Biostats_4_Measures of Association Flashcards

1
Q

Precision takes into account a measurement’s (or set of measurement’s) … ?

A

Reliability

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The consistency and reproducibility of a test.
The absence of random variation in a test.

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Reliability refers to how similar the data points are to each other: when reliability is low, the data points are more widely dispersed. When reliability is high, the data points are more close together.

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2
Q

What does the precision do to the standard deviation (SD)?

A

SD decreases when the measurements are more precise

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3
Q

Accuracy takes into account a measurement’s (or set of measurement’s) … ?

A

Validity

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The closeness of test results to the true values.
The absence of systematic error or bias in a test.

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Validity refers to how close the data points are to the true value: when validity is low, the data points do not approximate the true.

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4
Q

An analysis that renders values such as these would have (high/low) precision/accuracy?

A

Low reliability and High validity

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5
Q

An analysis that renders values such as these would have (high/low) precision/accuracy?

A

High reliability and Low validity

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6
Q

An analysis that renders values such as these would have (high/low) precision/accuracy?

A

Low reliability and Low validity

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7
Q

An analysis that renders values such as these would have (high/low) precision/accuracy?

A

High reliability and High validity

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8
Q

Random error will impact the … ?

A

precision in a test.

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9
Q

Systemic error will impact the …?

A

accuracy in a test.

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10
Q

Specificity and sensitivity would relate to precision or accuracy?

A

Both of these measures (using standardized values) are of tests of validity and refers to the ability of a test to correctly identify those who do not have a certain disease (specificity) or the ability of a test to correctly identify those who have the disease (sensitivity).

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11
Q

What is Attributable Risk (AR)?

A

The excess incidence of a disease due to a particular factor (exposure). This measure of association is used in cohort studies. AR is also known as the ‘risk difference’ and is the absolute value in terms of risk between the exposed and unexposed groups.

Formula: AR = Incidence in Exposed - Incidence in Unexposed.

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12
Q

What is another term for attributable risk?

A

Absolute risk increase

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13
Q

What does Attributable Risk (AR) measure?

A

Excess risk due to exposure in the exposed group.

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The absolute risk attributable to exposure in the exposed group.

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Calculated as: incidence rate in the exposed group - incidence rate in unexposed group

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14
Q

How is Attributable Risk (AR) calculated?

A

AR = | (Incidence in Exposed) - (Incidence in Unexposed) |

For example, 100 people are analyzed.

60 were exposed and 40 were not exposed.

In the exposed group, 50% of the members experienced disease (30 out of 60).

In the unexposed group, 25% of the members experienced disease (10 out of 40).

The AR = (30/60) - (10/40) = 0.5 - 0.25 = 0.25 (or 25%).

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15
Q

If a study needed to determine how much an exposure or risk factor has contributed to the incidence of a disease, and the relative risk was provided, what measure of assoication would be appropriate and how would this be calculated?

A

This would require the Attributable Risk Percent (AR%), which is the proportion of disease incidence in the exposed group attributable to the exposure.

Formula: AR% = [ ( RR - 1) / ( RR ) ] x 100 = (Attributable Risk / Incidence in Exposed) × 100

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16
Q

How is Attributable Risk Percent (AR%) calculated?

A

AR% = ( [Attributable Risk] / [Incidence in Exposed] ) × 100.

AR% = [ ( RR - 1) / ( RR ) ] x 100.

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17
Q

What is Population Attributable Risk Percent (PAR%)?

A

The proportion of disease incidence in the total population attributable to the exposure.

In order to determine this, the incidence of the disease within the entire population (irrespective of whether they were exposed to the risk factor) is subtracted by the incidence of developing the disease in the unexposed group (which is assuming random chance of developing the disease). That value is then placed within a ratio to the entire population’s incidence where the numerator is the value obtainted from subtracting out the random chance and the demoninator is the incidence of the entire population.

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18
Q

How is Population Attributable Risk Percent (PAR%) calculated?

A

To determine population attributable risk percent:

1) First calculate the incidence of the disease in the study population as a whole. For example, if a study population of 100 people (where 60 were smokers and 40 were non-smokers) had 30 individuals from the smoker group and 10 individuals from the non-smoker group who developed respiratory disease or symptoms, then the overall incidence of developing respiratory disease or symptoms in this study population would be 40/100.

2) Next, calculate the difference in risk of developing respiratory disease among the study population as a whole and among non-smokers (40/100 - 10/40 = 0.4 - 0.25 = 0.15). To explain this further, 40/100 accounted for the incidence of developing disease or symptoms in the entire population while 10/40 was the risk based on random chance.

