Correlation and Linear Regression

Correlation and linear regression Q. Explain briefly the differences between simple linear regression and correlation and indicate the assumptions common to both Correletion Correletion no assumption made whether one variable is dependent on the other(s) and is not concerned with the relationship between variables; it gives an estimate as to the degree of association between the variables

Regression regression attempts to describe the dependence of  a variable on one (or more) explanatory variables; it implicitly assumes that there is a one-way causal effect from the explanatory variable(s) to the response variable, regardless of whether the path of effect is direct or indirect

assumptions Both methods attempt to describe the association between two (or more) variables y

Overview What is correlation ? A correlation is a number between -1 and +1 that measures the degree of association between two variables (call them X and Y). y

What is regression? A regression is a number that measure the degree of dependence of 1 variable to a other variable y

What term that use to summarize correlation ? correlation coeeficient y

What factors that summarize the regression ? slope and intercept y

What is correlation coefficients ? term that summarize the stregth of association between 2 variable y

What is the function of correlation coefficients ? to test the hypotheses therefore, we can determine either the association is due to chance or random error y y

Does the correlation examine the direction of relationship ? No y

What are 2 type of correlation coefficients ? spearmen correlation coefficient pearson correlation coefficient y y

What is pearson correlation coefficients ? correlation coefficients that based on original data y

What is spearman correlation coefficients ? correlation coefficients that based on ranked or categorical data y

What is the symbol for correlation coefficients ? R y

What is R ? Does R has values ?

y y

dimensionless dimensionless value range between -1 to + 1

What are 2 type of correlation coefficients ? positive correlation & negative correlation y

What is positive correlation coefficients ? What are 2 type of positive correlation coefficients ? strong positive correleation weak positive correlation y y

What are 2 types of negative correlation coefficients ? no correlation weak negative correlation y y

Does correlation coefficients is affected by units of measurements ? no y

Does correlation can be use for non- linear relationship ? no y

What are 2 cautions that has to be considered to measure coefficients ? first, the presence of outliers second , if the variable measure more than 1 distinct group y y

Overview What is regression ? examine the dependence of one variable to other variable y

How does relationship of regression regress ion summarize ? the relationship is summarize by slope and intercept y

Summary What is slope? the amount of the dependent variable increase as teh independent variable increase y

What is intercept? the value of independent variable when the dependent variable is zero y

Classification What are 2 type of regression ? multivariate regression & linear regression y

What is multivariate regression ? regression that examine simultaneous relationship of continuous variable y

What is formula for multivariate regression ? y= a + b1 + b2x2 y

Give example? predicted hemoglobin level for different age and hematocrit level Hb= 5.24 + 0.11( age ) + 0.097 ( Hct) What is linear regression ? examine on how the changes in one variable causes the changes in other variable y

Give example of linear regression ? hemoglobin increases with age y

What are 2 components of linear regression ? y axis is independent variable x axis is dependent variables y y

What is y variables ? independent variable y

What is x variables ? dependent variables y

Regression line What is regression lines? it is the regression equation that describe the relationship between dependent variable and independent variable y

Give regression equation ? y= a + bx where a is intercept and b is slope y y

How do we calculate b ? b= ( x- x) ( y ² y) /(x- x)2 y

Measures of data symmetry What are 2 types of data symmetry ? Data may be symmetric distribution distribution or data may have skewed distribution y

How does symmetric data look like? First, the data mean & median will be closed Second, the data can be expressed as mean & SD y y

How do we expressed symmetric data? By mean & SD y

How does asymmetric distribution looked like ?

What is skewed distribution ? If data, skewed to the right when its tail is longer to the right  Or skewed to the left if data is skewed when its tail is longer to the left  How do we expressed the data? Data is expressed as median and interquartile range y

Why we don't use mean & SD? Because mean & SD are very sensitive to skewness y

What is skewness? It is an index To which Distribution not symmetric Or The tail of the distribution Skewed/extend to left or right  y y y y y y

How do we calculate skewness ? Sk= 3(mean-median)/SD y

How do we know form the data distribution that the data is normaly distributed. The datas mean & median are closed y

What is the used of skewness ? To assess if the data is normally normally distributed y

What is skewness for normal distribution ? The normal distribution has a symmetric distribution Therefore , it skewness is zero y y

What about skewness to the left and right ? If the data is skewed sk ewed to the left then it has distribution with a negative skewness y

y

y

y

When a curve has extreme scores on the right hand side of the distribution, it is said to be positively skewed When a curve has extreme scores on the left hand side of the distribution, it is said to be positively skewed If the data is skewed to the right then it has distribution distribution with a positive skewness

how does curve for skewness looked like?

