stats week 1

stats week 1

1. choice of stats test

   • depends on scale of measurement - categorical vs discrete/continuous
   • depends on properties of data - normally distributed = parametric - not normally distributed = non-parametric
   • depends on research aims and design - description or inference, relational vs experimental (differences) - if experimental - between or within subjects, no. of ivs, no of iv levels
   • choice of descriptive stats - mean and SD for discrete/continuous which is normally distributed - median and range- discrete or continuous which is not normally distributed - mode/frequencies - categorical data

2. scales of measurement

   • nominal = numbers or names serve as labels - but no numerical relationship between values - e.g gender, political party, religion - this is categorical
   • ordinal - data organised by rank, values represent true numerical relationships, but intervals between values may not be equal e.g race position, likert scale ratings - discrete or continuous
   • interval - true numerical relationships and intervals between values are equal - but scale has no true 0 e.g temp, shoe size - discrete or continuous
   • ratio - true numerical relationships, equal intervals, has true 0 - e.g height, distance - discrete/continuous
   • discrete - only whole numbers - continuous - 1.8 pieces of cake is possible

3. features of normal distribution

   • kurtosis - normally distributed data are mesokurtic - data with extreme variations from mesokurtosis cannot be normally distributed - i.e parametric stats not appropriate
     • platykurtic - large SD, flat looking - leptokurtic - very little spread, small SD
   • skew - normal are not skewed - extremely skewed data cannot be considered normal - negative skew - most towards 0, positive most towards 100
   • bimodal distribution - two peaks - uniform - all the same

4. research designs

   • relational - explores the relationship between observed behaviours/phenomena - is able to make predictions but can't imply causality - simplest model comprises two variables (predictor and outcome) - typically, both variables are measured on a discrete or continuous scale - outcome variable must be parametric
   • experimental - seeks to examine the influence of one or more variables on other variables (iv on dv) - can make claims about causality if we have controlled for confounding variables using random allocation, counterbalancing etc - not always possible (quasi experimentally)

5. sample statistics

   • sampling error - degree to which the same stats differ from the equivalent pop. parameters - minimising error - sample must be representative, randomly selected, sufficient in size
     • scores from a normal distributed population can be converted into z-scores (sample mean - population SD / population SD
       • standard normal distribution - 95% of values lie within 1.96 SDs of the mean
   • the sampling distribution is the distribution of a stat across an infinite number of sample
     • plotting all possible sample means gives us the sampling distribution of the mean - its mean is equivalent to the population mean - its standard deviation (the standard error) can be used to express how far an individual sample mean deviates from the population mean
       • in the real world, we would never collect data from all the possible samples, so we would never know true standard error - but we know standard error is related to sample standard deviation- we know that SE is a function of sample size (SE decreases as n increases because the larger the sample size the lower the sampling error) - so we can estimate EW - the sample SD divided by the square root of the sample size
         • sampling distribution of the mean is always normally distributed, its mean is the equivalent to pop. mean, applying hat we know from sample normal distribution. we can say that 95% of the sampled means fall within 1.96SE of the pop mean
           • confidence intervals are estimates of pop. parameters - we have 95% confidence that the pop mean falls between _ and _ - we are declaring that theres still a chance our estimate is wrong
             • so theres a 95% chance that pop. mean lies within the 95% CI for sample mean - to work out 95% CI - sample mean +- 1.96 * ESE
               • however, 1.96 Is based on the z distribution which relates to populations - when calculating the CIs without knowledge of pop. parameters, we actually used the t-dist. for 95% CI it is sample mean +- t0.975 * ESE - the critical value of t is dependent on the degrees of freedom (n-1) - with large samples, the critical value of t reaches 1.96 - but with smaller samples, the boundary is wider

6. hypothesis testing

   • null = no difference between pop. means - always start by assuming null is true - p-vaue - the probability of measuring a difference of that magnitude when the null is true - we set threshold of 0.05 where we are willing to reject the null - so if p is less then 0.05, we will reject the null
     • type 1 error = rejecting null when its actually true, type 2 error = fail to reject null when it isn't true