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chapter 10: hypothesis testing Flashcards

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1
Q

Procedure for the scientific method (hint: 5 steps)

A
  1. observing nature
  2. asking questions
  3. formulating hypotheses
  4. conducting experiments
  5. developing theories and laws
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2
Q

two types of hypotheses

A

scientific hypothesis and statistical hypothesis

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3
Q

definition of scientific hypothesis

A

a scientific hypothesis is a testable supposition that is tentatively adopted to account for certain facts and to guide in the investigation of others; a statement that requires verification

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4
Q

what are the 3 characteristics common to all scientific hypotheses?

A
  1. intelligent informed guesses about phenomena of interest
  2. can be stated in the if-then form
  3. their truth, or falsity, can be determined by observation and experimentation
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5
Q

give a good example of scientific hypothesis

A

students who study the material in spaced intervals perform better on the exams compared to students who cram

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6
Q

definition of a statistical hypothesis

A

a statistical hypothesis is a statement about one or more parameters of a population distribution that requires verification

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7
Q

good example of a statistical hypothesis

A

a new class registration procedure at BU will reduce time required for students to register

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8
Q

what is the process of choosing between H0 and H1 (null hypothesis and alternative hypothesis) called?

A

the process of choosing between H0 and H1 is called HYPOTHESIS TESTING

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9
Q

this chapter on hypothesis testing does not focus on “proving” anything. what does it actually do?

A

through hypothesis testing we are simply saying that the occurrence of an event is improbable, not impossible

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10
Q

what does it mean to not reject Hº (the null hypothesis)

-hint: 3 different possibilities

A
  1. Ho is true and should not be rejected
  2. Ho is false and should be rejected, but the particular sample that was used to estimate µ and 𝛔 is not representative of the population
  3. Ho is false and should be rejected, but the experimental methodology is not sufficiently sensitive to detect the true situation
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11
Q

what does it mean to not reject Hº (the null hypothesis)
-hint: 3 different possibilities

this is bad because we want to be able to reject the null hypothesis

A
  1. Ho is true and should not be rejected
  2. Ho is false and should be rejected, but the particular sample that was used to estimate µ and σ is not representative of the population
  3. Ho is false and should be rejected, but the experimental methodology is not sufficiently sensitive to detect the true situation
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12
Q

what are the two options if we fail to reject the null hypothesis (Ho)

A
  1. state that we fail to reject the Ho ——> Ho remains credible
  2. suspend judgement about the Ho and scientific hypotheses until the completion of a new, improved experiment
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13
Q

statistical test is….

A

the process of deciding wether to reject Ho.

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14
Q

the decision of wether to reject Ho is based on what 3 things?

A
  1. a test statistic computed for a random sample from the population
  2. hypothesis testing conventions
  3. a decision rule
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15
Q

5 step research process

A
  1. state the null and alternative hypothesis
  2. specify the test statistic based on the hypothesis being tested, info known about the population, and assumptions about the population that appear to be tenable
  3. specify the size of the sample (n) and make assumptions that permit specification of the sampling distribution of the test statistic, given that Ho is true
  4. specify significance level (⍺)
  5. obtain a random sample of size n from the population, compute the test statistic, and make a decision
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16
Q

what is significance level?

A

significance level is the acceptable risk of making a decision error (example: rejecting the null hypothesis when it is true)

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17
Q

what is the critical region?

A

the critical region is the region under the t-distribution curve for rejecting Ho

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18
Q

in general we use a significance level of ⍺=.05

A

(only 5 times out of 100 will we observe a discrepancy between x̄ and µ as large or larger as expected)

by convention a probability of .05 is the largest risk a researcher should be willing to take of rejecting a true hypothesis

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19
Q

decision rule

A

reject Ho if test statistic falls in critical region; otherwise do not reject Ho

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20
Q

what is critical value

A

critical value is the value of t that cuts off the critical region of the sampling distribution of t

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21
Q 
step 1: stating the statistical hypotheses 
using the example: a new class registration procedure at BU will reduce time required for students to register
A

current procedures: x̄ = 3.10 hours
the statistical hypothesis postulates: µ< 3.10 hours
-we can also postulate that µ ≥ 3.10 hours
(these two statistical hypothesis are mutually exclusive and exhaustive)

µ< 3.10 hours is the alternative hypothesis (H1)
µ ≥ 3.10 hours is the null hypothesis (Ho)
-we want to test the tenability of this
-we want to reject it
if we reject Ho then H1 is the only tenable hypothesis

reminder: the process of choosing between Ho and H1 is called hypothesis testing
* we are only saying that the occurrence of an event is improbable

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22
Q

µ and σ are estimated during hypothesis testing using…..

A

µ and σ are estimated during hypothesis testing using the sample statistics from the experiment (x̄ and σ ∧)

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23
Q

step 2: specify the test statistic that will be used to test the population mean

A

we can either use
t-statistic (sampling distr. is the t distribution) or
z-statistic (sampling distr. is the standard normal distr.)
choice of which statistic is based on what 3 things?

  1. the hypothesis being tested
  2. info known about the population
  3. assumptions about the population that appear to be tenable
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24
Q

step 2: specify the test statistic used to test Ho: µ ≥ 3.10 hours

  1. this hypothesis contains the mean of a single population
  2. the population standard deviation is unknown
  3. the population is assumed to be normally distributed
A

because of this we use the t-statistic

*appropriate if the population of registration times is normally distributed

(see notes for formula)

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25
Q

alternative hypothesis

A

This is the hypothesis that is potentially inferred given a rejection of the null hypothesis.

