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Can I Believe It? Understanding Statistics in Published Literature. Keira Robinson – MOH Biostatistics Trainee David Schmidt – HETI Rural and Remote Portfolio. Agenda. Welcome Understanding the context Data types Presenting data Common tests Tricks and hints Practice Wrap up.

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Can i believe it understanding statistics in published literature

Can I Believe It?Understanding Statistics in Published Literature

Keira Robinson – MOH Biostatistics Trainee

David Schmidt – HETI Rural and Remote Portfolio


Agenda
Agenda

  • Welcome

  • Understanding the context

  • Data types

  • Presenting data

  • Common tests

  • Tricks and hints

  • Practice

  • Wrap up


Understanding statistics
Understanding statistics

  • Never consider statistics in isolation

  • Consider the rest of the article

    • Who was studied

    • What was measured

    • Why was that measure used

    • Where was the study completed

    • When was it done

  • It is the author’s role to convince you that their results can be believed!



Examples of data table 1 diamond et al 2006
Examples of data – Table 1Diamond et al. 2006


Types of data1
Types of data

  • Numeric

    • Continuous (height, cholesterol)

    • Discrete (number of floors in a building)

  • Categorical

    • Binary (yes/no, ie born in Australia?)

    • Categorical (cancer type)

    • Ordinal categorical (cancer stage)


Histograms
Histograms

  • Represents continuous variables

    • Areas of the bars represent the frequency (count) or percent

  • Indicates the distribution of the data



  • Stem and leaf plot heights
    Stem and leaf plot- heights

    6* 11

    6* 2

    6* 3333333

    6* 44444444444

    6* 555555555555

    6* 66666666666666666666666

    6* 777777777777777777777777777777

    6* 8888888888888888

    6* 99999999999999999999999999999999

    7* 0000000000000000000000000

    7* 1111111111111111111

    7* 222222222222

    7* 333333

    7* 44

    7* 55



    Salient features the mean
    Salient features- the mean

    • The average value:


    Salient features the median
    Salient features- the median

    • The observation in the middle

      • Example- newborn birth weights

      • 3100, 3100,3200,3300,3400,3500,3600,3650 g

        • (3300+3400)/2 = 3350

  • Not affected by extreme values

  • Wastes information



  • Mean and median
    Mean and Median

    • Mean is preferable

    • Symmetric distributions mean ~ median

      • Present the Mean

  • Skewed distributions

    • Mean is pulled toward the ‘tail’

      • Present the Median



  • Variability standard deviation and variance
    Variability – Standard deviation and variance

    • The average distance between the observations and the mean

    • Standard deviation :

    • with original units , ie. 0.3 %

    • Variance =

      • With the original units squared


    Range
    Range

    • Example, infant birth weight

    • 3100, 3100,3200,3300,3400,3500,3600,3650, 3800

      • Range = (3100 to 3800) grams or 700 grams

    • Interquartile range: the range between the first and 3rd quartiles (Q1 and Q3)

      • 3100, 3100,3200,3300,3400,3500,3600,3650 , 3800

        • IQR = (3200 to 3600) grams or 400 grams


    Presenting variability
    Presenting variability

    • Present standard deviation if the mean is used

    • Present Interquartile range if the median is used


    Graphics for continuous variables
    Graphics for Continuous Variables

    • Boxplot :

    outlier

    Maximum in

    Q3

    75th percentile (Q3)

    IQR

    Median

    Minimum in Q1

    25th percentile (Q1)



    Bar charts
    Bar charts

    • Relative frequency for a categorical or discrete variable


    Bar chart vs histogram
    Bar chart vs Histogram

    • Histogram

      • For continuous variables

      • The area represents the frequency

      • Bars join together

    • Bar chart

      • For categorical variables

      • The height represents the frequency

      • The bars don’t join together


    Pie chart
    Pie chart

    • Areas of “slices” represent the frequency



    Presenting statistics
    Presenting statistics

    • Tables should need no further explanation

    • Means

      • No more than one decimal place more than the original data

      • Standard deviations may need an extra decimal place

    • Percentages

      • Not more than one decimal place (sometimes no decimal place)

      • Sample size <100, decimal places are not necessary

      • If sample size <20, may need to report actual numbers



    Sampling
    Sampling

    Inference

    Sampling


    Sampling cont d
    Sampling, cont’d

    • A statistic that is used as an estimate of the population parameter.

