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Basic Statistics for Research: Choosing Appropriate Analyses and Using SPSS Dr. Beth A. Bailey Dr. Tiejian Wu Department of Family Medicine

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Overview Two primary objectives of this workshop: Two primary objectives of this workshop: Learn how to choose the appropriate statistical tests to analyze data Learn how to choose the appropriate statistical tests to analyze data Learn the basics of conducting these tests in SPSS Learn the basics of conducting these tests in SPSS First objective – learn what is important in choosing analyses, and information about some of the more common statistical analyses First objective – learn what is important in choosing analyses, and information about some of the more common statistical analyses Second objective – will get a data set and walk through how to conduct some specific analyses Second objective – will get a data set and walk through how to conduct some specific analyses

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Levels of Measurement Which statistics you can use to analyze your data are determined by the level of measurement of each variable Which statistics you can use to analyze your data are determined by the level of measurement of each variable Four levels of measurement: Four levels of measurement: Nominal Nominal Ordinal Ordinal Interval Interval Ratio Ratio

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Levels of Measurement - Nominal The term “measurement” applied to nominal data collection is actually incorrect The term “measurement” applied to nominal data collection is actually incorrect Nominal refers to differences in quality not quantity Nominal refers to differences in quality not quantity Data is nominal when the best you can do is group it into classes with no particular order Data is nominal when the best you can do is group it into classes with no particular order Numbers can be used to represent the categories, but have no inherent meaning Numbers can be used to represent the categories, but have no inherent meaning Example: religion (Christian, Jewish, Muslim) – can’t say one has “more” Example: religion (Christian, Jewish, Muslim) – can’t say one has “more”

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Levels of Measurement - Ordinal Data has an inherent order, but the distance between the groups is unknown Data has an inherent order, but the distance between the groups is unknown So, categories represent a higher or lower level of the variable, but you don’t know how much higher or lower So, categories represent a higher or lower level of the variable, but you don’t know how much higher or lower Example: weight categories (underweight, normal, overweight, obese) Example: weight categories (underweight, normal, overweight, obese) A variable with only 2 categories can be ordinal if there is an inherent order (ex: course grade recorded as “pass” or “fail”) A variable with only 2 categories can be ordinal if there is an inherent order (ex: course grade recorded as “pass” or “fail”)

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Levels of Measurement - Interval Data categories have an inherent order and the distance between the categories is known Data categories have an inherent order and the distance between the categories is known The data represent a true magnitude so that the difference between equal units is the same The data represent a true magnitude so that the difference between equal units is the same Example: patient temperature – 99, 101, 103 – difference of 2 degrees means the same thing Example: patient temperature – 99, 101, 103 – difference of 2 degrees means the same thing In theory, data could be decimalized when a variable is interval (not always measured with that level of precision, though) In theory, data could be decimalized when a variable is interval (not always measured with that level of precision, though)

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Levels of Measurement - Ratio Data categories have an inherent order and the distance between the categories is known Data categories have an inherent order and the distance between the categories is known In addition – there is a true 0 point that represents the absence of something In addition – there is a true 0 point that represents the absence of something Example: drug dosages – 10mg, 20mg, 30mg, 40mg – 40mg is twice as much as 20mg – 0mg would represent the absence of any drug Example: drug dosages – 10mg, 20mg, 30mg, 40mg – 40mg is twice as much as 20mg – 0mg would represent the absence of any drug Why is temperature not a ratio level variable? Why is temperature not a ratio level variable? For purposes of choosing statistical analyses, the distinction between interval and ratio is unimportant For purposes of choosing statistical analyses, the distinction between interval and ratio is unimportant

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Levels of Measurement A single variable can have more than one level of measurement, depending on how the data are collected. A single variable can have more than one level of measurement, depending on how the data are collected. Example: weight Example: weight assessed as either overweight or not overweight assessed as either overweight or not overweight assessed as an actual value in pounds assessed as an actual value in pounds Since more statistical analysis options are typically available at higher levels of measurement, and you have more power to find effects, data collection should be done at the highest level of measurement possible – it can always be reduced later (ex: weight) Since more statistical analysis options are typically available at higher levels of measurement, and you have more power to find effects, data collection should be done at the highest level of measurement possible – it can always be reduced later (ex: weight)

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Levels of Measurement - Quiz 1. IQ scores 2. Gender 3. Income (as a dollar amount) 4. Income (in 6 categories) 5. Likert scale scores (1=strongly disagree, 2=slightly disagree, 3=neutral, 4=slightly agree, 5=strongly disagree) 6. Cancer status (has cancer, does not have cancer) 7. Practice location (rural, urban) 8. Cigarette smoking (# cig/day) 9. Cigarette smoking (none, up to ½ ppd, ½ ppd-<1 ppd, 1 ppd+)