What is kurtosis? Measure of the extent  In which Observation are clustered in the tails y y y

What is the use of kurtosis ? To assess if the data is normally normally distributed Use with skewness y y

What is the values of kurtosis if the data is normally distributed? Zero values y

What is the kurtosis for normal distribution ? Zero y

How does the curve look like?

What happened if the data has negative kurtosis ? The distribution of data becomes lighter Data kurus=kurtosis kurus=kurtosis Less cases will fall into tail Curves will contain more score in the center than a normal curve it tend to have higher peaks y y y y y

y

also reffered as leptokurtic

What happened if the data has positive kurtosis ? The distribution of data becomes larger Many cases will fall into tail Curves that have fewer scores in the center than the normal curve y y y

Non parametric test Define nonparametric data ? Nonparametric data is the qualitative data such as ordinal or nominal not in normal distribution , numerical Example ; ordinal data, nominal data

y

y

What is nonparametric test Overview Statistical test that is used to analyse ordinal and categorical data y

what is the function of test This test compare the medium It doesn't compare the means It doesn't estimate standard of deviation

y y y

Advantage of using non-parametric test? 1. Doesn't need to know the the means and SD 2. The outlier has no much effect in the statistical outcomes 3. Doesn't need to rely on estimation of parameter 4. Appropriate for small sample size what is the Disadvantage Not powerful as parametric test not as likely to detect the difference as the parametric test y y

Give example of non-parametric test Wilco xon signed rank Mann-Whitney U Rank correlation (eg Spearman) Chi-squared y y y y

Type y y y y y y

of test use for non-normal distribution the various forms of chi-square tests the Fisher Exact Probability test the Mann-Whitney Test the Wilcoxon Signed-Rank Test the Kruskal-Wallis Test and the Friedman Test

Wilco xon signed-rank test The Wilcoxon signed-rank test is a non-parametric that equivalent to to the paired Student's t-test This test analyze the difference between two paired observation Like the t-test, the Wilco xon test involves comparisons of differences between measurements, It doesnt make an assumption of the distribution between the two variable so it requires that the data are measured at an interval level of measurement. y

y y

y y y

Mann y

However

it does not require assumptions about the form of the distribution of the measurements Whittney test a non-parametric statistical test----equivalent to unpaired T test or two sample test that two independent sample came from the same population

Wilco xon rank sum test y

a non-parametric statistical test----equivalent to unpaired T test or two sample test that two independent sample came from the same population

Kruskal-Wallis one-way analysis of variance

y

y

y y

Kruskal-Wallis one-way analysis of variance is a non-parametric method for testing equality of population medians among groups it is identical to a one-way analysis of variance with the data replaced by their ranks. It is an extension of the Mann-Whitney U test to 3 or more groups the Kruskal-Wallis test does not assume a normal population, unlike the analogous one-way analysis of variance

Parametric test What is parametric data? Parametric data is the quantitative data that involve population parameters such as continous data and discrete data y

what is continuous data?

What is parametric test? Statistical test that is used to analyse normally distributed continous data y

y

This

test is used to analyse numerical data such as cardiac output , renal blood flow

What are five parametric test? t-test ANOVA MANOVA Regression Correlation y y y y y

Parametric test? parametric statistical test is one that makes assumptions about the parameters (defining properties) of the population distribution(s) from which one's data are drawn Statistical test that is used to analyse normally distributed continous data This test is used to analyse numerical data such as cardiac output , renal blood flow y

y y

Q. In a clinical trial why is adequate power important? What factors affect the determination of an adequate sample size? Power of statistical tests what is power of statistical test ? I t is the likelihood to detect there is a difference in the studies y y it is the probablity of the study that can predict the difference when the real difference actually exist How

does we relate power of study to the null hypothesis? I t is the probablity of rejecting y of  rejecting null hypothesis when it is false y rejecting null hypothesis means- reject the statement of no difference in treatment

y

How y

when it false means----there is a difference between treatment does it relate to type 2 error? It

is represent as 1-B(beta)

how does we calculate of power of study? Need to know beta or type 2 error y y Researcher usually set the B at value between 0.05 to 0.2 y The power of test; 1-B y Example ; power of test for study that compare the duration of neuromuscular block in normal and postpartum patient with power analysis of B=0.1 , a=0.05 what is the significance of power of study y y y

To

estimate appropriate samples size for the study I f sample size to small> lack of precision to provide reliable answer I f samples to large> waste time, resources, put patient at risk

How

does the power of study relate to the observation of difference between studies ? y the greater the power the study, y the smaller the difference that will be detected by the test y that means your test is to effeicient in detecting the true nothing but the true difference , therefore tak banyaklah difference can be detected