3) Divide the difference in risk between the two groups by the incidence of respiratory disease in the population as a whole (0.15/0.4 = 0.375) to determine that Based on the calculation, 37.5% of the yearly respiratory disease in the study population is attributable to smoking.

PAR% = [(Incidence in Total Population - Incidence in Unexposed) / Incidence in Total Population] × 100.

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19
Q

What is Number Needed to Treat (NNT)?

A

The number of patients that need to be treated to prevent one additional adverse outcome.

Formula: NNT = 1 / Absolute Risk Reduction (ARR).

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20
Q

How is Number Needed to Treat (NNT) calculated?

A

1) First determine the absolute risk reduction, ARR = (Mortality Rate in Control - Mortality Rate in Treatment).

2) Then take the reciprocle of this value.

For example if a new treatment regimen now has a death rate of 25/50 = 0.5 over 5 years, whereas in patients kept on the conventional regimen had a mortality rate of 75/100 = 0.75, then the absolute risk difference between the two groups would be 0.75 - 0.5 = 0.25. Taking the reciprocal (1/0.25 = 4) of the absolute risk difference allows for the NNT to be determined.

Example: = 0.75 - 0.5 = 0.25; NNT = 1 / 0.25 = 4.

Based on this result, we can conclude that we need to treat 4 patients with the new regimen as opposed to the conventional regimen in order for one more patient to survive 5 years without relapse.

NNT = 1 / Absolute Risk Reduction (ARR)

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21
Q

What insight does Number Needed to Treat (NNT) provide?

A

Practical insight into the effectiveness of a treatment.

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22
Q

What does Attributable Risk Percent (AR%) show?

A

The proportion of disease incidence in exposed individuals that is due to the exposure.

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23
Q

What does Population Attributable Risk Percent (PAR%) demonstrate?

A

The impact of exposure on disease incidence in the entire population.

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24
Q

How is a normal distribution set?

A

1 sd = 68 % of all values (+/- 1 sd from the mean is +/- 34%)

2 sd = 95% of all values (+ / - 2 sd from the mean is +/- 14%)

3 sd = 99% of all values (+ / - 3 sd from the mean is +/- 2 %)

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25
Q

What is used to determine the accuracy of the mean?

A

The likelihood of the estimated mean to be accurate is “standard error of the mean (SEM)”

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The standard error of the mean is a specific kind of standard deviation: while SD describes the dispersion of sample data in relation to its mean, SEM describes the dispersion of means of different samples from a population mean. As the SD increases and the sample size decreases, SEM will increase.

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26
Q

Would increasing the amount of measurements alter the standard deviation?

A

No, the standard deviation measures the dispersion or spread in data and is an intrinsic property of the population from which the sample is drawn. Increasing the sample size may increase the accuracy of estimating the standard deviation, but it will not change the standard deviation itself.

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27
Q

Would increasing the amount of measurements alter the standard error of the mean?

A

Yes, the standard error of the mean (SEM) is a measure of the dispersion of a random set of sample means around the true population mean. It is dependent on the variability (i.e., standard deviation) of the measured values and the sample size (SEM = SD/√n). By increasing the sample size, the sample means approach the true population mean, resulting in a smaller SEM.

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28
Q

How would a larger standard deviation alter the standard error of the mean?

A

A greater standard deviation will increase the SEM, resulting in a less accurate estimate.

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29
Q

How would a smaller sample size affect the standard error of the mean?

A

A smaller sample size will increase the SEM, resulting in a less accurate estimate.

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30
Q

When a sample is measured and population mean is then subtracted from the sample measurement and this result is then divided by the standard deviation, what is this value if we assume that all measurements follow a normal distribution?

A

Z-score

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This value is used to express data in terms of units of standard deviation and how many standard deviations from the mean a particular value is is represented in its value. With a z-score a research can compare values between other populations with different means and standard deviations.

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31
Q

How are confidence intervals (CIs) calculated?

A

CIs are defined as the mean ± standard error of the mean, which is calculated by multiplying a Z-score (for 95% confidence intervals this is always 2) by the standard deviation (SD) divided by the square root of the sample size (Mean +/- Z-score (SD/√sample size)). A larger sample size or a decreased SD (based on data precision) will decrease the standard error. Including more disparate data or reducing the sample size, will increase the standard error, thus expand the CI.

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32
Q

The average of the squared differences of values in a data set from the mean value is … ?

A

Variance

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The variance allows interpretation of how far a set of data is spread out. A variance of zero means that there is no variability in the values. Largely different numbers in a set of data lead to a large variance.

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33
Q

What is the functional use of dividing the standard deviation by the mean?