    • Example: average parity

    Population

    Mean

    Sample

    Mean


    Confidence intervals
    Confidence intervals

    • We are confident the true mean lies within a range of values

    • 95% Confidence Interval: We are 95% confident that the true mean lies within the range of values

    • If a study is repeated numerous times, we are confident the mean would contain the true mean 95% of the time

    • How does confidence interval change as the sample size increases?



    Hypothesis testing
    Hypothesis testing

    • Is our sample of babies consistent with the Australian population with a known mean birth weight of 3500 grams?

    • Sample mean = 3800 grams, 95% CI of 3650 to 3950 grams

    • 3800 lies outside of this confidence interval range, indicating our sample mean is higher than the true Australian population


    Hypothesis testing1
    Hypothesis testing

    • State a null hypothesis:

      • There is no difference between the sample mean and the true mean: Ho = 3500

      • Calculate a test statistic from the data t = 2.65

      • Report the p-value = 0.012


    What is a p value
    What is a p-value?

    • The probability of obtaining the data, ie a mean weight of 3800 grams or greater if the null hypothesis is true

    • The smaller the p-value, the more evidence against the null hypothesis

      • < 0.0001 to 0.05 – evidence to reject the null hypothesis (statistically significant difference)

      • > 0.05 – evidence to accept the null hypothesis (not statistically significant)


    Summary confidence intervals and p values
    Summary – Confidence intervals and p values

    • P –value: Indicates statistical significance

    • Confidence interval: range of values for which we are 95% certain our true value lies

    • Recommended to present confidence intervals where possible



    T tests
    T tests

    • What are they used for?

      • Analyse means

      • Provide estimate of the difference in means between the two groups and the 95% confidence interval of this difference

      • P-value – a measure of the evidence against the null hypothesis of no difference between the two groups


    T tests paired vs independent
    T tests- paired vs independent

    • Paired:

      • Outcome is measured on the same individual

        • Eg: before and after, cross-over trial

        • Pairs may be two different individuals who are matched on factors like age, sex etc.


    Paired t tests
    Paired T-tests

    • Calculate the difference for each of the pairs

    • The mean weight at baseline was 93 kg and the mean weight at 3 months was 88 kg. The weight at 3 months was 5 kg less compared to the baseline weight 95% CI (-3, 12)


    Paired t tests1
    Paired T-tests

    • There was no evidence that there was a significant change in weight after 3 months (p value = 0.19)

    • Assumptions

      • Bell shaped curve with no outliers

      • Assess shape by graphing the difference

        • Use a histogram or stem and leaf plot


    Independent t tests
    Independent T tests

    • Two groups that are unrelated

    • Eg: weights of different groups of people


    Independent samples t tests
    Independent samples t-tests

    • Same assumption as for paired t tests plus the assumption of independence and equal variance


    Interpretation independent t tests
    Interpretation –independent t tests

    • The mean weight in NW Public was 62 kg and the mean weight in SW Public was 61 kg

    • The mean difference in weight between the two schools was 1 kg (-22, 24)

    • There was no evidence of a significant difference in weight between the two schools (p=0.92)


    One way analysis of variance anova
    One-way Analysis of Variance (ANOVA)

    • What happens when there are more than two groups to compare?

