Tests of Significance — MCQs
After applying a statistical test, an investigator gets a p-value of 0.01. What does this indicate about the null hypothesis?
A group of 80 people is being studied to determine the effect of diet modification on cholesterol levels. To compare the mean cholesterol levels before and after the diet modification in this group, which statistical test should be used?
What is the most appropriate statistical test to test the statistical significance of the change in blood cholesterol levels after a month's treatment with atorvastatin?
What does the P-value represent in hypothesis testing?
A study was undertaken to establish the relationship between the consumption of a vegetarian or non-vegetarian diet and the presence of diseases. Which statistical test should be used?
What is the common threshold for statistical significance in hypothesis testing?
A study was done to assess malnutrition among young children. 100 children were selected each from rural and urban areas. Out of these, 30 among rural and 20 among urban were found to be malnourished. Which of the following statistical tests is used to compare the data sets?
In the context of hypothesis testing, what does statistical power refer to?
What is the sensitivity of EEG for detecting brain tumours as per the information given below?
For a screening test, 90% specificity means that 90% of non-diseased persons will give a
Tests of Significance Indian Medical PG Practice Questions and MCQs
Question 1: After applying a statistical test, an investigator gets a p-value of 0.01. What does this indicate about the null hypothesis?
- A. There is a 1% probability of incorrectly rejecting the null hypothesis when it is true.
- B. The test has a 99% chance of detecting a true effect if it exists.
- C. The null hypothesis is likely to be rejected.
- D. There is a 1% probability of observing the data, or something more extreme, if the null hypothesis is true. (Correct Answer)
Explanation: ***There is a 1% probability of observing the data, or something more extreme, if the null hypothesis is true.*** - A **p-value** is defined as the probability of obtaining observed results (or results more extreme) assuming that the **null hypothesis is true**. - A p-value of 0.01 means there is a **1% chance** of observing the data if there truly is no effect or no difference. *There is a 1% probability of incorrectly rejecting the null hypothesis when it is true.* - This statement describes the **Type I error rate (alpha level)**, which is typically set *before* the experiment, usually at 0.05 or 0.01. - While a low p-value suggests the possibility of a Type I error if the null hypothesis is rejected, it doesn't directly represent the probability of making *that specific error*. *The null hypothesis is likely to be rejected.* - A p-value of 0.01 is **statistically significant** at common alpha levels (e.g., 0.05 or 0.01), leading to the rejection of the null hypothesis. However, this option is about the *action* taken, not the *interpretation* of the p-value itself. - The decision to reject or not reject depends on comparing the p-value to a pre-defined **alpha level**. *The test has a 99% chance of detecting a true effect if it exists.* - This statement describes the **power of the study (1 - beta)**, which is the probability of correctly rejecting a false null hypothesis. - Power is a separate concept from the p-value and is influenced by factors like sample size, effect size, and alpha level.
Question 2: A group of 80 people is being studied to determine the effect of diet modification on cholesterol levels. To compare the mean cholesterol levels before and after the diet modification in this group, which statistical test should be used?
- A. Paired t-test (Correct Answer)
- B. McNemar test
- C. Chi-square test
- D. Wilcoxon signed-rank test
- E. Independent t-test
Explanation: ***Paired t-test*** - A **paired t-test** is appropriate for comparing means from two related samples, such as "before" and "after" measurements on the **same individuals**. - It assesses whether there is a statistically significant difference between these **dependent observations**. *Independent t-test* - The independent t-test compares means between **two separate groups** (unrelated samples). - It is inappropriate here because we have **paired data** from the same individuals measured twice, not two independent groups. *McNemar test* - The McNemar test is used for comparing **paired nominal data**, typically in a 2×2 table, for example, before-after changes in a proportion or categorical outcome. - It is not suitable for **continuous data** like cholesterol levels. *Chi-square test* - The chi-square test is used to assess the association between **two categorical variables** or to compare observed frequencies with expected frequencies. - It is not designed for comparing means of **continuous variables** in paired samples. *Wilcoxon signed-rank test* - The Wilcoxon signed-rank test is a **non-parametric alternative to the paired t-test**, used when the data are not normally distributed or when the sample size is small. - While it's used for paired data, the paired t-test is generally preferred when parametric assumptions (like **normality**) can be met, especially with a sample size of 80.
Question 3: What is the most appropriate statistical test to test the statistical significance of the change in blood cholesterol levels after a month's treatment with atorvastatin?
- A. Paired t-test (Correct Answer)
- B. Unpaired or independent t-test
- C. Analysis of variance
- D. Chi-square test
Explanation: ***Paired t-test*** * A **paired t-test** is appropriate when comparing two means from the **same group of subjects** measured at two different time points (before and after treatment). * In this scenario, a single group's blood cholesterol levels are measured *before* and *after* atorvastatin treatment, making the observations dependent. *Unpaired or independent t-test* * An **unpaired t-test** is used to compare the means of two *independent* groups. * It would be used, for instance, if cholesterol levels were being compared between a group receiving atorvastatin and a separate control group. *Analysis of variance* * **Analysis of variance (ANOVA)** is used to compare **three or more means**. * It would be appropriate if there were multiple treatment groups or multiple time points for comparison beyond just two. *Chi-square test* * The **Chi-square test** is used to examine the association between **categorical variables**. * It would not be suitable here, as blood cholesterol level is a continuous numerical variable, not a categorical one.
