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Prepared by Sarah Perry Johnson Slide 2 Review of Levels of Measurement The 4 Levels of Measurement are: Nominal Ordinal Interval Ratio The subsequent slides will allow us to revisit each level of measurement and review the characteristics of each variable. Slide 3 Slide 4 Nominal Variable Nominal (nom=name) Qualitative No numerical value Discreet Examples: religion, nationality, occupation, etc. Nominal variables are also considered to be categorical. Slide 5 Ordinal Variables Ordinal (order) Quantitative In order of cases greater than or less than; a range Discreet Examples: level of conflict (low to high), socioeconomic status (SES), Starbucks sizes, educational attainment, etc. Slide 6 Slide 7 Interval Variables Interval Quantitative Numerical/integer value; no absolute/fixed 0 point Continuous Example: temperature, depression score (starts at 6, ends at 60) Slide 8 Ratio Variables Ratio Quantitative Numerical/integer value; has an absolute fixed zero point Continuous Examples: number of children, number of cigarettes smoked, number of feet/miles, number of votes Slide 9 Slide 10 Basic Template for Relationships Questions Relationships question: Is there a relationship between [the IV] and [the DV]? Example: Is there a relationship between the number of hours a person studies per day and GPA? Independent Variable: # of daily study hours Dependent Variable: Grade Point Average (GPA) Used for Pearson, Spearman, and Regression Questions Slide 11 Basic Template for Differences Questions Differences question: Is there a difference between [categories of the IV] based on [the DV]? Is there a difference between the United States, China, and Sweden based on GDP? Independent Variable: countries (US, China, and Sweden) Dependent Variable: Gross Domestic Product (GDP score) Used for Chi-Square, T-Test, and ANOVA Questions Slide 12 Charts and Templates Slide 13 Six types of Tests: Variables needed Test NameIVDVSymbol Chi-SquareDiscreet T-TestDiscreetContinuoust ANOVADiscreet (2+)ContinuousF Pearson Correlation Continuous r Spearman Correlation Ordinal rsrs RegressionContinuous -- Slide 14 Chi-Square Test: Variables and Reporting Chi-Square Test Independent Variable: Discreet Dependent Variable: Discreet Report template Is there is a difference between [categories of the IV] based on the [DV]? There is a difference between [categories of the IV] based on the [DV] (chi-square[=?], p-value[p=?]). Slide 15 t-Test: Variables and Reporting t-Test Independent Variable: Discreet (limit: 2 categories) Dependent Variable: Continuous Report template Is there is a difference between [categories of the IV] based on the [DV]? There is a difference between [categories of the IV] based on the [DV] (t-score[t=?], p-value[p=?]). State which category of the IV has more...[Cat 1 has around __% more than Cat 2.] Slide 16 ANOVA: Variables and Reporting ANOVA Independent Variable: Discreet (2 or more categories) Dependent Variable: Continuous Report Template Is there is a difference between [2+ categories of the IV] based on the [DV]? There is a difference between [2+ categories of the IV] based on the [DV] (F-score[F=?], p-value[p=?]). State which category of the IV has the most and the least [Cat 1 has the most and Cat 2 has the least. There is no significant difference between Cat 3, however, the difference between Cat 1 and Cat 2 were significant.] Slide 17 Pearson Correlation: Variables and Reporting Pearson Correlation Independent Variable: Continuous Dependent Variable: Continuous Report Template Is there is a relationship between [the IV] and [the DV]? There is a relationship between [the IV] and [the DV] (r-score[r=?], p- value [p=?]). State the strength and direction: This is a [state strength], [state direction] relationship. State the R (square the r value): [The IV] explains about __% of the variance in [the DV]. Slide 18 Spearman Correlation: Variables and Reporting Spearman Correlation Independent Variable: Ordinal Dependent Variable: Ordinal Report Template Is there a relationship between [the IV] and [the DV]? There is a relationship between [the IV] and [the DV] (r s - score[ r s =?], p-value [p=?]). State the strength and direction: This is a [state strength], [state direction] relationship. No R-square: ordinal variables Slide 19 Regression: Variables and Reporting Regression Independent Variable: Continuous Dependent Variable: Continuous Slide 20 Regression: Variables and Reporting (cont.) Is there a relationship between [the IV] and [the DV]? There is a relationship between [the IV] and [the DV] (p-value[p=?]). State the strength and direction: This is a [state strength], [state direction] relationship. Slide 21 Regression: Variables and Reporting (cont.) State the slope: For each additional [1 unit of the IV] of the [units of