A

The coefficient of variation (CV)

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Used to measure and compare the dispersion around the mean of multiple data sets.

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CV, which is a statistical relative measure of dispersion, allows SD to be interpreted relative to the mean, allowing for the comparison of multiple data sets that may have means of different magnitudes or units of measurement, as CV is dimensionless. A high CV indicates that values are widely spread around the mean.

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34
Q

How does the CV differ from the SD?

A

SD, which is an absolute measure of dispersion, describes the variability of data in relation to the mean within a single data set. CV is a relative measure of dispersion.

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35
Q

In both positively and negatively skewed distributions, what is the new “peak?”

A

The mode becomes the apex of the curve.

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For the positively skewed distributions, the mode (peak) is displaced to the left.

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For the negatively skewed distributions, the mode (peak) is displaced to the right.

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36
Q

With negatively skewed distributions, the mean is displaced to the ______

A

left

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The Peak is to the right and the tail is to the left.

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Going left to right is mean (“-“ tail), median, mode (apex).

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37
Q

In a negatively skewed distribution, which (mean, median, mode) is greatest?

A

Mean < median < mode

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38
Q

With positively skewed distributions, the mean is displaced to the ______

A

right

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The peak is to the left and the tail is to the right.

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Going left to right is mode (apex), median, and mean (“+” tail).

39
Q

In a positively skewed distribution, which (mean, median, mode) is greatest?

A

Mean > median > mode

40
Q

What can produce a positively skewed distribution?

A

Having a single or group of outliers that are higher and value in proportion to the majority of the range of values in the study. This will push the mean in a positive direction, and create a towel on the positive end while maintaining the mode more towards the negative end and the median between both of these. The mean will be smaller than both the median and mode.

41
Q

What statistical test is used to check differences between the means (quantitative) of TWO groups (qualitative)?

A

t-test

42
Q

If a researcher was comparing the mean heart rate between men and women, what would be used to make this comparison?

A

T-test

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Calculates the difference between the means of two samples or between a sample and population or a value subject to change; especially when samples are small and/or the population or a value subject to change distribution is not known.

43
Q

What are the different types of T-tests?

A

One-sided, Two-sided, paired and unpaired

44
Q

When a researcher wants to determine whether the means of two groups differ from one another, what statistical analysis is used?

A

One sample t-test

45
Q

When a study uses the means to compare two independent variables, what is used to compare them?

A

Two-sided sample T (student’s T test)

46
Q

What is the Two-sample t test (Student’s t test) used for?

A

It is used to compare means of two independent groups. The basic requirements are the two mean values, sample variances, and sample size.

47
Q

How is the p-value obtained for the two-sample t test (also called Student’s t test)?

A

The t statistic is then obtained to calculate the p value.

48
Q

In a two-sided t-test, if the p-value is less than 0.05, what is the implication?

A

If the p-value is less than 0.05, the null hypothesis is rejected, indicating a statistically significant difference, and the two means are assumed to be statistically different.

49
Q

In a two-sided t-test, if the p-value is more than 0.05, what is the implication?

A

When the p value is large (i.e. greater than 0.05), then the null hypothesis is retained.

50
Q

An investigator compares an average standardized depression score in two groups of patients, those who take beta-blockers and those who do not. Which statistical analysis was likely used by the investigator to analyze the study results?

A

Two-sided sample T (student’s T test)

51
Q

When the same individual mean is followed over time, what is used to study any comparison?

A

paired T test

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In a paired t-test, data is derived from study subjects who have been measured at two different points in time (e.g., before and after a treatment). The difference between the means of a continuous outcome variable of this group is compared. The null hypothesis is that the group mean is equal at these two different times. A statistically significant difference rejects the null hypothesis.

52
Q

When is the Paired t test used?

A

The Paired t test is used to compare two means when the data is dependent on an intervention in the same individuals, such as a comparison between a baseline BMI and BMI after a particular treatment.

53
Q

When two different groups (categorical, e.g. cases and controls) are sampled at the same time and their means (continuous outcomes) are used for comparison, what statistical analysis is used? How will this relate to the two hypotheses?

A

An unpaired t-test evaluates two different groups (independent samples) that are sampled at the same time. The difference between the means is a continuous outcome variable of these 2 groups being compared.

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The null hypothesis is that the mean of these two groups is equal and the alternative hypothesis states that there’s a statistically significant difference in the means, thus, will reject the null hypothesis.

54
Q

Unpaired t-test is used to compare the difference between a continuous outcome variable for

A

2 group(s) at 1 point(s) in time

55
Q

What statistical test is appropriate for comparing BMI before and after treatment in 100 patients?

