statistics

• What is the first step in doing a statistical test?

  Write a null hypothesis.
• What is the second step in a statistical test?


  Select a statistical test.
• What is the third step in a statistical test?

  Calculate a test statistic.
• What is the fourth step in a statistical test?


  Identify degrees of freedom.
• What is the fifth step in a statistical test?


  Compare test statistic (calculated value) to critical value for p=0.05.
• What is the sixth step in a statistical test?

  Interpret, accept or reject null hypothesis.
• If the calculated value is greater than the critical value for p=0.05, what do you do with the null hypothesis?

  Reject.
• If the calculated value is lower than the critical value, what do you do with the null hypothesis and why?

  Accept, as there is a greater than 5% probability that the difference between the categories of (context) is due to chance, the differences are not significant.
• Why do we then reject null hypothesis for chi-squared?

  As there is a less than 5% probability that the differences between the two categories of (context) are due to chance and so the differences are significant.
• How do you calculate degrees of freedom for chi-squared?

  Number of categories minus 1.
• What is the equation for chi squared?


  χ² = Σ((O - E)² / E)
• What does Σ mean?

  Sum of.
• What does 'O' mean in equation?

  The collected data.
• What does the 'E' mean in equation?

  Expected results, null hypothesis.
• Do we reject the null hypothesis if the calculated value is equal to the critical value for p=0.05?

  Yes.
• What does Spearman's rank test for and how do you write null hypothesis?

  Testing for the strength of a correlation, the correlation between the (x-axis) and the (y-axis) is due to chance.
• What is the equation for spearman's rank?


  $\rho=$$1-\frac{6 \sum d_{i}^{2}}{n (n^{2}-1)}$
• What is 'd' in the equation of spearman's rank?

  Difference between the two ranks of each row.
• What is 'n' in the equation of spearman's rank?

  Number of things you tested.
• Why would you reject the null hypothesis if the calculated value is equal or larger to critical value for spearman's rank?

  As there's a 5% or less probability that the correlation is due to chance, the correlation is significantly positive/negative.
• What if the calculated value is less than the critical value for spearman's rank?

  As the calculated value doesn't exceed the critical value for p=0.05, this means that there is a greater than 5% probability that the correlation is due to chance, we accept the null hypothesis. The correlation isn't significant.
• what's the formula for standard deviation?

  σ = √(∑(x−¯x)  2 /n (or n-1),
• why do we use standard deviation?

  Measuring variance around a mean.
• How do you calculate the range of where 95% probability that the real mean lies between in standard deviation?

  Mean value + and - (2x standard deviation value)
• what does it mean if the standard deviation values from the samples overlap?

  There's a 95% probability that the differences are not significant and so less than 5% probability that differences are due to chance.
• What does x mean in standard deviation?

  the value in the sample
• what does x bar mean in standard deviation?

  The mean of the sample.
• When would we divide by n-1 in standard deviation?

  when only testing a certain number from a large sample, e.g. there is 100 in a population but we only sample 8 so we use n-1, 8-1=7
• What does n mean in standard deviation and when do we use it?

  n represents the sample size in standard deviation and it is used when the entre population is sampled.
• What does a low standard deviation value mean?

  Repeatable.
• how do we present data produced from chi squared test?

  Bar chart.
• How do you present data produced from a spearman's rank test?

  Line graph with line of best fit showing correlation.
• If the value from spearman's rank is -1, what does it mean?

  perfect negative correlation.
• If the value from spearman's rank is -1.01, what does it mean?


  Invalid. The value of Spearman's rank correlation coefficient cannot be less than -1 or greater than 1.
• What's the equation for t-test?

  t= mean 1 - mean 2/ square root of (standard deviation 1 squared/number of bit of info in sample 1) + (standard deviation 2 squared/number of bit of info in sample 2)
• What does the t-test find out?

  If there is a significant difference between the means of two groups.
• If there is a larger difference between the 2 means, what does this mean for the t-test?

  That statistically, there will more likely be a significant difference between the 2 means.
• If the number of bits of information in the sample increase, what does this mean for the t-test?

  Increased chance of there being a significant difference between 2 means.
• If variance of the 2 samples is large, what does this mean for the t-test?

  The t-test is less likely to detect a significant difference between the means of the two samples.
• What would the null hypothesis be for a t-test?

  There's no significant difference between the 2 means of...(context of question).