Q. Write short notes on bias in drug trials and how its influence may be reduced Bias What is bias? y Bias is a systematic non-random deviation of result and inferences from the truth or process that lead to deviation y Bias is any trend in the collection , analysis, interpretation , publication or review of data that lead to coclusion that systematiccly different from truth y Effect of bias; distortion of the truth Why bias is systematic errors ? y Bias is systematic errors that is caused by any factors that systematically affect measurements of variable across sample

y

and it cannot be compensated by increasing sample size

What is the difference between bias and random errors ? y Random errors is errors that is caused by any factors that randomly affect the measurements of variable across sample y It can be minimize/alleviate by studying large number of patients y Bias is systematic errors that is caused by any factors that systematically affect measurements of variable across sample and y it cannot be compensated by increasing sample size

What are some sources of bias? Selection bias Systematic differences in the group that being compared due to incomplete randomisation Example ;volunteer vs non-voluteer, employed vs unemployed , selective refferal, loss to follow up y y

Detection bias The bias that occur when the measurements of the outcome of one group are not as vigilant as the other group Example, pain score , some researcher may have comprehensive pain scoring y

y

Observer bias The bias that occur when the measurements of outcomes is made by the person judgement Example y y

Reporting bias or recall bias The bias that occur due to intentional or unintentional differential recall and thus reporting of information about the exposure or outcome of an association by subjects in one group compared to the other.

y

Response bias Bias that occur when the patients that enrolled the study given the answer that do not reflect their true beliefs Example answer questions in the way they think the questioner wants them to answer rather than according to their true believe y

y y

Publication bias The bias that occur when the studies that has negative result is less likely to be submitted or accepted Publication bias arises from the tendency for researchers and editors to handle experimental results that are positive (they found something) differently from results that are negative (found that something did not happen) or inconclusive y y

How to control bias ? After carefully reviewing our study determining what might effect our results that are not part of the experiment, we need to control for these biases. To control for selection bias, most experiments use what·s called Random Assignment , which means assigning the subjects to each group based on chance rather than human decision. To control for the placebo effect, subjects are often not informed of the purpose of the experiment. This is called a Blind study, because the subjects are blind to the expected results. To control for experimenter biases, we can utilize a Double-Blind study, which means that both the experimenter and the subjects are blind to the purpose and anticipated results of the study y y y y y y y y y

Q. Define Standard Deviation. Explain its application to the use of drugs in clinical anaesthetic practice Overview y

standard deviation is a most common measure of statistical dispersion, measuring how widely spread the values in a data set are.

relationship y y y

If

many data points are close to the mean, then the standard deviation is small; if many data points are far from the mean, then the standard deviation is large. I f all the data values are equal, then the standard deviation is zero.

Formula y

For a population, the standard deviation can be estimated by a modified standard deviation (s) of a sample. ,

y

sigma , 

application in clinical practice standard deviation is imporatance in stating the finding of unknwon parameter the standard deviation can be stated in confidence interval 95% CI = x +/- 1.96 x s/ _/n y y y

Example y y y y y

let say you want to study the mean dose of opioid that can give pain score of 1 in 24 hours therefore , you take let say 100 samples from the sample calculate the means dose opioid to give pain score of 1 , let say x gram then calculate the standard deviation ,  form the value of x and standard deviation you can state the means dose of opioid

Standard deviation & measurements of dispersion How do you describe your data dispersion or variability or scatter? Range I nterquartile range Standard deviation Degree of freedom y y y y

What is variability ? How do they cluster around the central location y y y y

How do we describe variability ? Range, percentile, SD, degree of freedom

What is range ? Range is measure of data dispersion given by the smallest & the largest values Vulnerable to outliers y y

What is interquartile ranges ? Distance between 25th centile and 75th centile Not vulnerable to outliers What is standard deviation ? Is a measure of dispersion of data from the means y y y y

y y

What is abbreviation and formula for standard deviation SD or s or sigma

y

Formula= SD= _/( x- x1)2/ n-1

Give example What is n-1? I t is degree of freedom y

What happened if the data , x is scattered over wide location ? The s or standard deviation would become large y

Can you show it in the graph of normal distribution ?

What is variance? I t is measure of dispersion of values about the mean y

What is the formula? S2= {( x- x1)2/ n-1 I t is square of standard deviation y y

What is coefficients of variations ? SD divided by means x 100% y

For a data of normal distribution , how much is the chance that the data would be dispersed or fall within 1 SD? 68.26% y

For a data of normal distribution , how much is the chance that the data would be dispersed or fall within 2 SD? 95.45% y

For a data of normal distribution , how much is the chance that the data would be dispersed or fall within 3 SD? 99.7% y

Can you draw 1 SD Can you draw 2 SD How many population fall within 1 SD