Lecture 12: Biostatistics: Choosing a Statistical Test

A Statistical test provides a mechanism for making ...... decisions about a process or processes?

Quantitative - It is a way to evaluate the evidence the data provides against a hypothesis. - It gives information about the relationship/ association between 2 or more variables

The Coefficient of Determination is denoted as ....?- which is calculated as .....?

R^2 r squared - The correlation coefficient of 0.9 corresponds to a coefficient of determination (R2) of 0.81, suggesting that about 81% of the variability of the survival time can be explained by the relationship with BMI levels.

Assumptions of Pearson Correlation include: 1- The data is derived from a ....., or at least representative, sample, 2- Both variables are ......, jointly normally distributed, random variables?

Random - If the data are not representative of the population of interest, one cannot draw meaningful conclusions about that population. Continuous - They follow a bivariate normal distribution in the population from which they were sampled.

Spearman coefficient is a Pearson correlation coefficient calculated with the .... of the values of each of the 2 variables instead of their actual values?

Ranks - Example- ranking survival time and BMI and then look for a relationship

Graphical Representation of a Linear Relationship can be done via a ..... plot with a .... line?

Scatter Regression - A negative relationship is represented by a falling regression line (regression coefficient b < 0) - A positive one by a rising regression line (b > 0). - the plot shows a linear association between 0 and +1 but not exactly +1 because the best fit line is not exactly the same

In the Simple Linear regression equation Beta 0 refers to .... intercept and Beta 1 refers to the ..... ?

Y Slope

Strength of Correlation- ID the Values of r

-A --> +1 -B --> less than +1 greater than 0 -C --> 0 -D --> -1 -E --> between -1 and 0

T Tests are further broken down into Paired t tests(Dependent) and Unpaired T tests (Independent)- when are each used?

-Dependent t tests are used when we are measuring the same 2 groups in different time periods eg: people with cancer survival time measured after 5 months and then measure again after 10 months so group is the same -Independent t tests are used when the 2 groups are different eg: those who smoke vs those who don't smoke

Scatter Plot for Our Data

-r= -0.9 - linear relationship -So as BMI increases survival time decreases

The Correlation coefficient of 0.9 corresponds to a coefficient of determination (R2) of ....., suggesting that about .....% of the variability of the survival time can be explained by the relationship with BMI levels? Thus, as ....% of the variability is yet unexplained, there must be 1 or more other relevant factors that are related to survival time?

0.81 81% 19%

A Coefficient of .... indicates a very Strong relationship, a correlation coefficient of .... could either be interpreted as a "good" or "moderate" correlation depending on the applied rule of thumb?

>0.9 >0.65 - It is also quite capricious to claim that a correlation coefficient of 0.39 represents a "weak" association, whereas 0.40 is a "moderate" association.

Covariance

A measure of linear association between two variables. Positive values indicate a positive relationship; negative values indicate a negative relationship

A Chi-Square test is used to test if there is an association/relationship between 2 ..... variables?

Categorical - A chi-square test for independence compares two variables in a contingency table to see if they are related. - In a more general sense, it tests to see whether distributions of categorical variables differ from each another.

Summary of Tests: 1- For Categorical data we use the .... test 2- For Categorical, 2 Groups- Continuous we use the .... test or .... test 3- For Categorical, more than 2 Groups- Continuous we use the .... test or .... test 4- For 2 sets of Continuous variables we use the ..... test

Chi-squared T test or Z test ANOVA Regression

Regression analysis is a type of statistical evaluation that enables three things- .... , ...... and ......?

Description - Relationships among the dependent variables and the independent variables can be statistically described by means of regression analysis. Estimation - The values of the dependent variables can be estimated from the observed values of the independent variables Prognostication - Risk factors that influence the outcome can be identified, and individual prognoses can be determined

A Monotonic relationship between 2 variables is one in which either: 1- As the value of 1 variable ....., the value of the other variable ....... 2- As the value of 1 variable ..... , the other variable value ....

Increases, Increases Increases, Decreases

How to Choose a Statistical Test?: 1- Is the data .....distributed? 2- Is the ..... aka ...... variable quantitative or categorical? 3- Is the ..... aka ...... variable quantitative or categorical? 4- How many .....are being compared?

Normally Predictor aka Independent Outcome aka Dependent Groups

A Pearson's Correlation Coefficient of: R= +1 denotes a .... Linear and Monotone relationship R= 0 denotes ..... linear or Monotone relationship R< 0 negative indicates a ..... relationship R> 0 negative indicates a ..... relationship

Perfect No Inverse (high values of one variable tend to occur together with low values of the other variable) Positive (high values of one variable tend to occur together with high values of the other variable)

Simple Linear regression equation

y = mx+c - know what each variable corresponds to

A Spearman coefficient is commonly abbreviated as .... which ranges from .... to ...... and has the same interpretation as r? Because ordinal data can also be ranked, use of a Spearman coefficient is not restricted to ..... variables?

ρ (rho) or "rs." r Continuous - By using ranks, the coefficient quantifies strictly monotonic relationships between 2 variables (ranking of the data converts a nonlinear strictly monotonic relationship to a linear relationship).

Practice Q1

Ans: B Mean levels of comparing 2 groups --> T tests - Linear regression --> 2 continuous variables

Practice Q3

Ans: C

Practice Q2

Ans: C - we have 2 categorical groups - symptom severity and type of inhaler A,B,C --> Means D --> 2 continuous variables

A T-test Compares the differences in the Mean of a .... variable between .... groups?

Continuous 2

Analysis of variance (ANOVA) and is a test of hypothesis that is used compare a ..... variable in ..... or more independent comparison groups?

Continuous 3

Pearson's Correlation Coefficient describes a .... relationship whose values range from .... to .....? It is denoted by ....?

Linear +1 to -1 (including 0) r

The (one-way) ANOVA procedure is used to compare the .... of the comparison groups?

Means - Example: Is the mean survival time for women with breast cancer the same among the different races (our dataset has 4 groups)? -Comparing the means of 2 groups --> T test -Comparing the means of more than 2 groups --> ANOVA

Correlation is a measure of a ..... association between 2 ...... random variables?

Monotonic Continuous

Spearman's Rank Correlation describes a .... relationship? Spearman rank correlation can be used for an analysis of the association between data that appears to be ..... but .....?

Monotonic Monotonic Non-Linear

Pearson's Correlation Coefficient provides information about the ... and .....of a relationship between two continuous variables?

Strength Direction - No distinction between the explaining variable and the variable to be explained is necessary

Paired t-tests are considered more powerful than unpaired t-tests because using the same participants or item eliminates ..... between the samples that could be caused by anything other than what's being tested?

Variation - Paired t-tests are used when the same item or group is tested twice, which is also known as a repeated measures t-test.