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L6 A&B - Biostatistics Describe, calculate and interpret basic…

- - - - Descriptive Data
        What might me want to know about our sample?
        • What is the average BMI?
        • What is the spread/distribution of BMI?
        • What is the range of BMI ?(Excluding outliers)
        • Anything else?
- - - - Some typical null hypotheses are:
        
        3. The correlation between age and aggression is zero
        
        4. The average income for men is similar to that for women
        
        2. Nationality is (perfectly) unrelated to music preference
        
        1. The average population income was equal over 2012 through 2016
        
        E.g. Is the mean BMI for men, aged 45-64 living in Perth, equal to 27?
        
        H0; mean = 27
        
        H1: Meant =/= 27
    - - p-value
        P-value = probability comparison
        Probability of obtaining our sample mean value, given that the null hypothesis is true
        
        p-value > 0.05
        Fail to reject the null hypothesis
        
        p-value < 0.05
        The null hypothesis is rejected (statistically significant difference) (Pis low and null must go)
      - Should be noted that conclusions are being made with respect to degrees of probability
        
        Type I Error
        Decision to reject the null hypothesis when, in actual fact, it is true
        E.g. if the p-value = 0.03, the null hypothesis should be rejected, yet their is still a 3% chance that the null hypothesis is in fact true
        
        Type II Error
        Failure to reject the null hypothesis when in actual fact it is false
        E.g. p-value = 0.50, we fail to reject the null-hypothesis, when in actual fact there is still a 50% that it is false
      - Failure to find a statistically significant effect in sample data is consistent with either of two interpretations:
        
        The effect does not exist in the underlying population, and the sample data
        merely confirm this state of affairs.
        
        The effect does exist in the underlying population, but the study has
        insufficient power to detect it.
        
        Therefore a on-significant result is INCONLUSIVE
  - - - The number of trials with power ≥80% was low (7%) but increased over time: from 5% in 1975 1979 to 9% in 2010 2014.
      - Determined by;
        For any given effect size and alpha level, increasing the sample size will
        increase power.
        
        Alpha (a)
        Usually set to be 0.05
        
        the probability of a type I error
        
        Effect Size
        The size of the effect in the population. The bigger it is, the easier it will be to find.
        
        Sample Size
        A larger sample size leads to more accurate parameter estimates, which leads to a greater ability to find what we were looking for.
        
        Small samples may be Underpowered
        => fails to capture large population effects
        
        Large Samples may be overpoweed
        =. Captures trivial effects that are not significant
      - Increasing Power
        
        1. Increasing Alpha
        Not Recommended
        
        2. Minimising number of dependant variables in the study.
        Fewer DV’s => less severe statistical correction needed => more power
        Not always possible
        
        3. Reduce Error
        Error variance is non-systematic variability that obscures real population effects
        
        A major source of error derives from unreliable measurement instruments
        
        Only use measurement instruments that have a
        internal reliability of 0.8+ when possible (see lecture week 5)*
        
        4. Increasing the magnitude of the treatment effect
        
        Decreases generalisability
        
        E.g. Research may suggest that the impact of a new quit smoking program is likely to be greatest for adolescents. The impact of the program (and, by implication, the power of any study designed to evaluate the program) can therefore be increased by targeting adolescents.*
        
        5. Recruit the correct number of participants (appropriate sample size) for the statistical test you are planning
- - - - 95% CR = Mean - (1.96 x Standard Error), Mean + (1.96 x S.E.)
      - 99% CR = Mean - (2.58 x Standard Error), Mean + (2.58 x S.E).
      - 90% CR = Mean - (1.64 x Standard Error), Mean + (1.64 x S.E).
      - Standard Error (S.E.) = Sd / (sqrt of n)
      - Emperical Rule
        For large samples samples which can be represented as a normal distribution, 95% of data falls within 2 Sd's of the mean -
        
        Statistical Distribution
        
        95% Sure that the mean falls between within the Confidence Interval
        
        95% of the data will fall between 2Sd's of this Mean