Flashcards
Lecture 6
Cards in this deck (122)
- 1What type of procedures are the t-test and correlation?Parametric
- 2What's the essential characteristic of parametric procedures?They make certain assumptions about the data
- 3What are the assumptions of parametric procedures?1. Homogeneity of variance
2. Comes from a population that is normally distributed (normality)
3. Dependent measures that use at least an interval level of measurement (i.e., interval or ratio, not nominal or ordinal).
4. Independence of error - 4Why is normality framed in terms of the population even though we are looking at the sample?Basis of statistical testing.
Because we don't know what the population distribution actually looks like, we estimate that from what the sample looks like. If the sample is normally distributed, odds are that it comes from a population that's normally distributed. - 5Who came up with NOIRS.S Stevens
- 6What's the idea behind levels of measurement?Quantitative data conveys information, the nature of the information that you can derive from numbers depends on its level of measurement.
- 7How does SPSS divide the levels of measurement?Into three categories, Nominal, Ordinal and Scale.
Rolls interval and ratio into one. - 8Provide lecture examples of variables that met the level of measurement assumption1. Occupational prestige (interval)
2. Parents year of education (ratio) - 9What do you do if those assumptions aren't met?Use non-parametric equivalents.
- 10Provide lecture examples of variables that don't meet the assumption for parametric testsNominal:
1. Sex
2. Race
3. Occupational category
Ordinal:
1. How happy you find your life
2. How exciting you find your life - 11If you change the numbers ascribed to categorical variables, would it make a difference for you analysis? (marker of a nominal variable)No, aslong as the members of each group share the same number.
- 12Provide examples of ordinal levels of measurement1. Horse racing
2. Olympics (1,2,3)
(were you sit in some rank order) - 13When do we use non-parametric procedures?1. When you have variables that ARE NOT interval or ratio? (e.g., sex differences in how exciting people find their lives)
2. Assumptions aren't met and you can't fix them - 14What are non-parametric tests also called?Rank order tests
Rank sum tests
Assumption free tests - 15Why is 'rank' included as part of the terminology for the tests?Most of the procedures operate by ranking the data and running the analysis on the ranks, not the actual scores.
(e.g., if we line up people according to their height, the tests would run the analysis on height rankings not the height). - 16Provide additional examples of how the procedures operate by ranking the data and running the analysis on the ranks, not the actual scores.1. Lowest score given a rank of 1, next lowest score given a rank of 2, and so on.
2. High scores have high ranks; low scores have low ranks. - 17What's an advantage of using non-parametric?Gets rid of problems with outliers and skew (i.e., really high scores just get a higher rank; the actual value is ignored).
- 18When do we use non-parametric procedures? (in more detail)(1) When assumptions are violated and can’t be fixed up with transformations, particularly when the sample size is small
(i.e., less than 20)
(2) When the level of measurement is clearly nominal or ordinal. - 19Expand on: (1) When assumptions are violated and can’t be fixed up with transformations, particularly when the sample size is small (i.e., less than 20)E.g., when using variables that you would normally analyse using parametric procedure but the variable catastrophically fails assumption tests (normality & HOV), particularly when the sample size is small (e.g., < 20).
Two together would urge use of non-parametric tests - 20Does the use of non-parametrics follow a convention?No, it depends on the researcher. A conservative researcher may use non-parametric tests when there's slight deviation. Other researchers rarely use non-parametrics.
- 21When does John say we HAVE TO use non-parametric tests? When does John say we are more obliged to use non-parametric tests?1. When the level of measurement is clearly nominal or ordinal.
2. When assumptions are violated and can’t be fixed up with transformations, particularly when the sample size is small
(i.e., less than 20) - 22Why are non-parametric tests called distribution free tests?Because they don't make assumptions about the distribution of the data
- 23What are the non-parametric equivalents of Pearson's product-moment correlation?Non-parametric correlation:
Kendall’s tau (τ) and Spearman’s rho (ρ) - 24In which scenario would you use Kendall’s tau (τ) and Spearman’s rho (ρ) instead of (r)?When you don't have scale levels of measurement as the assumption of interval scales underlies pearson's r.
- 25When would you use non-parametric correlations? (LECTURE NOTES)1. Use when ONE or BOTH variables is clearly ordinal in nature, or when the
2. Assumptions underlying Pearson’s r are not met (normality).
3. (At a pinch) when the relationship between variables is not linear (curvy linear etc) - 26Why "at a pinch"?There are better methods than non-parametric correlations for analysing non-linear correlations.
- 27Provide an example of a research question that would enlist a non-parametric correlationWhat is the relationship between how exciting people report their lives to be, and how happy they are with their lives?
- 28Frame this as a statistical questionIs there a statistically significant correlation between how exciting people report their lives to be and how happy they report their lives to be?
