Stats MDR + Stats Equations

Types of Data

Categorical (nominal)

• Qualitative

• Quantitative

Ordinal - characterizations of data that have an inherent order

Numerical - observations for which the differences between numbers have meaning on a numerical scale

Types of Numerical Scales

Continuous (interval or ratio)

• Has values on a continuum (e.g. age)

Discrete

• Has values equal to integers (e.g. number of fractures)

Normal distribution of data

Positively skewed data

Negatively skewed data

What happens if you run parametric tests on nonparametric (not normally distributed) data?

It will artificially decrease your p value

QQ Plot

Quantile vs quantile plot

The data is plotted in theoretical vs actual quantiles of the data being analyzed

Dotted line shows an exact Gaussian distribution

What statistical tests can be used to determine normality?

Shapiro-Wilk

D’Agostino-Pearson

What is the central tendency of normally distributed data reported as?

Mean value

• Arithmetic average of the observations

What is not normally distributed data reported as?

Median value

• Middle observation

What is the spread of data for a normally distributed dataset presented as?

Standard deviation

When the data is not normally distributed, what is the spread opften reported as?

Either the 25-75th percentiles (interquartile range), the range, or both

• Interquartile range is used when trying to display the central 50% of data regardless of shape

• Range is used when the purpose is to emphasize extreme values

Null Hypothesis

A statement claiming that there is no difference between either an assumed value or between groups

P Value

The probability that the null hypothesis should be rejected

If the P value is less than 0.05 then those results are considered “significant”

• Accepting there is a less than 5% change that rejecting the null hypothesis was the wrong decision

The lower the P value, the less change that rejecting a correct null hypothesis has occurred

Type 1 Error

Rejecting the null hypothesis when it is correct

Power

The probability of rejecting the null hypothesis when it is false

The ability to detect a true difference

Powered to 80-90% means 80-90% probability that the testing will detect a difference in the sample sets if there is truly one

Type II Error

Accepted the null hypothesis when it was actually false

Sensitivity

True positive rate

Measures the proportion of true positive cases correctly identified by the test or model

Quantifies the ability of the test to detect individuals who have the condition or attribute being tested for

What does high sensitivity indicate?

The test has a low false negative rate

It can effectively identify most of the true positive cases

Good screening test

Specificity

True negative rate

Indicates the proportion of true negative cases correctly identified as negative

Evaluates the ability of the test to accurately exclude individuals who do not possess the condition or attribute being tested for

What does a high specificity suggest?

A low false positive rate

The test can effectively rule out most of the true negative cases

Good for diagnosing

Sensitivity Equation

True positives/(true positives + false negatives)

Specificity Equation

True negatives/(true negatives + false positives)

When is a higher sensitivity desirable?

When the consequences of false negatives are severe

When is higher specificity desirable?

When the consequences of false positives are significant

Positive Predictive Value (PPV)

Measure of the probability that individuals with a positive test rest truly have the condition of interest

Proportion of true positives among all the individuals who tested positive

What does a high PPV indicate?

A positive test result is highly indicative of the presence of the condition

Suggests that a positive test result is highly reliable and can be used to make accurate predictions regarding the presence of the condition

PPV Equation

PPV = (true positives/(true positives + false positives)) x 100

Negative Predictive Value (NPV)

Measure of the probability that individuals with a negative test result truly do not have the condition of interest

Determines the proportion of true negatives among all the individuals who tested negative

What does a high NPV indicate?

A negative test result is highly indicative of the absence of the condition

Suggests that a negative test result is highly reliable and can be used to make accurate predictions regarding the absence of the condition

NPV Equation

NPV = (true negatives/(true negatives + false negatives)) x 100

What influences PPV and NPV?

The prevalence of the condition in the population

• As the prevalence of the condition increases, the PPV tends to increase, while the NPV tends to decrease, and vice versa

1 Sided Tests

Assume difference between groups occur only in one direction

Rarely used

2 Sided Tests

Difference between groups could occur in either direction