Exam #3 Study Guide
★ NOTE: The chapters jump back and forth, so we’ll take it concept-by-concept!
👦🏻 PART 1: Probability, significance, hypotheses, and errors 👴🏻
● In statistics, we use tools to help determine whether we think an event is as likely, more
likely, or less likely to be caused by chance than what we [originally] expect.
1. Prediction: “Will it happen?”
2. Probability: “How likely is it to happen?”
3. Significance: “Is this likeliness due to chance or something else?”
● Probability: A tool that gives us the ability to calculate the odds a research outcome is
(or is not) due to chance.
○ “The probability that results are NOT due to chance”
● To explain [↑], an outcome is unlikely if it occurs less than 5% of the time (p < .05)
➢ 👴🏻: Any occurrence UNDER this % is caused by something other than chance.
○ 👦🏻: But why?
➢ 👴🏻: Such an unlikely result (low p-value) is too extreme to have happened by
chance right? Therefore, we consider it “significant” in the sense that something
real (beyond chance) is going on!
■ High p-value (large #) → Results = chance → Null hyp. (IV x DV)
■ Low p-value (small #) → Results = not by chance → Alt. hyp. (IV → DV)
● Statistical significance: The degree of risk you’re willing to take when saying the IV did
not affect the DV when it actually did.
○ “How confident we can be that a particular outcome is true?”
● Directional hypothesis: Predicts a specific outcome (↑, ↓)
,● Non-directional hypothesis: No specific outcome (↭, ↻)
● When doing a study, we usually test 2 hypotheses (can be direct or not!)
1. Null hypothesis (H0); What you DON’T WANT to happen!
a. “The IV won’t have an effect on the DV because the results happened by
chance.”
i. Thus, there’s no significant relation between IV and DV and both
groups will be the same (BAD)
1. p > .05 = not significant
b. Non-directional equation: µt = µc
i. “Group 1 will be the same as Group 2”
c. Directional equation: µt ≥ / ≤ µc
i. “G1 will be better/worse than OR equal to Group 2”
1. If your alt. hypothesis says G1 will be better, the null
hypothesis should say the opposite!
2. Alternative hypothesis (H1); What you WANT to happen!
a. “The IV will have an effect on the DV because results did not happen by
chance.”
i. Thus, there’s a significant relationship between IV and DV and
both groups will differ (GOOD)
1. p < .05 = significant
b. Non-directional equation: µt ≠ µc
i. “Group 1 will differ from Group 2”
c. Directional equation: µt > / < µc
i. “G1 will be better/worse than G2”
, ★ EXAMPLE #1: What are the chances the professor makes 99 consecutive basketball
shots?
1. IV: The professor’s basketball skills.
2. DV: The professor’s performance.
3. Null hypothesis: Skill (IV) won't affect the performance (DV).
4. Alt. hypothesis: Skill (IV) will affect the performance (DV).
○ Results: Obviously, there’s a low probability the professor manages this, but
what exactly does this mean?
■ Remember, low p-value (small #) → Results = not by chance.
● Suppose there's a 0.05 (5%) chance the professor DOES make
the shots; if this happens, it means something other than chance
influenced his performance, perhaps something like skill!
● P < 0.5 → Results = not by chance → Alt. hyp. (IV affects DV!)
★ If it’s not clear let me know! I’ll try rewording it :)
★ EXAMPLE #2: Suppose you’re a teacher testing a new study method and want to
know if it helps students perform better.
1. IV: The study method.
2. DV: Student’s test scores.
3. Null hypothesis: The study method (IV) won't affect the results (DV).
■ Non-directional: The scores of students who use the study method (µt)
will not differ (=) from the scores of students who didn’t use the study
method (µc).
● H0 → µt = µc
★ NOTE: The chapters jump back and forth, so we’ll take it concept-by-concept!
👦🏻 PART 1: Probability, significance, hypotheses, and errors 👴🏻
● In statistics, we use tools to help determine whether we think an event is as likely, more
likely, or less likely to be caused by chance than what we [originally] expect.
1. Prediction: “Will it happen?”
2. Probability: “How likely is it to happen?”
3. Significance: “Is this likeliness due to chance or something else?”
● Probability: A tool that gives us the ability to calculate the odds a research outcome is
(or is not) due to chance.
○ “The probability that results are NOT due to chance”
● To explain [↑], an outcome is unlikely if it occurs less than 5% of the time (p < .05)
➢ 👴🏻: Any occurrence UNDER this % is caused by something other than chance.
○ 👦🏻: But why?
➢ 👴🏻: Such an unlikely result (low p-value) is too extreme to have happened by
chance right? Therefore, we consider it “significant” in the sense that something
real (beyond chance) is going on!
■ High p-value (large #) → Results = chance → Null hyp. (IV x DV)
■ Low p-value (small #) → Results = not by chance → Alt. hyp. (IV → DV)
● Statistical significance: The degree of risk you’re willing to take when saying the IV did
not affect the DV when it actually did.
○ “How confident we can be that a particular outcome is true?”
● Directional hypothesis: Predicts a specific outcome (↑, ↓)
,● Non-directional hypothesis: No specific outcome (↭, ↻)
● When doing a study, we usually test 2 hypotheses (can be direct or not!)
1. Null hypothesis (H0); What you DON’T WANT to happen!
a. “The IV won’t have an effect on the DV because the results happened by
chance.”
i. Thus, there’s no significant relation between IV and DV and both
groups will be the same (BAD)
1. p > .05 = not significant
b. Non-directional equation: µt = µc
i. “Group 1 will be the same as Group 2”
c. Directional equation: µt ≥ / ≤ µc
i. “G1 will be better/worse than OR equal to Group 2”
1. If your alt. hypothesis says G1 will be better, the null
hypothesis should say the opposite!
2. Alternative hypothesis (H1); What you WANT to happen!
a. “The IV will have an effect on the DV because results did not happen by
chance.”
i. Thus, there’s a significant relationship between IV and DV and
both groups will differ (GOOD)
1. p < .05 = significant
b. Non-directional equation: µt ≠ µc
i. “Group 1 will differ from Group 2”
c. Directional equation: µt > / < µc
i. “G1 will be better/worse than G2”
, ★ EXAMPLE #1: What are the chances the professor makes 99 consecutive basketball
shots?
1. IV: The professor’s basketball skills.
2. DV: The professor’s performance.
3. Null hypothesis: Skill (IV) won't affect the performance (DV).
4. Alt. hypothesis: Skill (IV) will affect the performance (DV).
○ Results: Obviously, there’s a low probability the professor manages this, but
what exactly does this mean?
■ Remember, low p-value (small #) → Results = not by chance.
● Suppose there's a 0.05 (5%) chance the professor DOES make
the shots; if this happens, it means something other than chance
influenced his performance, perhaps something like skill!
● P < 0.5 → Results = not by chance → Alt. hyp. (IV affects DV!)
★ If it’s not clear let me know! I’ll try rewording it :)
★ EXAMPLE #2: Suppose you’re a teacher testing a new study method and want to
know if it helps students perform better.
1. IV: The study method.
2. DV: Student’s test scores.
3. Null hypothesis: The study method (IV) won't affect the results (DV).
■ Non-directional: The scores of students who use the study method (µt)
will not differ (=) from the scores of students who didn’t use the study
method (µc).
● H0 → µt = µc