26
Q

t-statistic is used…

A

when dealing with a single population and unknown standard deviation
*assume that population is normally distributed

27
Q

z-statistic is used…

A

when dealing with a single population and KNOWN standard deviation
*assume that population is normally distributed

28
Q

difference between t and z statistic

A 
t = random variable-constant/random variable 
z = random variable-constant/constant

*z and t look alike but in z-statistic the denominator is a constant, in t-statistic the denominator is a random variable

29
Q

step 3: specifying n and making assumptions that permit specification of the sampling distribution of the test statistic

A

specifying n and making assumptions that permit specification of the sampling distribution of the test statistic

30
Q

students t-distribution

A

symmetrical with a mean of 0

the t-distribution is a family of distributions whose shapes depend on the degrees of freedom

31
Q

what does it mean that dispersion of the t distribution (standard deviation) depends on the sample size

A

standard deviation of the t-distribution depends on degrees of freedom

32
Q

degrees of freedom

A

degrees of freedom refers to the number of scores who’s values are free to vary

33
Q

smaller df vs. greater df.

A

smaller degrees of freedom= more leptokurtic
greater degrees of freedom= more normally distributed
(central limit theorem)

  • n of 30 is often taken as the dividing point between large and small samples
34
Q

2 purposed served by the normality assumption

A

we can test numerator or t-statistic without regards to sample size

and both the denominator and numerator of the t-statistic are statistically independent (don’t affect each other)

35
Q

location and size of the critical region are determined by what? and why is this important

A

the location and size of the critical region determined by H1 and α

-this is important for step 4 of the process which is specifying significance level

36
Q

what is step 5?

A

obtain a random sample from the population of interest, compute the test statistic, and make a decision using the decision rule

37
Q

what is the decision rule?

A

reject the null hypothesis if the test statistic falls in the critical region; otherwise do not reject the null hypothesis

38
Q

what is critical value?

A

critical value is the value of t that cuts off the critical region of the sampling distribution of t

this helps determine if we can reject the null hypothesis because we reject it if the test statistic falls in the critical region

39
Q

faced with non rejection of the null hypothesis what can a researcher conclude

A

a researcher can either conclude that the evidence does not support the original scientific hypothesis or suspend judgment pending the completion of a new, improved experiment

40
Q

what can a researcher conclude if the null hypothesis is rejected?

A

researcher can conclude that the scientific hypothesis is probably true.

41
Q

why is the inclusion of a control group (participants who do not receive treatment) an experimental design consideration?

A

control groups provide data on the effects of extraneous variables.

there is a possibility that samples can pull a “john henry effect” and over-perform because they know they are being observed. control groups are used in consideration of this

42
Q

when is a one-tailed test used?

A

when the researcher makes a directional prediction (one-sided hypothesis)
*the critical region will be located in either the upper or lower tail of the sampling distribution

43
Q

when is a two-tailed test used?

A

when the researcher just wants to show a difference, but is nondirectional (two-sided hypothesis)
* the critical region will be located in both the upper and lower tails of the sampling distribution

half the significance level is assigned to the upper tail and the other half to the lower tail

44
Q

why are most significance tests in the behavioral sciences two tailed?

A

because we lack the information necessary to formulate directional hypotheses

45
Q

type 1 error

A

rejecting Ho when Ho is true and shouldnt be rejected

-probability = α

46
Q

type II error

A

not rejecting Ho when Ho is false and should be rejected

-probability = 𝛃

47
Q

correct rejection (1- 𝛃) is power

A

to compute, you must know 𝛍 (true population mean) and 𝛔 (population standard deviation)

48
Q

type I vs. type II errors

A

as the probability of one increases the probability of the other decreases (inverse relationship)

49
Q

which error is worse?

A

it depends on what youre studying but usually type I errors are worse

50
Q

indicate type of error: a false null hypothesis was rejected

A

correct rejection

51
Q

indicate type of error: the researcher did not reject a true null hypothesis

A

correct acceptance

52
Q

indicate type of error: the null hypothesis is false and the researcher failed to reject it

A

type II error

53
Q

indicate type of error: the researcher rejected a true null hypothesis

A

type I error

54
Q

indicate type of error: a false null hypothesis was not rejected

A

type II error

55
Q

cohens d

A

effect size that expresses the magnitude of the absolute mean difference (𝛍-𝛍𝗈) one wants to detect in units of the population standard deviation
*see notes for formula

small effect= .2
medium effect= .5
large effect= .8

-cohens d helps specify sample size, n

56
Q

what are the 5 pieces of information needed to estimate sample size?

A
  1. effect size d= 0.2, 0.5, 0r 0.8
  2. significance level 𝛂= 0.5 or 0.1
  3. acceptable power 1-𝛃=.80, .90 or .95
  4. type of statistical hypothesis: one or two tailed
  5. type of test: one or two sample test
57
Q

what is statistical significance concerned with?

A

statistical significance is concerned with wether a result is due to chance or sampling variability

58
Q

what is practical significance concerned with?

A

practical significance is concerned with whether the result is useful in the real world

59
Q

what is p-value?

A

probability value is the probability of obtaining a value of the test statistic equal to or more extreme than that observed, given that Ho is true.
*p value should be divided by two when dealing with two-tailed tests

60
Q

how to not confuse p value with significance level

A

significance level is the probability a researcher has specified an acceptable level of falsely rejecting a null hypothesis (type I error)
-it is commonly set at 𝛂= .05 or .01

61
Q

the decision rule can be formulated in terms of the p value and significance level. explain

A

reject the null hypothesis if the p value is less than or equal to the preselected significance level
that is if p≤𝛂
otherwise, do not reject the null hypothesis

psych stats (9 decks)

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