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| What nonparametric test do researchers use the most? | chi-square test |
| What are the two most widely used chi-square tests? | 1) chi-square test of independence; 2) Pearson's chi-square test |
| What does the chi-square test provide? | 1) To make inferences about existing relationships between two categorical variables; 2) To make crosstabulated "contingency tables" |
| What is the "null hypothesis" for the chi-square test? | The "null hypothesis" for the chi-squared test stipulates the absence of a relationship between the independent and dependent variables. |
| Specifically, when is the chi-squared test used? | 1) When the independent and dependent variable are measure on a nominal scale; 2) When the variables can be best described through percentages, rather than the mean. |
| Can the chi-squared test be used for the ordinal-level? | Yes, but only when there are a "few catagories". |
| When can the chi-squared test be used for "interval or ratio date"? | 1) When the data has been grouped into catagories; 2) When it is preferable to use more powerful parametric tests (such as ANOVA or t test, with the raw ungrouped data). |
| What does the chi-square test assume? | It assumes that the observed frequencies are "random and an independent sample from the population of interest. |
| With the chi-squared test what is the qualifications for the participants? | Each participant must qualify for only one cell on a contingency table. |
| What does the chi-squared test not do? | 1) It does not make any assumptions about the distribution of values in the population; 2) It does not make assumptions about the homogeneity of group variances. |
| What should the sample size for the chi-squared test be like? | The chi-squared test requires that the "expected frequency" be greater than zero. |
| What is recommend for the expected frequency with the chi-squared test? | The expected frequency is recommended to be at "least 5"; especially, if the number of cells is small (such as with a 2x2 contingency table). |
| With the chi-square test, when there are a large number of cells, what will the test yield? | It will yield valid results if "20% of the cells have less the a 5 frequency" as long as it is "greater than 0"; 2) That all the cells are "greater than 0". |
| With the chi-square test, are "expected and observed frequencies" acceptable? | No, just "expected frequencies". |
| With the chi-squared test, what happens to the "expected frequencies" when the size of the sample increases? | The "expected frequencies" also increase. |
| If the chi-squared test is invalid because of low "expected frequencies (especially with the 2xw table)", in this case what other test can be use? | Fisher's exact test |
| What does the chi-squared test contrast? | It contrasts the "observed frequencies" in each cell of a contingency table with the "expected frequencies". |
| What are the "observed frequencies"? | The "observed frequencies" are the actual data. |
| What are the "expected frequencies"? | The number of cases in each cell that would make the "null hypothesis true". |
| What will the chi-square atatistic be if the actual observed frequencies in a crosstabs table are "identical" to the expected frequencies? | The chi-square statistic would be "0" (the value of the chi-square for two unrelated variables). |
| Why will a "chi-square statistic" not exactly equal "0"? | That is because of sampling error. |
| What needs to be done with the "chi-square statistic" because of an "sampling error"? | The "chi-square statistic" needs to be compared to a "critical value" in a table to determine if the statistic is "improbable" at a "specified significance criteron". |
| What are the "critical value statistics" based on? | They are based on "sampling distribution of the chi-square statistic". |
| Are there more than one "chi-square distribution"? | Yes, dependIng on the the degrees of freedom (that depends on the number of catagories for each variable. |
| What happens to the "sampling distribution" of the "chi-square test" when there are "only two levels (2x2)"? | It "corresponds less closely" to "the chi-square distribution" (when the "levels" are "increased for at least one variable" then the "correspondence is greater"). |
| What "correction factor" is used for a "smaller frequency" such "as the 2x2 tables" in order to "improve the correspondence of the variables"? | The "Yates continuity correction" is used in these cases and it is "routinely calculated" in "SPSS (Statistical Packages for the Social Sciences) for 2x2 contingency tables". |
| How is the "Yates continuity correction" calculated? | The "Yates continuity correction" involves substracting "0.5" from the "absolute value of O-E (observation minus the expected frequencies)" for "each cell before this value is squared (thus, "making the value of the statistic smaller)". |
| Why is the "Yates continuity correction" controversial? | The reason it is controversial is because it "reduces the power". |
| When should the "Yates continuity correction" not be applied? | It should not be applied when the "expected frequencies" are "large". |
| Can the "Yates continuity correction" give researchers a false "null hypothesis" or "non-null hypothesis"? | Yes, especially when the "expected frequencies" are "large". |
| When SPSS executes a command to produce the chi-square statisitc, can it compute other similar statistics? | Yes, it can. |
