OTHY305 Week 2

OTHY305 Week 2

1. Weighted average

   • Weighted mean= ∑ ni Xi / N
   • ∑ is summation, ni is the number of observations (or participants) in each group, • N is the total number of observations (or participants), and • Xi is the mean of each group.

2. Measure of Variability.

   • A measure of how observations vary about the centre of the distribution. 1. Range, 2. Interquartile range (IQR), 3. Variance. 4. standard deviation.
   • Range: the difference between the largest and the smallest observation
   • Pros: Easily determined.
   • Cons: Depends on only 2 observations. Dependant on the number of observations.
   • IQR & Variance
     • IQR in a box plot is the Upper quartile- lower quartile and represents the middle 50% of the sample.
     • Variance: - Mean of all squared deviations from the mean. - Reflects the contribution of all observations. - allows us to account for the total amount of variation.

3. Standard deviation

   • One problem with eh variance is that the final number obtain is in a squared form ( that is, we squared all the deviations from the mean and do the final number is "inflated" in this way making it difficult to interpret)
   • One solution is to take the share root of the variance so that the number is no longer in a sacred form( or "inflated". the square root of the variance is called the SD
   • the smaller the SD the less spread out the data and the more reliable (consistent)
   • the larger the SD the more spread out the data and the less reliable (consistant)

4. Choosing the measure of variability for your variables.

   • For ordinal, categorical variables: calculate the range and inter-quartile range
   • For continuous variables (ratio or interval scale): you can calculate the range, the IQR, the variance and the standard deviation. the variance and the SD provide the most information since they use all the key values in the distribution in the calculation.

5. Probability distributions. collected data can follow many different types of probability distributions.

   • probability distributions: - Normal distribution. - T distribution. - F distribution. - chi-square. - binomial distribution. - Z distribution.
   • Normal Distribution: a bell shaped and symmetrical theoretical distribution as compared to an empirical distribution with the mean, the median and the mode all coinciding at its peak and with frequencies gradually decreasing at both ends of the curve. it is used with continuous variables.

6. Confidence intervals: the limits within which the true population mean probably lies are called the CI which gives a range of values that might reasonably contain the true population parameter.

   • A CI is defined by the lower confidence limit and the upper confidence limit. this would mean that any proposed value of the population parameter below the calculated lower confidence interval is too low to be accepted as a reasonable value higher than the upper confidence limit is too high

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