RM; Conditions for statistical tests

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  • Created by: mint75
  • Created on: 29-04-15 14:06

The basics

  • A p value is the probability of obtaining the observed result if the null hypothesis is true. In psych, the minimum accepted stringency level is p=<.05, a 1/20 chance of the result being due to chance. 
  • The different types of data you can have are;
    • 1) Nominal; Data that is catagorically discrete
    • 2) Ordinal; Data that can be ordered, data that has a natural order. But, you can't say for certain that the differences between the values are equal. (e.g a 6th and 7th place difference is not the same as a 1st and 2nd place difference)
    • 3) Interval; Similar to ordinal in that data is ordered, but unlike ordinal the differences between values is always equal, for example 1 degree and 2 degrees.
    • 4) Ratio; Building on ratio, data has equal values between points BUT unlike interval, has an absolute zero, a score of zero is significant, not an absence of a score.
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Binominal test

  • This is a test for NOMINAL DATA with a SINGLE dichotomy.
  • The expected (usually chance, .5) and observed distribution are compared.

Conditions

  • Nominal data
  • A SINGLE dichotomy
  • Scores are from a RANDOM sample of the population
  • Independent scores, each pp contributes one data point
  • The expected distribution is KNOWN
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x2 test of independence

  • A test for NOMINAL data with TWO dichotomies.
  • This tests for an association between two variables, the null hypothesis is that there is none.

Conditions

  • Data is NOMINAL
  • Scores are independent (each pp only contributes one data point)
  • Scores are from a RANDOM sample of the population
  • N >=40 **
  • Each category has n>=5. (expected frequency) **

If ** conditions are not met, use Fishers exact test result.

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One way x2 test (Goodness of fit)

  • This is a test for NOMINAL data, with one variable that has three + categories. It uses the same method as the x2 test of independence.

Conditions

  • Data is NOMINAL
  • Scores are independent, each pp contributes one data point
  • N >= 5
  • Scores are from a random sample of the population

**There is NO alternative test for the One way x2 goodness of fit test.

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T-tests; the basics

  • The t-statistic is a ratio between between-group and within-group variance.
  • A larger t-value means that there is a larger variance between between and within conditions.
  • The meaningfulness of the difference between samples depends on the variability of the sample. 
  • So, the T is the probability that we will obtain the observed result if the null-hypothesis is true.

Conditions

  • These are the main assumptions behind parametric t-tests in general.
    • Data is INTERVAL or RATIO
    • Data is normally distributed
      • To test for this, there needs to be N of > 12
      • Use visualisations of the data e.g boxplots/stem and leaf to check for skew
      • You want a NON-SIGNIFICANT result on shapiro and smirnov tests, these test whether the observed distribution is abnormal.
    • Homogeneity of variance (factor of 3)
      • Use levenes test of equality of variance, also want a non-significant result
    • No extreme outliers (z score > 3)
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Independent samples t-test

  • This test compares the MEANS from two independent groups.

Conditions

  • Data is INTERVAL or RATIO
  • Scores are independent, each pp contributes one data point.
  • Normally distributed data
  • Homogeneity of variance

If these conditions are violated, use the non-parametric alternative, Mann-Whitney U testthis test uses ranks and median rather than the means.

Conditions

  • Random sample of the population
  • Scores are independent, one data point per participant
  • Data is ORDINAL, INTERVAL or RATIO
  • Approximately equal sample sizes of conditions
  • At least 4 participants per condition!
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Paired-Sample t-test

  • This test compares the MEANS from within the group/condition.

Conditions

  • Data is INTERVAL or RATIO
  • The differences between scores of the two conditions need to be normally distributed!
  • N>=12.
  • (T-test general assumptions)

If these assumptions are violated, use the non-para alternative, Wilcoxon-signed-ranks test. This test is based on ranks, results are ordered from low to high. The important value is W, the smallest of the 2 sums of ranks.

  • At least 6 participants.
  • Two data points per participant.
  • Data is at least ORDINAL level.

Non-para tests are generally less powerful than para and so you are more likely to make type 2 errors. But, there are less rules and assumptions to violate.

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One-sample t-test

  • This test compares the MEAN from a set of scores to a pre-determined value. (e.g speed limit)

Conditions

  • Data is INTERVAL or RATIO
  • Scores are independent, each pp contributes one data point
  • Data is normally distributed
  • The comparison value is KNOWN

If these assumptions are violated, use the non-para alternative, the One-sample Wilcoxon signed-ranks test. Rather than the mean, it compares the median of the set of scores to the known value.

Conditions

  • One data point per pp
  • ORDINAL, INTERVAL or RATIO data
  • Test value is known
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