- 29What is the null?In the population, there is no correlation between how exciting people report their lives to be and how happy their lives are, and any deviation that we see from this in our sample is a reflection of sampling error only.
- 30What are the steps for running the non-parametric alternatives?1. Analyse
2. Correlate
3. Bivariate
4. Enter ordinal variables
5. Check Kendal's tau-b and Spearman - 31Which test to use: Kendall’s or Spearman’s?Spearman’s is most popular.
Kendall’s is recommended for small data sets as it may produce a more reliable outcome. - 32How would you write up the results for a non-parametric correlation?A non-parametric correlation revealed a significant positive correlation between the level of excitement that people reported in their lives, and their overall level of happiness with life, rs = .34, p < .001/τ = .33, p < .001.
(Refer to pg 4 of lecture notes~!) - 33Is the range and interpretation for non-parametric correlations the same as pearson's r?Yes (-1 to +1)
Strength & direction etc are the same. - 34How do you write up Spearman's?rs = .34, p < .001
- 35How do you write up Kendall's?τ = .33, p < .001.
- 36Why is the 's' on the r of the non-parametric test?Subscript that identifies it as Spearman's rho
- 37Do you italicise subscript?NO!!
- 38What are the APA rules re non-parametric correlations?1. No leading zeros
2. To 2 decimal places - 39How do you write in scientific notation in word?Type alphabet (lower and upper case) and then use symbol font
- 40What is the non-parametric equivalent of the independent samples t-test?Mann-Whitney U test
- 41Pose a research question that would require the use of a non-parametric testIs there a sex difference in how happy people report their lives to be?
- 42Reframe this question as a statistical questionIs there a significant difference in the mean ranks associated with how men and women report the happiness in their lives
- 43Is it better to convert questionnaires so that they are interval/ratio?Yes. However, for convenience some questions may need to be simplified
(a 3 point questionnaire rather than a 10 minute questionnaire on happiness) - 44Why is this question framed in terms of ranks? Is there a significant difference in the mean ranks associated with how men and women report the happiness in their livesBecause the mean ranks are being analysed in the test
- 45What is the null hypothesis in this scenario?In the population, there is no difference in how happy men and women report their lives to be, and any deviation that we see in that in our sample is just due to sampling error.
- 46How do you run a Mann-Whitney U test?1. Analyse
2. Non-Parametric tests
3. Legacy Dialogs
4. 2 independent samples
5. Enter test variable
6. Enter grouping variable (with group codes)
7. Ok - 47What do we have to remember with the Mann-Whitney u test?It analyses data on the MEAN RANK, not the arithmetic mean.
- 48What score does the Mann-Whitney get converted into?z-score
(for hypothesis testing purposes) - 49How would you write up the results?A Mann-Whitney U test found that men were found to have a significantly higher mean rank associated with self-reported happiness compared with women, U = 260,818, z = 2.03, p = .042
~italicise U, z and p! & comma in U score - 50Are parametric or non-parametric tests more statistically powerful?Commonly help view that non-parametric tests are not as powerful as their parametric counterparts.
However, there are contradictions in the literature. - 51What are the APA rules in regard to the Mann-Whitney U test1. Uppercase English U
2. Lowercase z (to 2 decimal places)
3. Italicised p
4. Comma in Mann-Whitney statistic if needed
5. Can keep or remove negative score in z score - 52What is the non-parametric equivalent of the Paired Samples t-test?The Wilcoxon Signed Rank Sum Test
- 53What would be a research question in this scenario?Have people’s lives become more exciting over the past year?
- 54How would this be framed as a statistical question?Is there a significant difference in the mean rank associated with responses to the question of how exciting people report their lives now compared with the same question last year?
- 55What is the null in this scenario?In the population, there will be no difference in mean rank associated with the question of how exciting people report their lives to be now compared with last year, and any difference that we see in the sample is nothing more than sampling error.
- 56How do you run a non-parametric equivalent of a paired samples t-test?1. Analyse
2. Nonparametric Tests
3. Legacy dialogs
4. 2 Related Samples
5. Enter variables
6. Wilcoxon
7. Ok - 57What is the non-parametric equivalent of a paired samples t-test called?Wilcoxon Signed Ranks Test
- 58What would a write-up look like?A Wilcoxon Signed Rank Sum Test found a significant difference in the mean rank associated with responses to the question regarding how exciting people self-reported their lives to be this year versus last year, z = 9.44, p < .001, with the overall sample reporting their lives to be more exciting this year.
- 59What is a simple non-parametric test that is used for nominal data?The single sample OR one way or simple χ2.
Chi-square Test. Superscript is the non-italicised 2. - 60What is the chi-square test used for?Study.com:
A statistical test used to compare expected data with what we collected.
John:
See if there's a significant difference in the counts or number between groups. T - 61Provide an example of a chai-sqaure research questionDoes your sample have an equal number of males and females?
