Finding the Intercept: Teaching an Old Dog New Tricks: Implicit Person Theory and Perceived Statistics Ability Sonya M. Stokes Research Question Statistical Methods Data Visualization Implicit person theory describes beliefs about the malleability of individuals’ characteristics. IPT is measured on a continuum with two extreme types of theorists: entity theorists who believe that individuals are basically static and do not change intrinsically and incrementalists who believe that people are capable of change and development over time. Implicit person theory has been implicated as a driver of performance in domains such as the workplace and family life. It is reasonable to conclude, then, that implicit person theory would also impact academic endeavors– particularly in challenging settings such as collegiate statistics courses. Entity theorists, for example, are less likely to perceive themselves as capable of change and might shy away from challenges while incrementalists are more likely to see the challenges presented in a difficult academic course as an opportunity for growth. To test my hypotheses, I will use regression. Comparison distribution: A sampling distribution of correlation coefficients with a sample size of 15 randomly selected from the population. Population 1: Individuals like those we studied. Population 2: Individuals for whom there is no relationship between Implicit Person Theory and confidence in statistical ability. Assumptions of Regression: Our sample is randomly selected: Not met. Only students in one particular class were sampled. The underlying population is normally distributed: Unknown, and our sample is too small to rely on the Central Limit Theorem. The data is homoscedastic: An examination of the scatterplot does not indicate ay issues with heteroscedasticity. Hypotheses Hypothesis Testing Discussion Null Hypothesis Individuals high on incrementalism theory (low on entity theory) will not be more confident in their ability to perform in statistics. 𝐻 0 : 𝛽≤0 Research Hypothesis Implicit person theory will predict individuals’ perceived capability of mastering statistics such that individuals high on incrementalism will be more confident in their abilities than those who are high in entity theory. 𝐻 1 :𝛽>0 My study examined whether individual’s implicit person theory (specifically incrementalism) predicted their perceived ability to excel in statistics. Although individuals who were high in incrementalism in my sample tended to be higher in confidence in their statistical abilities, the findings were not statistically significant and cannot be generalized to the population. However, this is likely a result of a small sample size and convenience sampling. In the future, studies using more individuals who are randomly sampled from the population might yield significant results. Additionally, confounding variables could be present that might affect the results. For example, a student’s GPA or past performance in math-based courses might also have an effect ton perceived ability to succeed in statistics. Additionally, overall self-efficacy might affect the more specific perceived efficacy in statistics. Despite methodological limitations, the results of my study are promising and very near significance. It is likely that a larger, more representative sample would yield statistically significant results. In practice, this could indicate that by emphasizing the learning curve in statistics and encouraging students that learning is an incremental process, students might feel more optimistic about their statistical abilities. IPT (X) (𝑿− 𝑴 𝑿 ) 𝑿− 𝑴 𝒀 𝟐 Conf. (Y) (𝒀− 𝑴 𝒀 ) 𝒀− 𝑴 𝒀 𝟐 (𝑿− 𝑴 𝑿 )(𝒀− 𝑴 𝒀 ) 7 2.27 5.14 6 0.4 0.16 0.91 1.4 1.96 3.17 1.27 1.60 3 -2.6 6.76 -3.29 5 0.27 0.07 0.37 4 -0.73 0.54 -1.03 2 -2.73 7.47 -3.6 12.96 9.84 -1.6 2.56 -0.43 1 -3.73 13.94 -5.23 13.44 -0.29 -0.6 0.36 -0.16 -1.73 3.00 -2.43 𝑀 𝑋 =4.73 Σ 𝑋− 𝑀 𝑋 2 =66.93 𝑀 𝑌 =5.60 Σ 𝑌− 𝑀 𝑌 2 =51.60 Σ 𝑋− 𝑀 𝑋 𝑌− 𝑀 𝑌 𝑋− 𝑀 𝑋 𝑌− 𝑀 𝑌 =24.40 Sample variances: s X = Σ X− M X 2 N = 66.93 15 =2.11 s Y = Σ Y− M Y 2 N = 51.60 15 =1.85 Correlation coefficient: r XY = Σ X− M X Y− M Y S S X S S Y = 24.40 66.93×51.60 =0.42 Data Collection I collected data from 83 undergraduate students from a statistics class at the University of Houston. Students were offered extra credit in their course for participation in the study. I randomly selected 15 students from the larger pool using SPSS. For the present study, I examine two items that were embedded in a larger survey. Participants rated the degree to which they agreed with statements on a scale of 1 (“Not at all”) to 7(“Completely agree”). The items were as follows: Implicit Person Theory: “As much as I hate to admit it, you can't teach an old dog new tricks. People can't change their deepest attributes.” (Item was reverse coded so higher scores indicate incrementalist theory) Confidence in Statistics Abilities: “I can learn statistics.” Z-score of X=0 𝑧= 𝑋− 𝑀 𝑋 𝑠 𝑋 = 0−4.73 2.11 =−2.24 Z-score of X=1 𝑧= 𝑋− 𝑀 𝑋 𝑠 𝑋 = 1−4.73 2.11 =−1.77 Finding the Intercept: Predicted Y when X=0 𝑧 𝑦 = 𝑟 𝑥𝑦 𝑧 𝑋 = 0.42 −2.24 =−0.94 Convert raw score (intercept) 𝑌 = 𝑧 𝑦 𝑠 𝑌 + 𝑀 𝑌 =−0.94 1.85 +5.60=3.86 Finding the Slope: Predicted Y when X=1 𝑧 𝑦 = 𝑟 𝑥𝑦 𝑧 𝑋 = 0.42 −1.77 =−0.74 Convert raw score 𝑌 = 𝑧 𝑦 𝑠 𝑌 + 𝑀 𝑌 =−0.74 1.85 +5.60=4.23 Calculate slope 4.23−3.86=0.37 Regression Equation: 𝑌 =3.86+0.37𝑋 Check that 𝛽=𝑟 𝛽=𝑏 𝑆 𝑆 𝑋 𝑆 𝑆 𝑌 =0.37 66.93 51.60 =.42 Calculate Critical Value 𝑑𝑓=𝑁−2=15−2=13 𝑟 𝑐𝑟𝑖𝑡 13 𝑓𝑜𝑟𝑝𝑛𝑒 𝑡𝑎𝑖𝑙𝑒𝑑 𝛼=.05: .441 Make a Decition .42<.44, so we fail to reject the null hypothesis