A

The Paired t test is appropriate because the means being compared are dependent (baseline vs. post-treatment in the same individuals).

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Think of quantum entanglement (electrons are paired in time and space).

56
Q

When a study compares the difference between the means of a continuous outcome variable of two or more categorical groups.

A

Analysis of variance (ANOVA)

57
Q

What statistical analysis would be used to determine if there is a statistically significant difference in the mean reduction of blood pressure (a continuous and dependent variable) between different dose groups (e.g., 5 mg, 10 mg, 15 mg; categorical groups) of a given antihypertensive therapy (independent variable)?

A

Analysis of variance (ANOVA)

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The measurement of the mean BP is the dependent variable that happens to be continuous.

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The three doses of antihypertensive therapy is the independent variable that is categorical.

58
Q

When proportions of any type are used for comparison, what studies are important?

A

Chi-squared for big sample sizes

Fisher’s exact test for small sample sizes

59
Q

Proportions, in the context of Chi-squared or Fisher’s exact test, are pseudonymous with …. ?

A

categorical

60
Q

What is the Chi-square test used for?

A

The Chi-square test is used to compare proportions of a categorized outcome, such as serum CRP levels categorized as ‘high’ or ‘normal,’ in a 2x2 contingency table.

61
Q

What is Fisher’s exact test, and when is it used?

A

Fisher’s exact test is used when the sample size is small, particularly when an expected value in either cell of a 2x2 contingency table is less than 10.

62
Q

Do the Chi-squared test or the Fischer’s exact test depend on the number of subgroups or categories?

A

No.

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As long as the dependent variables (e.g. cases [treatment group] vs control [non-treatment group]) as well as the outcomes (e.g. the degree of effect) are organized in a categorical sense.

63
Q

What statistical analysis is used to measure of the strength and direction of a linear relationship between two continuous variables?

A

Pearson correlation coefficient

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This is a statistical measure of the strength and direction of a linear relationship between two variables. A near perfect relationship is when the line that best fits is “1” and ranges anywhere from -1 to +1, where -1 represents a perfectly negative linear relationship and +1 represents a perfectly positive linear relationship.

64
Q

What is the primary aim of survival analysis?

A

To determine the average time to a given outcome identified on follow-up and to measure disease prognosis.

65
Q

What type of study design is survival analysis typically associated with?

A

It is always prospective in nature, often using data from cohort studies or randomized controlled trials (RCTs).

66
Q

What is the Kaplan-Meier curve used for in survival analysis?

A

It is used to analyze incomplete time-to-event data and estimate the survival probability of subjects over time, even if participants drop out or are lost to follow-up.

67
Q

How does the Kaplan-Meier curve visually represent survival analysis?

A

The Kaplan-Meier curve displays survival probability over time as a step-shaped diagram, where each step corresponds to an event such as death or recovery.

68
Q

What is the purpose of the log-rank chi-squared test in survival analysis?

A

The log-rank chi-squared test is used to determine if there is a statistically significant difference in survival curves between two or more groups and provides a p-value where less than 0.05 suggests there is a difference in survival between the two groups being evaluated.

69
Q

What is the value of a hazard ratio in survival analysis?

A

The hazard ratio compares the likelihood of an event occurring at any time point between two groups. A hazard ratio >1 indicates a higher risk in the exposed group, while <1 indicates a lower risk. A value of 1 means there is no difference between the groups being evaluated.

70
Q

What does censoring mean in the context of survival analysis?

A

Censoring occurs when participants do not experience the event of interest during the observation period, such as dropping out or being lost to follow-up. This is notated with either a vertical dash along the stair step curve or a dot.

71
Q

How is survival probability calculated in a Kaplan-Meier analysis?

A

It is calculated for each time interval as the number of patients for whom the event has not occurred divided by the number of patients at risk. For each range of time, probability is multiplied consecutively.

72
Q

What is the significance of the five-year survival rate in survival analysis?

A

It represents the percentage of patients who have survived five years after the initial diagnosis of a disease.

73
Q

What are competing risks in survival analysis?

A

Competing risks refer to events that prevent the occurrence of the primary event of interest, such as death from a different cause.

74
Q

The assumption that there is no association between two measured variables (e.g., the exposure and the outcome) or no significant difference between two studied populations other than what would be expected from sampling or experimental error, is called … ?

A

Null hypothesis

75
Q

When do you fail to reject the null hypothesis?

A

When RR or OR are 1

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If the p-value is less than the predetermined significance level ( \alpha )

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If the confidence interval does not include the null value (e.g., 0 for differences or effects), you reject the null hypothesis. If it includes the null value, you fail to reject the null hypothesis.

