presentation of quantitative data

• tables:

  • in results section of report, raw scores will be converted into descriptive statistics
  • should include title, followed by summary paragraph explaining conclusions drawn
• pie chart:

  • used for discrete data
• bar charts:

  • data can be divided into categories e.g discrete
  • categories on x axis, frequency on y
  • bars separated to show separate categories
• histograms:

  • data is continuous e.g scores, weight
  • x-axis = equal sized intervals of single category
  • y-axis = represents frequency within each interval
• scattergrams:

  • associations between covariables rather than differences
  • either covariable occupies x/y axis
  • each point on graph corresponds to x/y position of covariables
• line graph:

  • represents continuous data
  • uses points connected by lines to show how something changes over time
  • IV on x axis, DV on y axis
• distributions:

  • no skewness = symmetrical
  • positive skew = left modal
  • negative skew = right modal
• normal distributions:

  • symmetrical
  • most people located in middle, few at extreme ends - 68% of data values are within 1SD of mean
  • mean, median, mode all occupy same midpoint of curve
  • tails of curve never reach xaxis
• skewed distributions:

  • positive - most distribution concentrated towards left (mean = highest)
  • negative - most distribution concentrated towards right (mode = highest)
• sign test:

  • -for no improvements, + for improvements
  • remove values that stay the same
  • smallest category = sign
• probability + significance:

  • alternate (h1) - directional/non directional, null (h0)
  • stat test allows us to identify whether hypothesis is correct + whether we accept/reject null hypothesis
  • significant = accept alternate, reject null
  • not significant = reject alternate, accept null
• probability:

  • stat tests work on basis of probability not certainty
• significance level:

  • point where researcher claim to discover a large enough difference with correlation to claim effect has been found
• significance level pt2:

  • researcher can be 95%+ certain that findings are actual differences/correlations not chance - still up to 5% chance, findings arent true
  • if result is significant at 5% level - h0 is rejected, h1 accepted
• changes in significance levels:

  • more stringent levels e.g 0.01 - used with studies with human cost e.g drug trials
  • if study is significant at 0.05, researcher will check stringent levels - lower p value = more statistically significant
• type 1 + 2 errors:

  • occur when inappropriate level of significance is used
• type 1 error:

  • too lenient e.g 10% - results in rejecting null hypothesis which is true (false positive)
• type 2 error:

  • too stringent e.g1% - results in accepting null hypothesis which is false (false negative)