Test name When test should be used Scenario Normal Distribution 68% - 95% - 99.7% Rule One Sample T-Test Describing a Metric variable How many hours of homework do children aged 5-10 do per night. 68% of our data is captured in 1 standard deviation either side of the mean 95% of our data is captured in 2 standard deviations either side of the mean 99.7% of our data is captured in 3 standard deviations either side of the mean Binomial Test Describing a Categorical variable Do young couples prefer Pizza or Burgers for takeout. The normal distribution is described as a "symmetric, bell shaped curve". The normal distribution has a very special property. For any given mean and standard deviation, you can draw a normal curve, and regardless of what the mean and standard deviation happen to be, 95% of values fall within two standard deviations of the mean. So for the distribution of time spent watching TV, where the mean is 4.0 and the standard deviation is 1.5, 95% of values fall between 1 and 7. Pearson's r linear Exploring the relationship between two met- regression 6 = standard deviation of the population = 0.07 ric variables Does hours of homework affect hours of computer games played per night u= mean of the population Paired Samples t- test Repeated measure design between one met- ric and one categorical variable. It was hypothesised that number of online shopping purchases is higher in people who own a computer. It was hypothesised that people who walk to work have higher fitness levels than those who drive to work. 70 1000 x = data value x- u where z = standardised score Mean 2 std dev below mean Independent sam- Independent Group design exploring rela- tionship between one metric and one cate- gorical variable. 2 std dev above mean Proportion = ples t-test 95% 2.5% 2.5% So if 70 out of 1000 people supported tree planting, the proportion of people who support To get the percentage, just multiply this value by 100. In this case, the percentage of people in the mean. To standardise a value, we subtract the mean of the distribution and then divide the A standardised value, also known as a z-score, is just the number of standard deviations above 0 Chi-Sqaure statistic Exploring the relationship between two cate- It was hypothesised that people who own gorical variables. dogs are more likely to also own a cat. Z = 0 2 6 8 ALL FIGURES TO 2 DECIMAL PLACES EXCEPT FOR P VALUE Figure 1.17: Normal distribution with a mean of 4 and a standard deviation of 1.5. IF p < . 050 = significant. IF p >.050 = not significant. If p =. 000, report as p <. 001 If 95% of respondents watch between 1 and 7 hours of TV per day, that means only 5% of values fall outside this range - that's 2.5% of people watch more than 7 hours of TV per day and