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Prepared by Sarah Perry Johnson

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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.

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Nominal Variable Nominal (nom=name) Qualitative No numerical value Discreet Examples: religion, nationality, occupation, etc. Nominal variables are also considered to be categorical.

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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.

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Interval Variables Interval Quantitative Numerical/integer value; no absolute/fixed “0” point Continuous Example: temperature, depression score (starts at 6, ends at 60)

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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

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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

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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

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Charts and Templates

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Six types of Tests: Variables needed Test NameIVDVSymbol Chi-SquareDiscreet χ² T-TestDiscreetContinuoust ANOVADiscreet (2+)ContinuousF Pearson Correlation Continuous r Spearman Correlation Ordinal rsrs RegressionContinuous --

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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[χ²=?], p-value[p=?]).

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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.]

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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.]

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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 R² (square the r value): [The IV] explains about __% of the variance in [the DV].

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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

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Regression: Variables and Reporting Regression Independent Variable: Continuous Dependent Variable: Continuous

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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.

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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 R² (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]

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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].

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Multiple Regression: Variables and Reporting (cont.) Report on the Adjusted R²: [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 IV’s, you should write three separate statements: IV#1/DV, IV#2/DV, and IV#3/DV. (see next slide…)

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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=).

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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 IV’s paired with the DV.

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Strength and Direction of Relationship between Variables r -ValueStrength of RelationshipR² <0.20Slight or weak, almost negligible relationship <0.04 o.20-o.40Low correlation, definite but very small relationship Moderate correlation, substantial relationship High or strong correlation, marked relationship >0.90Very high correlation, very dependable relationship >0.81

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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.

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Strength and Direction (continued) Strength of the relationship According to our chart, the integer value 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 Pearson’s Correlation?

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Strength and Direction (continued) Report template for Pearson’s 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.

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Example: Spearman’s Rho According to the above Spearman’s rho chart, rs = 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 ____________.

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Spearman’s Rho (continued) Time to report on the value for a Spearman’s rho: There is a relationship between __________ and __________ (rs=_____;p=_____). This is a ________________ relationship.

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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].

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Most and Least (continued) Let’s 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?

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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.

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