    • Null hypothesis: means for all groups are approximately equal

    • No way to measure the difference in means between more than two groups, so the variance between the groups is analysed

    • Can measure variance within a group as well as variance between groups


    One way anova
    One-way ANOVA

    • Comparing multiple groups


    Interpretations one way anova
    Interpretations – One-way ANOVA

    • There was evidence of a difference between the average student weight between the four schools p<0.05

    • There was evidence of no difference between the average student weight between the four schools p>0.05

    • Not advised to compare all means against each other because there is an increased chance of finding at least 1 result that is significant the more tests that are done


    Assumptions anova
    Assumptions ANOVA

    • Normality, - observations for all groups are normally distributed,

    • Variance in all groups are equal

    • Independence – all groups are independent of each other


    Extensions of one way anova
    Extensions of one-way ANOVA

    • Two way-ANOVA:

      • Multiple factors to be considered. Eg school and type of school (public/private)

    • ANCOVA – Analysis of Covariance

      • Tests group differences while adjusting for a continuous variables (eg. age) and categorical variables


    Linear regression
    Linear Regression

    • Measures the association between two continuous variables (weight and height)

    • Or one continuous variable and several continuous variables (mutliple linear regression)

    • What is the relationship between height and weight?


    Scatter plot of weight and height
    Scatter plot of weight and height

    • Correlation between height and weight = 0.75


    Scatter plot of body fat and height
    Scatter plot of body fat and height

    • Correlation between body fat and height = -0.23


    Linear regression1
    Linear regression

    • Fits a straight line to describe the relationship

    • Assumes

      • Independence for each measure (each person)

      • Linearity (check with scatter plots)

      • Normality (check residuals with a graph)

        • Residuals are the difference between the data point and the regression line

      • Homscedasticity

        • Variability in weight does not change as height changes, ie


    Multiple linear regression
    Multiple Linear Regression

    • Extends the simple linear regression

    • Adjusts for confounding variables

    • Example: Does smoking while pregnant affect infant birth weight?

      • Outcome variable: infant birth weight

      • Exposure variable: maternal smoking

      • Covariates (other variables of interest):

        • Sex of the baby, gestational age


    Confounding variables
    Confounding variables

    • A variable (factor) associated with both the outcome and exposure variables

    • Gestational age is associated with both smoking (exposure) and the outcome (birth weight)

    • Confounders can be assessed by checking the correlation between the variable of interest and the outcome variable

    • Correlation coefficient : -1.0 <r<1.0

    • Rule of thumb: >0.5 or <-0.5 should be considered a confounder


    Example of weight vs height adjusting for sex
    Example of weight vs height adjusting for sex


    Summary for continuous outcomes
    Summary for continuous outcomes

    • Comparing means from two group

      • Use t- tests (paired for same person comparison, independent for independent groups comparison)

    • Comparing means for more than two groups

      • One-way ANOVA

    • Comparing means for two or more groups and adjusting for other variables (ANCOVA)


    Summary for continuous outcomes1
    Summary for continuous outcomes

    • Assessing the relationship between two continuous variables

      • Simple linear regression

    • Assessing the relationship between two or more variables

      • Multiple linear regression



    Chi square tests

    Chi-square tests

    What can a chi-square test answer?


    Chi square tests1
    Chi-Square tests

    • 2x2 tables:


    Chi square tests2
    Chi-square tests

    • Can be used for paired (same person under two different conditions) or independent samples (unrelated people in different groups)

    • Used often in case-control studies where the outcome is categorical (or dichotomous)

    • Tests no association between row and column factors

      • Smoking and low birth weight association

    • The study design defines the appropriate measure of effect


    Cohort studies
    Cohort studies

    • Exposure is determined by

      • Randomisation to different groups

      • followed over time

    • Outcome is determined at the end of follow up

    • Rate of outcome can be estimated


    Cohort studies continued
    Cohort studies continued

    • Eg. Rate of low birth weight in:

      • Smokers: rate = 25/100 = 0.25 = 25%

      • Non-smokers: = 5/105 = 5%

    • Relative risk (RR) = 25/5=5 times higher risk of low birth rate in smokers relative to non-smokers

    • Risk Difference (RD) = 25-5 = 20

    • No relative difference between the low birth rate in smokers and non-smokers RR =1.0

    • No absolute difference in the low birth rate in smokers and non-smokers = RD


    Cross sectional studies
    Cross-Sectional Studies

    • People observed at one point in time (questionnaire)

    • Exposure and outcome are measured at the same time

    • Causal associations cannot be deduced

    • Rate ratio (RR) = 25/5=5 times higher risk of low birth rate in smokers relative to non-smokers