Question 4: What does the P-value represent in hypothesis testing?
- A. The probability of obtaining results as extreme or more extreme than observed, assuming the null hypothesis is true. (Correct Answer)
- B. The probability of not rejecting the null hypothesis when it is true.
- C. The probability of rejecting the null hypothesis when it is false.
- D. The probability of observing the data given that the null hypothesis is false.
Explanation: ***The probability of obtaining results as extreme or more extreme than observed, assuming the null hypothesis is true.*** - The **P-value** quantifies the evidence against the **null hypothesis**, representing the likelihood of obtaining the observed results (or more extreme results) if the null hypothesis were indeed correct. - A **small P-value** (typically < 0.05) suggests that the observed data is unlikely under the null hypothesis, providing evidence to **reject** it. - It is NOT the probability that the null hypothesis is true or false, nor the probability of the data itself, but rather the probability of obtaining such extreme results by chance alone. *The probability of not rejecting the null hypothesis when it is true.* - This describes the **confidence level (1 - α)**, which represents the probability of correctly failing to reject a true null hypothesis. - It is not what the P-value directly calculates, which focuses on the probability of extreme results under the null hypothesis. *The probability of rejecting the null hypothesis when it is false.* - This is known as the **power of the test (1 - β)**, which is the probability of correctly detecting a real effect when it exists. - The **P-value** itself does not represent the power; rather, it is a tool used to make a decision about the null hypothesis based on observed data. *The probability of observing the data given that the null hypothesis is false.* - This statement is related to the **alternative hypothesis** and is not the direct definition of a **P-value**. - The P-value specifically assesses the probability of obtaining extreme results under the assumption that the **null hypothesis is true**, not false.
Question 5: A study was undertaken to establish the relationship between the consumption of a vegetarian or non-vegetarian diet and the presence of diseases. Which statistical test should be used?
- A. Chi-square test (Correct Answer)
- B. T-test
- C. ANOVA
- D. Fisher's exact test
- E. Mann-Whitney U test
Explanation: ***Chi-square test*** - The **chi-square test** is appropriate when analyzing the relationship between two **categorical variables**. In this scenario, "diet type" (vegetarian/non-vegetarian) and "presence of disease" (yes/no) are both categorical variables. - This test determines if there is a statistically significant association between the frequency counts of these two variables in a contingency table. *T-test* - A **t-test** is used to compare the **means** of two groups, typically when the dependent variable is continuous. - This test is unsuitable here because the presence of disease and diet type are categorical, not continuous, variables. *ANOVA* - **ANOVA** (Analysis of Variance) is used to compare the **means** of three or more groups, often with a continuous dependent variable. - Similar to the t-test, ANOVA is not applicable as the study involves categorical variables, not the comparison of means across multiple groups. *Fisher's exact test* - **Fisher's exact test** is similar to the chi-square test but specifically used for **small sample sizes** where the expected frequencies in any cell of the contingency table are less than 5. - While it analyzes categorical data, the chi-square test is the more general and commonly preferred test for larger sample sizes, which is generally assumed unless otherwise specified. *Mann-Whitney U test* - The **Mann-Whitney U test** is a non-parametric test used to compare differences between two independent groups when the dependent variable is **ordinal or continuous** but not normally distributed. - This test is not appropriate for analyzing the association between two categorical variables, as it requires at least one variable to have ranked or continuous data.
Question 6: What is the common threshold for statistical significance in hypothesis testing?
- A. 0.01
- B. 0.02
- C. 0.03
- D. 0.05 (Correct Answer)
Explanation: ***Correct: 0.05*** - A **p-value of 0.05 (or 5%)** is the most widely accepted and **conventional threshold** for statistical significance in most scientific fields, including medicine - This represents a **5% probability** of observing the results if the **null hypothesis** were true (Type I error or α level) - This is the **standard alpha level** taught in biostatistics and most commonly used in medical research *Incorrect: 0.01* - While 0.01 indicates **higher statistical confidence** (1% chance of Type I error), it is more stringent than the standard threshold - Used in studies requiring **greater certainty** or where false positives have severe consequences - Not the most common or default threshold in general hypothesis testing *Incorrect: 0.02* - A p-value of 0.02 represents a **2% chance of Type I error** - While statistically valid, it is **not a conventional alpha level** for most hypothesis tests - Not the standard threshold taught or applied in medical statistics *Incorrect: 0.03* - A p-value of 0.03 represents a **3% chance of Type I error** - This is **not a standard choice** for statistical significance testing - Not the conventionally prescribed alpha level in biostatistics
Question 7: A study was done to assess malnutrition among young children. 100 children were selected each from rural and urban areas. Out of these, 30 among rural and 20 among urban were found to be malnourished. Which of the following statistical tests is used to compare the data sets?
