Scientific Method & Reasoning

Cheatsheet Content

### What is Science? Science is an organized way of using evidence to learn about the natural world. - **Goal:** To investigate and understand the natural world, explain events, and make useful predictions. - **Scientists:** Collect and organize information, looking for patterns and connections. - **Explanations:** Scientists propose explanations that can be tested by examining evidence. ### How Science is Done Science begins with **observation**—the process of gathering information about events or processes in a careful, orderly way. - **Data:** The information gathered from making observations. #### Types of Data 1. **Quantitative Data:** Numbers obtained by counting or measuring. 2. **Qualitative Data:** Descriptions involving characteristics that cannot be counted. ### Hypothesis A **hypothesis** is a scientific explanation for a set of observations. - It is a possible answer to a question. - It must be stated in a way that makes it "testable" and can be thoroughly tested. - It is a prediction that has not yet been proven or disproven. ### Scientific Method Steps A series of steps used by scientists to solve a problem or answer a question. 1. **Observation / Asking a Question:** Identify a problem or question. 2. **Form a Hypothesis:** Develop a testable explanation. 3. **Design a Controlled Experiment:** Plan an experiment to test the hypothesis. 4. **Record and Analyze Results:** Collect and interpret data. 5. **Draw Conclusions:** Determine if the hypothesis is supported or disproven. ### Controlled Experiments - **Variables:** Factors in an experiment that can be changed (e.g., temperature, light, time). - A controlled experiment works with **one variable at a time**. - If several variables were changed, it would be impossible to know which variable caused the observed results. - In a controlled experiment, only one variable is changed, and all other variables are kept unchanged or "controlled." - An experiment is based on comparing a **control group** with an **experimental group**. - These two groups are identical except for one factor. - The **control group** serves as the comparison; the variable being tested is removed. - The **experimental group** shows the effect of the variable being tested. ### Types of Variables - **Independent Variable:** The variable that is **deliberately changed** by the scientist. - **Dependent Variable:** The variable that is **observed** during the experiment; it is the data collected as a result of changing the independent variable. - *Example:* If adding a vaccine ($independent\_variable$) to pills, the observed health of people ($dependent\_variable$) is measured. ### Recording & Analyzing Results 1. Collected data must be organized and analyzed to determine its reliability. 2. Determine if the data supports or does not support the hypothesis. ### Drawing Conclusions - Evidence from the experiment is used to determine if the hypothesis is **proven or disproven**. - Experiments must be repeated multiple times. - When repeated, the results should always be the same for a valid conclusion to be reached. ### Analysis Questions #### Why is a large sample size important? - It helps get a true picture of the experiment's results. - A small sample size can lead to inaccurate conclusions. - Testing a large number of individuals yields more accurate results. #### Why is it important to repeat experiments many times? - To ensure the same results are obtained each time. - Repetition gives validity to the test results. #### What is the importance of the control? - The control shows what happens when the experimental factor is omitted. - Without a control, there would be no basis for comparison, and the effect of the experimental factor would be unknown. #### How is a theory different from a hypothesis? - A **hypothesis** is an "educated guess" that is testable through observations and experimentation. - A **theory** is a broad statement believed to be true based on many experiments and considerable amounts of data. #### Why is it important for scientists to accurately describe their procedure? - It allows other scientists to repeat the experiment and verify the results, ensuring reproducibility and reliability. #### Why must all variables (except one) be kept constant in a controlled experiment? - If several variables were changed simultaneously, the scientist would not know which variable was responsible for the observed results. ### Problem Solving - **Logic:** The science of correct reasoning. - **Reasoning:** Drawing inferences or conclusions from known or assumed facts. - To solve