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Measures of Central Tendency Measures of central tendency allow us to summarize the data collected for a particular variable Measures of central tendency allow us to summarize the data collected for a particular variable Specifically, a measure of central tendency tells you the “typical” level or score of a variable Specifically, a measure of central tendency tells you the “typical” level or score of a variable Three primary measures of central tendency: Three primary measures of central tendency: Mean – average – interval & ratio only Mean – average – interval & ratio only Median – score in the middle – ordinal or higher Median – score in the middle – ordinal or higher Mode – most common score – all LOM Mode – most common score – all LOM

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Measures of Association - Intro Measures of association allow us to determine whether 2 or more variables are related Measures of association allow us to determine whether 2 or more variables are related The measure of association that is appropriate depends on The measure of association that is appropriate depends on the level of measurement of the variables (and number of categories if nominal or ordinal; normality of distribution if interval/ratio) the level of measurement of the variables (and number of categories if nominal or ordinal; normality of distribution if interval/ratio) whether the variables represent independent observations whether the variables represent independent observations Independence of observations Independence of observations Results from the same individual or matched individuals are not independent Results from the same individual or matched individuals are not independent Depends on the study design – the same questions can often be answered with both independent and dependent observations Depends on the study design – the same questions can often be answered with both independent and dependent observations

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Measures of Association - Intro Example: want to know if Drug X significantly lowers cholesterol Example: want to know if Drug X significantly lowers cholesterol There are at least 3 potential study designs: There are at least 3 potential study designs: Take a group of people, measure cholesterol initially and then again after they have taken Drug X for 8 weeks (same people – repeated measures) Take a group of people, measure cholesterol initially and then again after they have taken Drug X for 8 weeks (same people – repeated measures) Take a group of people, divide in to two groups based on age and gender, give 1 group the drug, one group a placebo, then measure cholesterol after 8 weeks (matched groups) Take a group of people, divide in to two groups based on age and gender, give 1 group the drug, one group a placebo, then measure cholesterol after 8 weeks (matched groups) Take a group of people, randomly divide in to two groups, give 1 group the drug, one group the placebo, then measure cholesterol after 8 weeks (independent groups) Take a group of people, randomly divide in to two groups, give 1 group the drug, one group the placebo, then measure cholesterol after 8 weeks (independent groups) What are the variables and levels of measurement? What are the variables and levels of measurement?

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Measures of Association Independent Observations – 2 Variables NominalOrdinal*Interval** Nominal (2 levels) ϰ 2 ; Fisher’s Exact Test Wilcoxon Mann- Whitney Test t-test (indep groups); point biserial Nominal (3+ Levels) ϰ2ϰ2ϰ2ϰ2 Kruskal Wallis one-way ANOVA Ordinal* ϰ 2 ; Mann-Whitney Test Spearman rank test one-way ANOVA; Spearman rank; linear regression Interval** logistic regression; point biserial Spearman rank test Pearson correlation; linear regression Outcome Predictor

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Measures of Association Dependent Observations – 2 Variables NominalOrdinal*Interval** Nominal (2 levels) McNemar test Wilcoxon signed ranks test paired t-test Nominal (3+ Levels) repeated measures logistic regression Friedman test one-way repeated measures ANOVA Outcome Predictor * Ordinal or interval but not normally distributed ** Interval and normally distributed

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Measures of Association - Exercises 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. a. Smoking – defined as positive or negative Birth weight – defined as LBW or normal Independent or dependent groups? Smoking – level of measurement? Birth weight – level of measurement? Appropriate statistical test?

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Measures of Association - Exercises 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. b. Smoking – defined as positive or negative Birth weight – defined as weight in g Independent or dependent groups? Smoking – level of measurement? Birth weight – level of measurement? Appropriate statistical test?

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Measures of Association - Exercises 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. c. Smoking – # cigarettes/day Birth weight – LBW or normal Independent or dependent groups? Smoking – level of measurement? Birth weight – level of measurement? Appropriate statistical test?

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Measures of Association - Exercises 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. d. Smoking – # cigarettes/day Birth weight – weight in gm Independent or dependent groups? Smoking – level of measurement? Birth weight – level of measurement? Appropriate statistical test?

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Measures of Association - Exercises 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. e. Smoking – none, < ppd, ppd+ Birth weight – LBW or normal Independent or dependent groups? Smoking – level of measurement? Birth weight – level of measurement? Appropriate statistical test?