| What other statistic can a "SPSS execution" compute? | The "chi-square" which is an alternative method of testing the null hypothesis of lack of relationship between rows and columns of a crosstab table. It is computed differently than the "Pearson chi-square" but it produces the same results and usually yields the same results. |
| What does this symbol "df" stand for in statistics? | "degrees of freedon" |
| What does this symbol "X^2" stand for in statistics? | "Chi-square statistic" |
| When a 2x2 contingency table has led to the rejection of the null hypothesis, how can the direction of the relationship between the two variables be determined? | It can be determined by "inspecting the percentages". |
| How is ANOVA and the chi-square test similar? | They both apply the data for the two variables "taken as a whole". |
| For tables greater than 2x2, what is not provided? | For tables greater than 2x2, a significant chi-square provides no information regarding which cells are reponsibile for rejecting the null hypothesis. |
| Which column on a contingency table helps to gain descriptive insight into the nature of the relationship? | It is "column "6" entilted "X^2". |
| How many cells are in a "4x2 contingency table"? | There are eight (8) cells. |
| On a contingency table, which cells tell researchers the ones that will most likely contribute to a disproportionate contribution to a higher "X^2"? | They would be the cells with the "highest values" and it would help in knowing those that led to the rejection of the null hypothesis. |
| What does the "chi-square test" help in understanding? | It provides information about the existence of a relationship between the two nominal-level variables. |
| What does the "chi-square test" not help in understanding? | It does not help in understanding the "magnitude of the relationship". |
| For a 2x2 contingency table, what can be used to determine the "magnitude of a relationship" between two nominal-level variables? | One can use the "phi coefficient" [its formula is "the square root of X^2 divided by the square root of "N (the number)]. |
| What is the range of the "phi coefficient"? | Its ranges from 0 to 1 (the "larger" the phi coefficient the stronger is the relationship between the variables (example: a reading of a "0.05" would indicate a "weak realtionship"). |
| What is used to measure the strenght of a realtionship between two nominal-level variables when the contingency table is "greater" than 2x2? | Researchers use the "Cramer's V statistic". |
| What is the range of the "Cramer's V statistic? | Its range is 0 to 1 (the "larger" the V statistic the stonger the relationship; also, the "larger" the value of the V statistic means that there is a tendency for particular categories of the independent variable to be associated with a particular category of the dependent variable). |
| Whe are "the odd ration (OR) and "relative risk (RR) most often used? | They are most often used with "2x2 contingency tables". |
| What tests can be used for the likelihood of a null hypothesis regarding the lack of relationship between a risk factor and an event (outcome)? | They are the following: 1) Cochran's chi-square; 2) Mantel-Haenszel's chi-square. |
| When can "Cramer's V statistic" be used for "any size table"? | It can be used for "any size table" as the "effective index" in a "power analysis". |
| When is a "power analysis" most used? | A "power analysis" is most often used in planning a study to estimate how large a sample is needed; in addition, researchers need to have an estimate of "Cramer's V statistic) in this situation. |
| What is a "Post-hoc power analysis"? | A "Post-hoc power analysis" is used sometimes to interpret results; especially, when the chi-square statistic is "non-significant". |
| When using "Carmer's V statistic", what is needed for "alpha"? | Different tables are needed for contingency tables of different dimensions and for different levels of alpha. |
| What is the most commonly used application of the "chi-squared statistic"?" | It is the "chi-square test of independence". |
| What is the "chi-square goodness-of-fit test"? | It is used to "draw inferences" when there is "one nominal-level variable" and when researchers have theoretical or other reasons for hypothesizing a specific population proportion (the "goodness-of-fit test" is similar to a "one-sample t test"). |
| When is the "Bonferroni correction" used? | When researchers are "testing hypothesis with multiple dependent variables (some feel that the "Bonferroni corredction" is too "conservative"). |
| When is the "McNemar test" used? | The "McNemar test" is used to test difference in proportions for "dependent groups" in a "2x2 contingency table" within-subject design (the McNemar test has only "one-degree of freedom"). |
| When is it better to use the "McNeamr test" rather than the "chi-square distribution"? | It is better to use the "Mcneamr test" over the "chi-square distribution" when the "sample size is very small". |
| What is the "Wilcoxon signed-ranks test"? | The "Wilcoxon signed-ranks test" is the "nonparametric" counterpart of the paired (depend groups) "t test". It is used when the outcomes are "measured on an ordinal scale"; further' it is used to test group differences in ordinal-level measurements when there are two paired groups or within a subjects design. |