76
Q

If using a confidence interval, what value must the interval have in order to fail to reject the null hypothesis?

A

If a null value of “0” is within the confidence interval, fail to reject the null hypothesis (accept the null).

77
Q

What is the probability of rejecting the null hypothesis when it is actually true (the likelihood of concluding that there is an effect or association when there truly is none)?

A

Alpha ( \alpha ) is the probability of committing a Type I error in hypothesis testing.

78
Q

What is the significance of the probability of committing a type 1 error?

A

This is the significance level and the probability of a type I error is denoted by alpha (α).

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This is expressed as the p-value.

79
Q

What type of error occurs when the null hypothesis is rejected despite it actually being true. Consequently, the alternative hypothesis is accepted, although the observed effect is actually due to chance (Wrongfully concluding that there is an association between exposure and disease when in fact there is none)?

A

Type I error

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“False positive”

80
Q

What is the probability of not committing a Type I error?

A

1-alpha

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This represents the confidence level.

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Correctly identifying a true null hypothesis (The probability of correctly failing to reject the null hypothesis when it is true).

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“True negative”

81
Q

When the null hypothesis is false (i.e., the alternative hypothesis is true), but the null is incorrectly not rejected, what type of error has occurred (wrongfully concluding that there is no association between exposure and outcome, when in fact there is one)?

A

Type II error (β)

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When the null hypothesis is false (i.e., the alternative hypothesis is true), but the null is incorrectly not rejected (accepted), a Type II error (β) has occurred. This means the test fails to detect a real association or difference, wrongfully concluding that there is no association between the exposure and the outcome, even though one exists.

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“False negative”

82
Q

When are studies more prone to type II errors?

A
  1. Low statistical power (e.g., small sample size or high data variability).
  2. Weak effect size (the true difference or association is small and hard to detect).
  3. Poor study design or inappropriate statistical tests.
83
Q

In a research study out of 1000 participants, there was no difference between the means. However it was discovered that 400 measurements were inadvertently left out of the analysis. What would happen in terms of the probability of correctly rejecting the no hypothesis if these 400 measurements were incorporated into the analysis?

A

This would increase the sample size. Increasing the sample size of the study by including the 400 patients would result in an increased probability of correctly rejecting the null hypothesis when the alternative hypothesis is true (i.e., increased statistical power). Increased power also leads to a lower likelihood of falsely accepting the null hypothesis when the alternative hypothesis is true (type II error).

84
Q

the probability that a study will detect a true difference is …. ?

A

Statistical power

85
Q

The probability of correctly rejecting the null hypothesis, i.e., the ability to detect a difference between two groups when there truly is a difference, is called … ?

A

(1 - beta)

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Statistical power

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This is the probability of rejecting the null hypothesis when it is false (i.e., correctly detecting the true difference).

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“True Positive”

86
Q

What increases statistical power?

A

Statistical power (1 - beta) positively correlates with the sample size and the magnitude of the association of interest (e.g., increasing the sample size of a study would increase its statistical power) but will inversely impact Type II error (β).

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The higher the precision, the greater the statistical power (1 − β).

87
Q

By convention, most studies set statistical power at … ?

A

Most studies set a statistical power to 80%

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Power primarily depends on the strength of the association (if present) and the size of the sample population. When researchers have an estimate of the strength of the association, they can perform power calculations to determine the sample size required to achieve 80% power.

88
Q

When designing a pilot study, the power is …?

A

fixed a priori (usually at a value ≥ 0.80) meaning from established knowledge.

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The study is then performed using a small number of participants (usually 10–50; the exact number depends on the type of study and type of statistical analysis) and the minimum detectable effect size is measured. Based on this information, a sample size that yields adequate power is calculated, and this sample size is used during the main study.

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The higher the β, the lower the statistical power.

89
Q

Does statistical power affect generalizability?

A

No, statistical power does not directly affect generalizability, but it plays an important role in the reliability of study results. Statistical power refers to the probability of correctly rejecting the null hypothesis when a true association exists (i.e., avoiding a Type II error). Generalizability, on the other hand, refers to how well the findings of a study apply to populations beyond the specific sample studied.

90
Q

Missing the signal is a type_______error.

A

II

91
Q

A false alarm is a type________error.

A

I

92
Q

the probability of incorrectly rejecting the alternative hypothesis is … ?

A

Statistical power

93
Q

The probability that the result of a given statistical test will be at least as extreme as the result actually observed, assuming that the null hypothesis is correct, is called the … ?

A

p-value