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PSY200 CH14 - Expected frequency = expected proportion n o...

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14 Chi-sqaure (X 2 ) test nominal data consist of independent observations in discrete, mutually exclusive and exhaustive categorie o can be used to see whether the distribution of observations in categories could have occurred by chance: if null = true, category is chosen at random compare actual observations with a model to determine how much goodness of fit we have—how well the model fits the data—how well the null fits our data o the closer the model and data, the closer our expected and observed frequencies of each kind of category, the better the model is random (null hypothesis) fits the data o the future apart the actual and expected frequencies, the less well the random categorization o just by chance, random sampling fluctuations, will always have some disparity btwn observed and expected frequencies as disparities become too large—reject null hypothesis model X 2 statistic tells how well null hypothesis model fits the data Compute X 2 : o Compare expected frequencies (null frequency) with observed frequencies
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Unformatted text preview: Expected frequency = expected proportion * n o X 2 equals sum of squared differences between expected and observed frequencies divided by expected frequency o X 2 =∑(O-E) 2 /E X 2 (k,n) o The degrees of freedom for X 2 equals # of deviations btwn observed and expected values that are free to vary Goodness of fit X 2 : df=k-1 o Two-way contingency tables Expected frequency (in each cell)=nCOL(proportionROW) proportionROW=nROW/n expected frequency=nCOL(nROW/n) df = # outcomes minus one (C-1) * # groups minus one (R-1) • df=(C-1)(R-1) • AVOID computing X 2 if: o More than 20% of cells have expected frequency of 5 or less o Any of the cells have an expected frequency of 3 or smaller o ∑(O-E) 2 /E; if using E, we are giving disproportionate weight to very unstable (low frequency) cells o Observations have to be independent for X 2 – cannot use for X 2 related (repeated) measures....
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