Nature of Science and Data Science

Unit 1: Nature of Science and Data Science

• Key learning outcomes involve identifying scientific method components, variable types, and error sources in experiments
• The outcomes include being able to calculate measures of central tendency (average, median, mode)

What is Science?

• Science utilizes evidence to understand the natural world, functioning as a body of knowledge
• Science deals strictly with the natural world to collect and organize data, which is used to formulate testable explanations

Steps of the Scientific Method

• The scientific method involves asking questions and making initial observations
• After forming a hypothesis, a controlled experiment is setup. The variables that are deliberately changed are 'manipulated variables' and will be the independent variable/x-axis,
• The variables that are observed are 'responding variables', also known as dependent variables and the y-axis
• The typical scientific method concludes by recording and analyzing data, drawing a conclusion and repeating the experiment

Review on Variables

• A variable is any factor in an experiment that can be controlled, changed, or measured
• Independent variables: manipulated variables changed in an experiment represented on the x-axis
  • Example: In an experiment determining the effect of temperature on solubility, the temperature will be the independent variable
• Dependent variables: responding variable that is measured or observed, represented on the y-axis, and is dependent on the state of the independent variable
  • Example: In the same experiment measuring effect on temperature, solubility is the dependent variable

Review on Variables, cont.

• Controlled Variables: Variables that do not change during an experiment. Example: Source of water, size of containers, or mixing time.
• Constant variables are kept the same to ensure a fair test, like the type of battery
• NOTE: Controlled and constant variables are often combined into one variable
• Extraneous Variables: "Extra" variables that may influence the experiment's outcome, ideally, won't impact the final conclusion. If known, they should be in the lab notebook

Scientific Method in Action

• Cricket chirping can be an example of using the sound to measure temperature
• Temperature - What kind of variable (dependent, independent, or controlled)?
• As the temperature decreases, a cricket will chirp fewer times.
• Cricket chirps are more frequent at a hotter temperature.
• The number of chirps is dependent variable
• Cricket subjects must be housed in the same environment such as same lighting, same food, and same water in order to be a controlled variable

Data Science

• Measures of Central Tendency determine what data set is most accurate
• Mean: Average value of given observations
• Median: Middle value of the given observations
• Mode: The most repeated value in the given observation

Variable Types - Categorical

• Nominal (qualitative): Unordered categories which are mutually exclusive. Examples: male/female, smoker/non-smoker
• Ordinal (qualitative): Ordered categories which are mutually exclusive. Examples: 1/2/3/4/5 or minimal/moderate/severe/unberable pain

Variable Types - Numerical

• Discrete (quantitative): Whole numerical value counts such as number of visits to the dentist.
• Continuous (quantitative): Any value within a range, such as height in cm, or pocket depth in mm

Nominal vs. Ordinal Scale

• Nominal (Name) scale: Variables categorized without a natural order or ranking - examples include: genotype, blood type, zip code, gender, race, eye color, political party
• Ordinal Scale (Order): Order matters, but not the difference between values's; examples include: socioeconomic status and education level

Interval vs. Ratio Scale

• Interval Scale: Order exists, and the difference between two values is meaningful - examples include: temperature (Farenheit), temperature (Celcius), pH, SAT score (200-800), credit score (300-850)
• Ratio Variable: Possesses all interval variable attributes, with a clear 0.0 definition indicating the absence of the variable; examples include: enzyme activity, dose amount, reaction rate, flow rate, concentration, pulse, weight, length, temperature in Kelvin (0.0 Kelvin really does mean “no heat"), survival time

Discrete vs. Continuous Variables

• Discrete variables can take on either a finite number of values, or an infinite, but countable number
• Examples include: Number of car accidents at an intersection
• Continuous variables can take on infinitely many values
• Examples include: Body temperature

Summary Statistics

• Equation to calculate average of a data set: average = X₁ + X2... + Xn / n
• Table to calculate Standard Deviation includes height, difference from average, and difference squared with formulas for variance and standard deviation.

Graphing Experimental Data

• A graph represents the relationship between paired variables
• Independent Variable: abscissa, plotted on the x-axis.
• Dependent Variable: Orindate, plotted on the y-axis.
• Equation of the line shows straight line relationships between x and y - commonly formatted as y = mx + b.

Unit 2 - Forces and Motion

• Learning outcomes include determining center of mass, differentiating mass and weight, and use of Newton's Laws
• Other skills include being able to define gravitational force and relate it to two bodies and the distance between them

Center of Mass

• Center of Mass is the point of an object where all the mass is concentrated
• To be in static equilibrium, there must be no net torque acting on the body, as the object is supported at its center of mass

Mass vs. Weight

• Mass: the actual amount of material contained in a body
• Weight: the force exerted by the gravity on that object, or how hard gravity pulls on an object
• Mass is constant, while weight varies based on gravitational force

Translational Motion vs. Rotational Motion

• Translational motion: Motion that involves the sliding of an object in one or more of the three dimensions: x, y, or z.
• Translational motion involves the motion of an (entire) object from one place to another, typically following a straight line
• Example: a boy running

Rotational Motion

• Rotational Motion: Where an object spins around an internal axis in a continuous way
• Rotational motion involves the motion of an object around a pivot point or axis or its center of mass
• Example: An ice skater spinning - to spin faster, the skater would move her arms inward, causing rotation speed to increase

Force vs Torque

• Translational motion affected by force
• Rotational motion affected by torque- the action that causes an object to rotate that can start, stop, or change direction. (torque =twist)
• The formula for Torque (τ) = F d (+ counterclockwise, - clockwise) where F = force (F = ma) and d = lever arm (moment arm) perpendicular distance from the center of rotation to a line along the direction of force

Newton's Law of Motion

• For every action, there is an equal and opposite reaction
• An object at rest will remain at rest unless acted upon by an unbalanced force. An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force - often called "the law of inertia"
• Acceleration is produced when a force acts on a mass, where the greater the mass (of the object being accelerated), the greater the amount of force needed (to accelerate the object)

Wrap-Up of Newton's Laws

• 1st Newton's Law: Natural tendency of objects to keep on doing what they're doing (inertia)
• 2nd Newton's Law: Heavier objects require more force to move the same distance as lighter objects (F = m x a)
• 3rd Newton's Law: For every force there is a reaction force that is equal in size, but opposite in direction

Review of Rules for Significant Figures in Calculations

• Addition and subtraction use the smallest/fewest number of places as they depend on the number of decimal places in the least accurate measurement
• Multiplication and division use small number wins based on the # of sig figs in the result = # in the least precise measurement used in the calculation
• Weakest link principle means the number of significant figures in the final result can't be greater than the weakest link used in the calculation