypothesis must be first
determined. The null hypothesis will be the state that reflects the absence of the phenomena
which is being tested which in this case is the HIV virus. The alternative hypothesis will indicate
the presence of HIV
H0 = The patient is HIV negative
H1 = The patient is HIV positive
A type I error occurs during HIV testing when a patient's null hypothesis is incorrectly rejected.
As such, this means a patient is HIV negative, but the result of the HIV self-test kit indicates that
the patient is positive.
A type II error occurs during HIV testing when the null hypothesis (H0 = The patient is HIV
negative) is incorrectly accepted. As such, this means the results for a patient who are HIV
positive are found to be HIV negative when tested using HIV testing kits.
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Overcoming Type I Error and Type II Errors in HIV Testing
The accuracy of HIV testing is crucial as this can mitigate the spread of the virus through
a population. As such, eliminating the type I and type II errors is can make HIV testing kits more
accurate. The table below shows the scenarios where type I and type II errors may occur in HIV
testing.
Type I and Type II errors HIV Testing Kits (Duffy, 2010)
Hypothesis Reality
Null Hypothesis is
True
Alternative Hypothesis is True
Null Hypothesis is
True
Correct HIV test Type II Error
Alternative
Hypothesis is True
Type I Error Correct HIV test
A comparison between the outcomes of type I and type II errors shows that type II errors
would most likely cause the spread of HIV through a population (Patel et al., 2018). This is due
to the fact that type I errors would result in individuals who do not have HIV being wrong tested
positive. However, type II errors would consist of individuals who are HIV positive being
wrongly diagnosed as HIV negative. As such, this would cause a spread in infection as HIV
positive individuals may unknowingly spread the virus to their partners (Chereau et al., 2017). A
solution to dealing with type I and type II errors in HIV testing kits would have to involve
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reducing type II errors. Reducing the probability of type II errors can be accomplished by
increasing the power of the test. In the case of HIV testing this can be accomplished by
increasing the number of times an individual is tested. Evidently, this is a viable solution as
patients are advised to get tested every three months to safeguard against inaccurate HIV results.
Summary
Type I and type II errors are errors that arise during hypothesis testing and result in false
negative and false positive when testing the null hypothesis. A type I error arises when the null
hypothesis is wrong rejected when it is accurate and a type II error occurs when the null
hypothesis is wrongfully accepted. Type I and type II errors are correlated and decrease type I
errors would increase type II errors.
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References
Chazard, E., Ficheur, G., Beuscart, J.-B., & Preda, C. (2017). How to compare the length of stay
of two samples of inpatients? a simulation study to compare type i and type ii errors of 12
statistical tests. Value in Health, 20(7), 992-998.
Chereau, F., Madec, Y., Sabin, C., Obel, N., Ruiz-Mateos, E., Chrysos, G., . . . Wittkop, L.
(2017). Impact of CD4 and CD8 dynamics and viral rebounds on loss of virological
control in HIV controllers. PloS one, 12(4).
Cunningham, W. A., & Koscik, T. R. (2017). Balancing Type I and Type II error concerns in
fMRI through compartmentalized analysis. Cognitive neuroscience, 8(3), 147-149.
Duffy, S. (2010). Random numbers demonstrate the frequency of Type I errors: three
spreadsheets for class instruction. Journal of Statistics Education, 18(2).
Figueroa, C., Johnson, C., Ford, N., Sands, A., Dalal, S., Meurant, R., . . . Baggaley, R. (2018).
Reliability of HIV rapid diagnostic tests for self-testing compared with testing by health-
care workers: a systematic review and meta-analysis. The lancet HIV, 5(6), e277-e290.
Omidikia, N., & Kompany-Zareh, M. (2016). Type (I, II) errors variable selection in quantitative
structure activity relationships. Chemometrics and Intelligent Laboratory Systems, 152,
10-17.
Patel, P., Rose, C. E., Collins, P. Y., Nuche-Berenguer, B., Sahasrabuddhe, V. V., Peprah, E., . . .
Levitt, N. S. (2018). Noncommunicable diseases among HIV-infected persons in low-
income and middle-income countries: a systematic review and meta-analysis. AIDS
(London, England), 32(Suppl 1), S5.
Singh, K. (2007). Quantitative Social Research Methods: SAGE Publications.
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Urbano, J., Lima, H., & Hanjalic, A. (2019). Statistical Significance Testing in Information
Retrieval: An Empirical Analysis of Type I, Type II and Type III Errors. Paper presented
at the Proceedings of the 42nd International ACM SIGIR Conference on Research and
Development in Information Retrieval.
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