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Measures of Association - Exercises 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. 1. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women during pregnancy and then delivery charts are reviewed and infant birth weight is recorded. f. Smoking – none, < ppd, ppd+ Birth weight – weight in gm Independent or dependent groups? Smoking – level of measurement? Birth weight – level of measurement? Appropriate statistical test?

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Measures of Association - Exercises 2. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women who smoked during their first pregnancy but not during their second pregnancy, and then delivery charts are reviewed and infant birth weight is recorded. 2. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women who smoked during their first pregnancy but not during their second pregnancy, and then delivery charts are reviewed and infant birth weight is recorded. a. Smoking – defined as positive or negative Birth weight – defined as LBW or normal Independent or dependent groups? Smoking – level of measurement? Birth weight – level of measurement? Appropriate statistical test?

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Measures of Association - Exercises 2. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women who smoked during their first pregnancy but not during their second pregnancy, and then delivery charts are reviewed and infant birth weight is recorded. 2. Study designed to look at the association between smoking during pregnancy and newborn birth weight. Smoking status is assessed for 200 women who smoked during their first pregnancy but not during their second pregnancy, and then delivery charts are reviewed and infant birth weight is recorded. b. Smoking – defined as positive or negative Birth weight – weight in gm Independent or dependent groups? Smoking – level of measurement? Birth weight – level of measurement? Appropriate statistical test?

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Measures of Association 3 or more Variables The analysis you choose here will depend on the nature of the question. Generally: The analysis you choose here will depend on the nature of the question. Generally: Regression (multiple or logistic) – 1 outcome (any level), multiple predictors (all interval level) Regression (multiple or logistic) – 1 outcome (any level), multiple predictors (all interval level) ANOVA (factorial ANOVA, ANCOVA) – 1 outcome (interval), multiple predictors (1 or more not interval) ANOVA (factorial ANOVA, ANCOVA) – 1 outcome (interval), multiple predictors (1 or more not interval) MANOVA/MANCOVA – 2+ outcomes (interval), 1+ predictor (1 or more not interval) MANOVA/MANCOVA – 2+ outcomes (interval), 1+ predictor (1 or more not interval) Multivariate multiple linear regression/canonical correlation – 2+ outcomes, 1+ predictor, all interval level Multivariate multiple linear regression/canonical correlation – 2+ outcomes, 1+ predictor, all interval level Repeated measures versions exist for dependent observations Repeated measures versions exist for dependent observations

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Measures of Association - Exercises 3. Same as study 1, but we are interested in looking at how both cigarette smoking and alcohol consumption impact birthweight 3. Same as study 1, but we are interested in looking at how both cigarette smoking and alcohol consumption impact birthweight a. Smoking – defined as # cigarettes/day Alcohol – defined as # oz/day Birth weight – weight in gm Smoking – level of measurement? Alcohol – level of measurement? Birth weight – level of measurement? Appropriate statistical test?

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Measures of Association - Exercises 3. Same as study 1, but we are interested in looking at how both cigarette smoking and alcohol consumption impact birthweight 3. Same as study 1, but we are interested in looking at how both cigarette smoking and alcohol consumption impact birthweight b. Smoking – defined as # cigarettes/day Alcohol – defined as none or any Birth weight – weight in gm Smoking – level of measurement? Alcohol – level of measurement? Birth weight – level of measurement? Appropriate statistical test?

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Measures of Association - Exercises 3. Same as study 1, but we are interested in looking at how both cigarette smoking and alcohol consumption impact birthweight 3. Same as study 1, but we are interested in looking at how both cigarette smoking and alcohol consumption impact birthweight c. Smoking – defined as # cigarettes/day Alcohol – defined as # oz/day Birth weight – LBW or normal Smoking – level of measurement? Alcohol – level of measurement? Birth weight – level of measurement? Appropriate statistical test?

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Measures of Association - Exercises 4. Same as study 3, but we are interested in looking at how smoking and alcohol impact both birthweight and prematurity 4. Same as study 3, but we are interested in looking at how smoking and alcohol impact both birthweight and prematurity Smoking – defined as positive or negative Smoking – defined as positive or negative Alcohol – defined as positive or negative Birth weight – weight in gm Prematurity – gestational age at birth in wks Smoking – level of measurement? Alcohol – level of measurement? Birth weight – level of measurement? Prematurity – level of measurement Appropriate statistical test?

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Basic Statistics for Research: Choosing Appropriate Analyses and Using SPSS Dr. Beth A. Bailey Dr. Tiejian Wu Department of Family Medicine

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