    • Rate Difference (RD) = 25-5 = 20

    • No relative difference between the low birth rate in smokers and non-smokers RR =1.0

    • No absolute difference in the low birth rate in smokers and non-smokers = RD


    Case control studies
    Case-control studies

    • Use for rare outcomes (example: child prodigies)

    • Children are selected based on being a prodigy

      • Eg. 100 child prodigies and 100 children with normal intelligence

    • Determine exposure retrospectively

    • Cannot obtain a rate

    • Must obtain the odds of the outcome and compare using an odds ratio



    Case control studies2
    Case-control studies

    • Odds of being a prodigy:

      • In exposed: 70/50 = 1.4

      • In unexposed: 0.6

      • Odds ratio:

        • 1.4/0.6 = 2.3

        • 2.3 times more likely to have a child prodigy if maternal fish oil supplements were taken during pregnancy

      • Null hypothesis

        • No association between the exposure and the outcome

        • Odds Ratio = 1


    Summary of rr and or
    Summary of RR and OR

    • Both compare the relative likelihood of an outcome between 2 groups

    • RR=1 or OR = 1

      • Outcome is as likely in the exposed and unexposed groups

    • RR>1 or OR >1

      • The outcome is more likely in the exposed group compared to the unexposed group

      • The exposure is a risk factor


    Summary of rr and or1
    Summary of RR and OR

    • RR<1 or OR<1

      • The outcome is less likely in the exposed group compared to the unexposed group

      • The exposure is protective

    • RR cannot be calculated for a case-control study

    • OR ~ RR when the outcome is rare


    Extensions of chi square
    Extensions of Chi-square

    • Small sample sizes

      • Fisher’s exact test

        • Recommended when n<20 or 20 <n<40 and the smallest expected cell count is <5

    • Paired data

      • Exact binomial test for small sample sizes

      • McNemar’s test

    • Multiple regression:

      • Logistic regression




    Fact or fiction
    Fact or Fiction

    • Vaccines and autism?

    • Cell phones and brain tumours?


    Common errors
    Common errors

    • 60.182 kg or 61kg?

      • Reporting measurements with unnecessary precision

    • Age divided into 20-44 years, 45-59 years, 60-74 years, 75+ years

      • Dividing continuous data without explaining why or how

      • Certain boundaries may be chosen to favour certain results

    • Presenting Means and SD for non-normal data

      • What should be presented instead?


    Common errors1
    Common Errors

    • “The effect of more exercise was significant”

    • “The effect of 40 minutes of exercise per day was statistically significant for decreasing weight (p<0.05)”

    • “40 minutes of exercise per day lowered the mean weight of the group from 95 kg to 89 kg, (95% CI = 75-105 kg, p= 0.03)

    • Checking the distribution of the data to determine the appropriate statistical test

      • Using parametric tests when data is not normal

      • Using tests for independent data when the data is paired


    Common errors2
    Common Errors

    • Using linear regression without confirming linearity

    • Not reporting what happened to all patients

      • Leads to bias of the results

    • Data dredging

      • Multiple statistical comparisons until a significant result is found

    • Not accounting for the denominator or adjusting for baseline



    Common errors3
    Common Errors

    • Selection Bias

      • Sampling from a bag of candy where the larger candies are more likely to be chosen

      • On November 13, 2000, Newsweek published the following poll results:




    Common errors4
    Common Errors

    • Other biases (measurement bias, intervention bias)

    • Using cross sectional studies to infer causality

      • More likely to have a c-section if attending a private hospital instead of a public hospital


    Practical example
    Practical example

    • Working in groups quickly read the article provided

    • Summarise

      • What data they used

      • What test

      • Do you believe their findings?

      • Can you explain why?


    Summary
    Summary

    • Statistics must be understood in the context of the whole article

    • Statistical tests must fit the data type

    • Findings should be presented appropriately

    • Beware flashy stats!

    • It’s the author’s job to justify their choices

    • If you don’t believe it- can you base your practice on it?



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