(Does our sample reflect the population adequately in terms of number of males and females) - 62Reframe this as a statistical questionIs there a significant difference in the number of males and females in the sample?
- 63What is the null?In the population, males and females will be equally represented (i.e., exactly 50% each) and any deviation that we see in our sample is nothing more than sampling error; χ2 = 0.
- 64If the two groups in a chai square are equally represented, what will chai square equal?0
- 65So what can a chai-square be used for?See if there's a significant difference in the counts or number between groups. This can include more than two groups.
(e.g., are occupational categories equally represented across our sample) - 66How do you run a chai-square?1. Analyse
2. Nonparametric tests
3. Legacy dialogs
4. Chi-square
5. Move variable into top box
6. Ok - 67What's the default split in SPSS for chai-square?50/50
- 68How would a 50/50 split be represented in the frequency count table of the chi-square output?Equal group numbers
- 69Break down the frequency tableIs asking if the 'Observed N' is significantly different from the 'Expected N'.
- 70What is the residual in the table?The difference of what you would get under a null hypothesis and what you actually found
Observed N - Expected N - 71what would the write up for a chai square look like?Men and women were found not to be equally represented in the sample; there was a significantly higher proportion of women (58%) versus men (42%), χ2 (1, N = 1517) = 39.57, p < .001.
- 72Recap: how do you write up results in APA style?Summarise briefly and then write up result in scientific notation
- 73Recap: Chi-square writeup ins scientific notation:χ2 (1, N = 1517) = 39.57, p < .001.
- 74How does a chai-square write up differ from other tests?Includes df and N (1, N = 1517) in parenthesis
- 75Does that chai-square result include a leading zero if small?Yes
- 76Why do we have percentages in a chai square write up?It's the convention because they are easier to consume
- 77What do we use if we want to look at the relationship between two NOMINAL variables? (not interval, ratio or even ordinal)Chi-square (χ2) Analysis
Also called Chi-square (χ2) Analysis of Contingency Tables - 78How is a Chi-square (χ2) different from a Chi-square (χ2) of Contingency (contingency is a fancy word for relationship)Chi-square (χ2) looks at one variable by itself and asks the question are people equally represented in the groups of that one variable whereas Chi-square (χ2) of Contingency Tables looks at the relationship between two variables.
- 79What is the formal definition?Chi-square is used to analysis the relationship between two categorical/nominal/grouping variables.
- 80What parametric test can this be liked to?Pearson's r
- 81Consider the following research scenario: A researcher wants to know whether there are sex differences in how exciting people report their lives. Do males report leading more exciting lives than females (exciting is framed as nominal i.e., exciting, routine or dull). What are the two nominal variables?Sex (nominal/categorical) and whether life is exciting, routine or dull (technically ordinal, but can be treated as nominal/categorical for the point of the example).
- 82What are the different ways in which this question can be framed/considered?1. What is the relationship between gender and life excitement?
2. Is life excitement dependent on gender?
3. Is there a different pattern in response to the life excitement question between men and women?
4. Is there a sex difference in how people respond to this item? - 83What do we have to keep in mind in relation to a chai-square?Chi-square is technically not a test of differences in the same way that a t-test is a test of differences. It’s actually a test of relationships.
Because the variables are nominal/categorical the relationship might actually be a reflection of a difference in the pattern of responding. - 84WHAT DISTINCTION DO WE NEED TO APPRECIATE?Must appreciate the distinction between what’s technically being tested = a relationship;
and what that relationship might be reflecting = a sex difference. - 85How would the research scenario be presented as a statistical question?Is there a statistically significant relationship between gender and whether people find their lives exciting, routine or dull.
- 86How do you get the table called a 'cross tabulation' associated with this test?1. Analyse
2. Descriptive statistics
3. Crosstabs
4. One variable in row and one variable in column
5. oK - 87how do you add % in cross tabs so that you can more easily compare groups?1. Analyse
2. Descriptive statistics
3. Crosstabs
4. One variable in row and one variable in column
5. *Add percentages in cells*
6. OK - 88How do we determine which percentage box to check (row, column etc)How we want to compare our data e.g., row would be appropriate for the example of pg. 17 of the lecture notes.
- 89What is the table (or test overall) on pg. 17 of the lecture notes telling us?There appears to be a relationship between gender and how exciting you report your life to be.
- 90What's the null hypothesis in this scenario?The pattern of response for that question in the population is exactly the same for men and women and any difference that we see in the sample is simply a reflection of sampling error. There is no relationship between sex and whether report their lives as being exciting, routine or dull. χ2 = 0.
- 91How is this written in scientific notation?χ2 = 0.
- 92What are the 'expected counts'? in this statistical test?The results we would see if the null were true (scores equally represented).
