Interval Data

• What does making an inference mean?


  It means taking something we can observe to make a conclusion about something we can't observe.
• When a researcher is taking a sample from a population, the sample...

  might or might not be representative of the population.
• When we analyse our data, we first assume there is no difference between our experimental groups. Then we calculate the probability of observing differences in samples, if there is no real difference between populations.
• What is the name of the statistical test we use to compare our samples?

  T-test
• What is a Null Hypothesis?

  The hypothesis that there is no difference between the experimental groups.
• The t-value gives the probability of observing our results if the null hypothesis is correct. As the t-value increases the probability decreases making the null hypothesis less likely to be correct.
• As the difference between the means get bigger, the probability of observing our results if the null hypothesis is correct gets smaller.
• The bigger the difference between the means, the smaller the probability of observing our results if the null hypothesis is correct. The bigger the t-value, the less likely it is our null hypothesis is correct.
• As the dispersion of the samples’ distributions gets bigger, the t-value gets smaller.
• The bigger the dispersion, the bigger the probability of observing our results if the null hypothesis is correct, and so the more likely it is that the null hypothesis is correct.
• As the sample size increases, the t-value gets bigger.
• As the sample size gets bigger, the probability of observing our results if the null hypothesis is correct gets smaller.
• The bigger the sample size, the bigger the t-value, and so the less likely that the null hypothesis is correct.
• What are the three factors that affect the t-value?

  The three values that affect the t-value are the difference between the means of the samples, the dispersion of the samples, and the sample size
• What is a p-value? (probability)


  The p-value tells us that the null hypothesis is correct, there will be a percentage probability (p-value) of observing the results.
• A bigger t-value causes a smaller p-value and as a result the null hypothesis becomes less likely to be correct.
• What is the p-value?


  The probability of observing our results, if the null hypothesis is correct.
• When researchers decide that their null hypothesis is correct, we say that they accept the null hypothesis.

  And when researchers decide that their null hypothesis is incorrect, we say that they reject the null hypothesis.
• To decide whether their null hypothesis is correct or incorrect, researchers must first decide the p-value at which they’ll switch from accepting the null hypothesis to rejecting it.
• What is the name of the value at which a researcher switches from accepting the null hypothesis, to rejecting it?

  Significance Level
• What is a type 1 error?

  When a researcher incorrectly reject the null hypothesis, and say there is a real difference between two experimental groups when there isn’t one.
• The significance level tells us how likely it is for the researcher to make a type one error.
• What is a type 2 error?

  When researchers fail to reject the null hypothesis, and say there isn’t a difference between the two experimental groups, when there actually is.
• To balance the risk of a Type 1 and Type 2 error, what value do we usually set the significance level at?

  5%
• We can test the null hypothesis without calculating the exact p-value given by our t-value if we know the critical t-value associated with our significance level.
• We reject the null hypothesis if the obtained t-value is bigger than, or equal to, the critical t-value for our significance level.
• When we use a table to find a critical value, we don’t use the sample size, we use the degrees of freedom.
• What is the degrees of freedom?

  The total sample size across the two groups subtract 2.
• What is the alternative hypothesis?

  The opposite of the null hypothesis
• If researchers are just interested in whether there is a difference between the groups in one particular direction, we say that they have a directional alternative hypothesis.
• If researchers are just interested in whether there is a difference between the groups in either direction, we say that they have a non-directional alternative hypothesis.
• When we test a non-directional hypothesis, we call it a two-tailed test. Whereas when we test a directional hypothesis, we call it a one-tailed test.
• What type of test do we use for an independent groups design?

  Unrelated t-test
• What type of test do we use for a repeated measures design?

  Related t-test
• What type of test do we use for a matched pairs design?

  Related t-test
• For the unrelated t-test, what is the degrees of freedom?

  The total sample size across the two groups subtract 2.
• For the related t-test, what is the degrees of freedom?

  The total sample size across the two groups subtract 1.