# Inferential Statistical Tests

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• Inferential Statistical Tests
• Sign Test
• Nominal Data
• Not Frequency Data
• Methods
• 1. State the alternative and null hypothesis.
• This is a non-directional hypothesis therefore requires a two tailed test.
• 2. Record data and work out the "sign".
• The "sign" is wether it is a + or - depending on wether the results are the same or diffrent
• 3. Find the observed value of "S"
• S= the number of times the less frequent value occurs
• 5. State the conclusion.
• If the observed value is smaller than the critical value we must accept the alternative hypothesis, and reject the null hypothesis.
• Chi Square Test
• Nominal Data (The level of data when they are in separate categories. Can includes numbers)
• Frequency Data (occurrences in each category)
• Example study:
• Method:
• 2. Draw up a contingency table. Include totals around it.
• Example of a contingency table
• 1. State the null and alternative non-directional hypothesis.
• The alternative hypothesis is non directional, requiring a two tailed test.
• 3. Compare the observed and expected frequencies (calculated by multiplying two totals, and diving that by the overall total)
• 4.Find the observed value
• 5. Add the critical value
• 6. State the conclusion
• If the observed value is more than the critical value, we accept the alternative hypothesis
• Spearman's Rho Test
• Correlation
• Used to determine the correlation between two co-variables is significant or not.
• Not nominal data
• Method:
• 2. Record and Rank the data.
• 1. State the alternative and null hypothesis.
• Null hypothesis (There will be no correlation) VS Alternative directional hypothesis. This makes Spearman's Rho a one tailed test.
• 3. Calculate the rank difference.
• 4.Find the observed value:    rho=1-(6?d²/ N(N² -1) )
• 5. State the conclusion
• If the observed value is greater than the critical value. It appears that you reject the null hypothesis.
• However, if the sign is in the wrong direction (e.g. negative), and does not support the alternative hypothesis, the null hypothesis is accepted.
• Pairs of scores: Repeated Measures
• Mann Whitney U Test
• Not Nominal Data
• Not correlational
• Independent Groups
• Method
• 3. Find the observed value of U.
• U=(n_1×n_2 )+((n_1×(n_1+1))/2- T-1
• 2. Record the data in a table and find the mean of each condition.
• 4.Find the critical value of U.
• 1. State the alternative hypothesis and null hypothesis.
• The alternative hypothesis is a directional hypothesis therefore requires a one tailed test.
• 5. State the conclusion.
• When p?0.05 for a one tailed test the critical value is (U) and the observed value is (_) therefore the data is significant. This means that we must (reject/accept) the null hypothesis and (accept/reject) the alternate hypothesis.
• If the observed value is smaller than the critical value we must accept the alternate hypothesis.
• 3.Then rank both conditions (all together) from lowest to highest
• 4. Add up all the ranks. (n1= the number of numbers)
• Ordinal Data
• Directional Hypothesis
• Wilcoxon T Test
• Not Nominal Data
• Not correlation
• Not Independent group
• Method
• 3. Rank
• 2. Record, and calculate diffrence
• 4. Find the observed valye of T
• T = the sum of the ranks of the less frequent sign.
• 1. State the alternative and null hypotheses
• Directional. Requires one tailed test.
• 5. Find the critical value of T
• N=sum of participants - omit results.   Look up the critical value in the table
• 6. State the conclusion
• If the observed value is smaller than the critical value, we must accept the alternate hypothesis
• Directional Hypothesis
• At least Ordinal Data