a problem, one must: - Understand the question. - Gather pertinent facts. - Analyze the problem (compare with previous problems, note similarities/differences). - Use tools like pictures or formulas. ### Scientific Observations & Inferences #### Scientific Observations - Can be made directly with senses or indirectly with tools. - Used as evidence to determine if explanations are correct. - **Correction:** Scientists build knowledge by developing ideas about how things work and then testing if observations support those explanations. #### Scientific Inferences - Explanations or interpretations of what you are observing. - Statements that explain observations. - **Process of Inferring:** - Observe an object, event, or situation. - Gather information through experimentation or observation. - Think about existing knowledge and new findings. - Compare results to previous thoughts. ### Deductive Reasoning - A type of logic that goes from a general statement to a specific instance. - **Syllogism:** An argument with two premises (major and minor) followed by a conclusion. - **Validity:** - If the conclusion is guaranteed by the premises, the argument is **valid**. - If the conclusion is not guaranteed (at least one instance where it doesn't follow), the argument is **invalid**. - **Crucial:** Do not confuse truth with validity! An argument can be valid but not true. #### Example 1 - **Major Premise:** All men are mortal. - **Minor Premise:** Socrates is a man. - **Conclusion:** Therefore, Socrates is mortal. (This is a valid syllogism). #### Example 2 - **Major Premise:** All students eat pizza. - **Minor Premise:** Claire is a student at ASU. - **Conclusion:** Therefore, Claire eats pizza. (Valid, but the major premise might not be true). #### Example 3 - **Major Premise:** All math teachers are over 7 feet tall. - **Minor Premise:** Mr. D. is a math teacher. - **Conclusion:** Therefore, Mr. D is over 7 feet tall. (Valid, but the major premise is certainly not true). #### Form of Deductive Arguments - If p, then q. (major premise) - x is p. (minor premise) - Therefore, x is q. (conclusion) ### Venn Diagrams A diagram consisting of overlapping figures (sets) contained in a rectangle (the universe). Used to visualize logical relationships. #### Examples - **All A are B (If A, then B):** Set A is entirely contained within Set B. - **No A are B:** Set A and Set B are separate and do not overlap. - **Some A are B (At least one A is B):** Set A and Set B overlap. #### Example: Construct a Venn Diagram to determine validity - **Argument:** - All smiling cats talk. - The Cheshire Cat smiles. - Therefore, the Cheshire Cat talks. - **Venn Diagram:** - Outer set: "Things that talk" - Inner set: "Smiling cats" (contained within "Things that talk") - 'x' representing the Cheshire Cat is placed within "Smiling cats". - **Conclusion:** Valid argument. #### Example: No one who can afford health insurance is unemployed. All politicians can afford health insurance. Therefore, no politician is unemployed. - **Venn Diagram:** - Set 1: "People who can afford Health Care" (containing "Politicians") - Set 2: "Unemployed" (separate from Set 1) - **Conclusion:** Valid argument. #### Example: Some professors wear glasses. Mr. Einstein wears glasses. Therefore, Mr. Einstein is a professor. - **Venn Diagram:** - Yellow oval: "Professors" - Blue oval: "Glass wearers" - The ovals overlap. If Mr. Einstein ('x') is in the blue oval but not in the overlapping region, the argument is invalid. - **Conclusion:** Invalid argument. ### Inductive Reasoning - Involves going from a series of specific cases to a general statement. - The conclusion in an inductive argument is **never guaranteed**, only probable. #### Example: Sequence 6, 13, 20, 27,... - **Observation:** The difference between consecutive terms is 7 ($13-6=7$, $20-13=7$, $27-20=7$). - **Inductive Conclusion:** The next term is likely $27+7=34$. - **Caveat:** This conclusion is not guaranteed. If the sequence represented dates (e.g., day of the month), the next number could be 3 (for a 31-day month), 4 (30-day month), 5 (29-day month/Feb. Leap year), or 6 (28-day month/Feb.). #### Deduction vs. Induction Summary | Feature | Deduction | Induction | | :-------------- | :-------------------------------------------- | :---------------------------------------------- | | **Association** | "Formal logic" | "Informal logic" / "everyday argument" | | **Process** | Reasoning from known premises to a conclusion | Drawing uncertain inferences from specific cases | | **Conclusion** | Certain, inevitable, inescapable | Probable, reasonable, plausible, believable |