Statistics Week 1

Statistics Week 1

1. Variables

   • Categorical - gender, football team, eye c colour etc
   • Continuous - temp, weight, height, speed
   • Discrete - no. of cars owned, no. of family members, cases of swine flu, goals scored

2. Population parameters = pop. mean and pop. S.D.

3. Sample stats = sample mean & sample SD

4. Descriptive stats

   • Q's like whats a typical score in my data, how variable are my data, what do my data look like
   • Measures of central tendency
     • Mean, median, mode
       • Which should I use? depends on data set but idea is to give a good indication of typical score
   • Measures of spread/variability
     • Range
       • Problem is that it doesn't always change for distributions with different shapes
     • Variance - calculate mean, calculate deviation for each score from mean, square each scores deviation, average (modified) the squared no.s (so no. of items (e.g 10) -1. So N-1)
       • S.D - all as above, but after calculating modified average then square root the answer

5. Plotting data

   • Box plots
   • Frequency histogram
   • Scatter plot
   • Data summary (e.g bar charts)

6. Samples & Populations

   • Sampling error - the error associated with examining a sample rather than a population - occurs because in our sample we do not have all members of the pop.
     • Pop. parameters differ from sample stats due to random sampling error
     • Sampling error depends upon the size of the sample - big sample, big sampling error less likely, small sample, big sampling error more likely
     • With larger sample, sample mean is more likely to be close to the pop. mean

7. Distributions of data

   • Histogram/frequency plot shows you the distribution of data (shape)
   • Many naturally occurring variables are normal - we say they are normally distributed - e.g IQ and female height - data clusters around a central 'most likely' value
   • Skewed data - positively skewed highest point is to the left, negatively skewed highest point to the right
   • Bimodal - highest points to left and right, dip in the middle