(Observed N - Expected N). - 93How do you obtain the expected counts in SPSS?1. Analyse
2. Crosstabs
3. Cells
4. Expected
5. Ok - 94What does the chai square do?Chai square:
1. Looks at the difference between what we actually saw and what we would expect to see under the null.
2. Asks if the observed scores are significantly different from the expected scores under the null. - 95What's the test also commonly called?A contingency table analysis
- 96When we talk about something being contingent, what are we talking about?Something being dependant or related to something else, emphasising the notion that we are looking at a relationship.
- 97What's the method for describing Chi-square (χ2) Analysis of Contingency Tables?2 x 3 contingency table analysis or 2 x 3 chai square (see pg. 18 of lecture notes)
2 levels of variable on left hand 2 (male, female)
x
3 levels (exciting, routine and dull). - 98Recap: how do you describe the design of a chai square*2 x 3* contingency table or *2 x 3* chai square
- 99How do you run a Chi-square (χ2) Analysis of Contingency Tables in SPSS?1. Analyse
2. Descriptive Stats
3. cross tabs
4. Check chi square under statistics
5. Ok - 100What row do you read when you run a Chi-square (χ2) Analysis of Contingency Tables?Top row only
Pearson Chi-Square - 101How do we read the test statistic? (example pg. 18)There is a statistically significant relationship between gender and whether people find their lives dull, routine, or exciting.
- 102Although we can frame this question in many ways (see easier slide), what does the use of the Chi-square (χ2) Analysis of Contingency Tables come down to?Is there a statistically significant RELATIONSHIP
between V1 and V2 - 103what information IS NOT provided by the Chi-square (χ2) Analysis of Contingency Table?What actually caused the statistically significant result
(e.g., higher percentage of men reporting their lives as exciting). - 104Do we read the numbers or percentages in a Chi-square (χ2) Analysis of Contingency Table***Percentages***
as groups may be unequal!! - 105What are the individual combinations of the two variables called?Cells
- 106How do you know how many cells there are?By counting the cells or simple multiplication
(e.g., 2 x 3 = 6 cells) - 107How can we find out what particular combination has led to that significant outcome?Standardised Residuals
can help “tease out” why the significant outcome occurred. - 108Define standardised residualsDifference between what you actually observed and what you would have expected under the null hypothesis, expressed as a standardised number.
- 109Flesh out standardised residuals using lecture example.12 men reported their life as 'Dull' whereas under the null the expected count would be '17.8'. The standardised residual looks at the difference between what we actually saw and what we would expect under the null and standardises it (turns it into a z-score)
- 1101. If the observed score is less than what we expect under the null, what (SR) z score would we get? 2. If the observed score is higher than what we expect under the null, what (SR) z score would we get?1. Negative
2. Positive - 111How do you obtain a standardised residual?1. Analyse
2. Descriptive Stats
3. Cross tabs
4. Cells
5. Residuals (unstandardised = simple mathematical difference)
6. Standardised = z scores - 112What is the residual in the table? What is the std. residual?1. Observed Count - the Expected Count
(check this)
2. The score standardised - 113What does the z score allow you to do?Directly compare the scores
- 114How can we determine which cell is contributing to the statistically significant result?The bigger the standardised residual (positive or negative), the more that that cell is contributing to the significant outcome.
However, there is a range of what can be thought of as making a notable contribution to the significant chi-square. - 115What range do is the rule of thumb for what makes a contribution?+2 or < -2 can be thought of as making a notable contribution to the significant chi-square.
- 116What happens if nothing falls between +2 or < -2 ?Read the 2-3 largest values
(positive or negative). The positive or negative sign provides info.
Example:
1. The disproportionate number of men who find their lives exciting (SR: 1.8)
2. the disproportionate low number of women who find their lives exciting
(SR: -1.6) - 117How do you interpret the previous example?One reason we got that significant chai square is because of the high number of men who reported their lives as exciting vs the relatively low number of women who reported their life as exciting.
- 118What are these after the fact tests that tease out the results called?Post hoc tests
- 119How would you report this finding? see lecture notes and lecture 2.04 fo alternative versions. (e.g., can write both χ2 or full English word but SN is preferred)A 2x3 χ2 analysis revealed a statistically significant relationship between sex and whether life was exciting, routine or dull, χ2 (2, N = 980) = 11.99, p = .002. Examination of the standardised residuals revealed that the relatively high number of men reporting their lives as exciting (1.8) versus the relatively low number of women reporting their lives as exciting (-1.6) contributed to the significant test result.
- 120Does a chai square take a leading zeroYes
- 121Do you report the SR/s if you don't get a significant result?No
- 122What does the fact that it is possible to get a sig. result using both the chai square and Mann-Whitney tell us?The relationship is there, just using diff tests to obtain it.
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- Flashcards on Lecture 6, created by Samar Castelli on 13/07/2018.
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- Samar Castelli · Jul 2018
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- Aug 9, 2018
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