analysis], the [DV] is expected to [increase/decrease] by [# units of the DV]. State the R (square the r value): [The IV] explains about __% of the variance in [the DV]. State the y-intercept: In the case that [the IV] is 0, it is predicted that [the DV] will be [amount and units of measurement]. Or: A [unit of analysis] that is [units of measurement of IV] is predicted to be [amount and units of measurement of DV] Slide 22 Multiple Regression: Variables and Reporting Multiple Regression Independent Variable: Continuous (2+) Dependent Variable: Continuous Report Template: Is there a relationship between [IV#1], [IV#2], and [IV#3] with [the DV]? State the Adjusted R 2 : [IV#1], [IV#2], and [IV#3] together explain about [___%] of the variance in [the DV]. Slide 23 Multiple Regression: Variables and Reporting (cont.) Report on the Adjusted R: [IV#1, IV#2, and IV#3] together explain about __% of the variance in [the DV]. Next, state the slope for each IV with the DV. Hint: if you have three IVs, you should write three separate statements: IV#1/DV, IV#2/DV, and IV#3/DV. (see next slide) Slide 24 Multiple Regression: Variables and Reporting (cont.) For each additional [1 unit of the IV#1] of the [units of analysis], the [DV] is expected to [increase/decrease] by [# units of the DV], holding constant for [IV#2] and [IV#3] (p=). For each additional [1 unit of the IV#2] of the [units of analysis], the [DV] is expected to [increase/decrease] by [# units of the DV], holding constant for [IV#1] and [IV#3] (p=). For each additional [1 unit of the IV#3] of the [units of analysis], the [DV] is expected to [increase/decrease] by [# units of the DV], holding constant for [IV#1] and [IV#2] (p=). Slide 25 Multiple Regression: Variables and Reporting (cont.) Each time you report on a slope, add to the end of the statement holding constant for and list the leftover variables. For example: For each additional [1 unit of the IV#1] of the [units of analysis], the [DV] is expected to [increase/decrease] by [# units of the DV], holding constant for [IV#2 and IV#3] (p=). For the test, regarding the slope, you will only have to report on one of the IVs paired with the DV. Slide 26 Slide 27 Strength and Direction of Relationship between Variables r -ValueStrength of RelationshipR 0.81 Slide 28 Example: Pearson correlation- Strength and Direction Is there a relationship between self-concept scores and depression scores? To determine whether there is a statistically significant relationship between the variables, look at the p-value. To determine the strength and direction of the relationship, look at the r-value. Slide 29 Strength and Direction (continued) Strength of the relationship According to our chart, the integer value 0.852 shows that there is a very high/strong relationship between self-concept scores and depression scores. Direction of the relationship According to our chart, the negative sign (-) in front of the integer denotes that the relationship is a negative one (as X increases, Y decreases). So how shall we report this data for a Pearsons Correlation? Slide 30 Strength and Direction (continued) Report template for Pearsons correlation Is there is a relationship between [the IV] and [the DV]? There is a difference between [the IV] and [the DV] (r- score[r=?], p-value [p=?]). State the strength and direction: This is a [state strength], [state direction] relationship. Report: There is a relationship between self-concept scores and depression scores (r=-0.852; p=0.004). This is a very strong, negative relationship. Slide 31 Example: Spearmans Rho According to the above Spearmans rho chart, rs =0.290. Direction: The integer value is positive/negative. Therefore, the direction of the relationship is positive/negative. Strength: According to the strength chart, the value is____________. Therefore, the strength of the relationship is ____________. Slide 32 Spearmans Rho (continued) Time to report on the value for a Spearmans rho: There is a relationship between __________ and __________ (rs=_____;p=_____). This is a ________________ relationship. Slide 33 Slide 34 Most and Least Report on the most and least based on the means report. Variable to Quantify: Jelly beans Sue: 56 Jenny: 39 Carly: 45 Sue has the most jelly beans and Jenny has the least [amount of jelly beans]. Slide 35 Most and Least (continued) Lets evaluate the same type of example from Lab 8. What is the unit of measurement? (Hint-it is contained in the box above the table) What is the largest value? What is the smallest value? Slide 36 Most and Least (continued) Variable to quantify: age Descriptors for least and most in relationship to age Least=Youngest Most=Oldest Perot voters are the youngest and the Clinton voters are the oldest. -Or- People who voted for Perot are the youngest and people who vote for Clinton are the oldest.