- A. Paired t-test
- B. Chi-square (Correct Answer)
- C. The standard error of mean
- D. ANOVA
Explanation: ***Chi-square*** - The Chi-square test is appropriate for comparing **categorical data** or proportions between two or more independent groups, as seen with malnutrition rates in rural vs. urban children. - It assesses whether there is a statistically significant association between the two categorical variables (region and nutritional status). *Paired t-test* - A **paired t-test** is used to compare the means of two related groups or repeated measurements on the same subjects, which is not the case here as the rural and urban groups are independent. - This test is typically applied when analyzing before-and-after intervention data or matched pairs. *The standard error of mean* - The **Standard Error of the Mean (SEM)** is a measure of the precision of the sample mean as an estimate of the population mean, not a statistical test for comparing data sets. - It quantifies the variability of sample means if multiple samples were taken from the same population. *ANOVA* - **ANOVA (Analysis of Variance)** is used to compare the means of three or more independent groups, or to analyze the effects of multiple factors on a continuous outcome. - While it can compare groups, it is primarily for continuous outcomes and not for comparing proportions or categorical data like malnutrition prevalence.
Question 8: In the context of hypothesis testing, what does statistical power refer to?
- A. The probability of failing to reject a true null hypothesis.
- B. The probability of correctly rejecting a false null hypothesis. (Correct Answer)
- C. The probability of incorrectly rejecting a true null hypothesis.
- D. The probability of incorrectly rejecting a false null hypothesis.
Explanation: ***The probability of correctly rejecting a false null hypothesis.*** - **Statistical power** is the probability that a statistical test will **correctly detect an effect** when there is a true effect present. - It represents the ability of a study to **avoid a Type II error (β)** (failing to reject a false null hypothesis), and is calculated as **1 - β**. - Higher statistical power means greater ability to detect a true effect when it exists. *The probability of failing to reject a true null hypothesis.* - This describes the **complement of Type I error (1 - α)**, representing the probability of correctly retaining a true null hypothesis. - This is a correct decision in hypothesis testing but is **not the definition of statistical power**. - Related to the specificity of the test when the null hypothesis is true. *The probability of incorrectly rejecting a true null hypothesis.* - This describes **Type I error (α)**, also known as a **false positive**. - It represents the significance level of the test, typically set at 0.05 or 0.01. - This is an error, not a measure of power, and represents concluding there is an effect when none exists. *The probability of incorrectly rejecting a false null hypothesis.* - This statement is **logically contradictory** and conceptually impossible. - If the null hypothesis is false, rejecting it is the **correct decision**, not incorrect. - The probability of **failing to reject a false null hypothesis** is **Type II error (β)**, and power = 1 - β.
Question 9: What is the sensitivity of EEG for detecting brain tumours as per the information given below?
- A. 90% (Correct Answer)
- B. 99.99%
- C. 0.07%
- D. 85%
Explanation: ***90%*** - Sensitivity is calculated as **True Positives / (True Positives + False Negatives)**. - Based on the table provided, among patients with brain tumors (disease positive), 36 cases were correctly identified by EEG and 4 cases were missed. - Sensitivity = 36/(36+4) = 36/40 = 0.9 or **90%**. - This indicates that the EEG test correctly identifies 90% of patients who actually have brain tumors. - High sensitivity is important for screening tests to minimize false negatives. *99.99%* - This extremely high percentage is incorrect and not supported by the data. - It would indicate near-perfect detection of all brain tumor cases, which contradicts the table showing 4 missed cases out of 40. - Results from miscalculation or misinterpretation of the sensitivity formula. *0.07%* - This extremely low value represents a fundamental calculation error. - Such low sensitivity would indicate the test is essentially useless for detecting brain tumors. - Does not correspond to any reasonable interpretation of the given data. *85%* - While close to the correct answer, this is mathematically incorrect. - Likely results from calculation error or rounding mistakes. - The correct calculation (36/40) yields exactly 90%, not 85%.
Question 10: For a screening test, 90% specificity means that 90% of non-diseased persons will give a
- A. False negative result
- B. True positive result
- C. True negative result (Correct Answer)
- D. False positive result
Explanation: ***True negative result*** - **Specificity** is defined as the proportion of **true negatives** among individuals **without the disease**. - A 90% specificity means that 90% of healthy individuals will correctly test negative for the disease. *False negative result* - A **false negative** occurs when a diseased person tests negative, which is related to the concept of **sensitivity**, not specificity. - This would imply missing actual cases of the disease. *True positive result* - A **true positive** occurs when a diseased person tests positive, which is also related to **sensitivity**. - This indicates accurate detection of the disease in affected individuals. *False positive result* - A **false positive** occurs when a non-diseased person inappropriately tests positive. - If 90% of non-diseased persons give a negative result (true negative), then 10% would give a **false positive result**.
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