What analysis test should be used?

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• one categorical variable from a single population.

1. Chi-square Goodness-of-fit (x^2)

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   • comparing the frequencies you observe in certain categories to the frequencies you might expect to get in those categories by chance using a contingency table.

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• For example you are asking adults which fizzy drink they prefer: Pepsi or Sprite, and comparing the answers given by each gender.

1. Pearson's Chi-square test (x^2)

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   • comparing the frequencies you observe in certain categories to the frequencies you might expect to get in those categories by chance using contingency table.
   • Equation: x^2= SUM OF[ (observed-model)/ model]

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• trying to fit a linear model to the data to outline correlation, i.e. y= bx+c, this model would explain current data and predict future patterns.

1. One predictor (measurement)
   1. Continuous
      1. Degree of relationship (Pearson correlation) r^2

         Annotations:

         • essentially calculates the gradient of the 'line of best fit', so if r^2=1 or -1 it has a perfect positive/negative correlation. As r^2 gets closer to 0, the correlation becomes much less significant.
      2. Form of relationship (Regression)

         Annotations:

         • simple regression analysis
   2. Ranks
      1. Spearman's rs

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         • A bivariate correlation coefficient that works on ranked data. *Ranking the data reduces the impact of outliers. *first rank the data, then apply Pearson's equation(r^2)...
         • EXAMPLE: want to assess how creativity compares to the position awarded in a storytelling competition. Positions recorded and results of a creative questionnaire. Although they use numbers the ranks are technically categories because has no numerical value although the ORDER does matter..
2. Multiple predictors (multiple regression)
   1. Multiple Regression analysis

      Annotations:

      • An outcome is predicted by a linear combination of two or more predictor variables. Outcome= Y, and predictors= X. Each predictor has a regression coefficient 'b' associated with it... Y= (b0 +b1X1 +b2X2 +......bnXn) + E
      • Predictor variables must be chosen based on a sound theoretical rationale- "do NOT just select all random predictors, bung them all into a regression analysis and hope for the best".

1. Two groups
   1. Independent measures/ between-subjects design

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      • so when the data is normally distributed- use independent t-test, if they are not normally distributed use Mann-Whitney. *so if you put the data in order of DV and assign a group- if normally distributed the two groups should have separated i.e. AAAAAABBABBB
      1. Independent sample t-test

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         • establishes whether two means collected from independent samples differ significantly.
      2. Mann Whitney

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         • also tests the difference between 2 samples but is non-parametric.
   2. Repeated measures/ within-subjects design

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      • both look at differences between 2 conditions that are experienced by 1 group. If data is based on a assumption of normal distribution of ranks use related sample t-test, or Wilcoxen if not.
      1. Related sample t-test
      2. Wilcoxen signed-rank test

         Annotations:

         • *NOT to be confused with Wilcoxen's rank-sum test that is similar to independent samples t-test. *Non-parametric version of related-samples so still looks at comparing the scores of 1 group in both conditions, however the test does not make assumptions of normal distribution.
2. Multiple groups
   1. Repeated measures/ within-subjects design
      1. Repeated measures ANOVA
      2. Friedman's ANOVA
   2. Independent measures/ between-subjects design
      1. One independent variable

         Annotations:

         • e.g. 3 groups(influenced differently i.e. luxury/bargain) of wine experts test 3 wines and mean average for each pt across the 3 wines produced for each group. So comparing 3 groups with 1 iv (average score given to wine)
         1. One-way ANOVA
         2. Kruskal-Wallis
      2. Multiple independent variables
         1. Factorial ANOVA