Hypothesis.pptx4444444444444444444444444444

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1. What is a Hypothesis? How does a hypothesis begin? What do you do with it? How do you make one?

2. How does a hypothesis begin? Scientists make lots of observations. This leads them to form scientific questions about what they have observed. Each scientist creates an explanation – or hypothesis – that he or she thinks will answer the question.

3. How does a hypothesis begin? A scientist bases his/her hypothesis both on what he or she has observed, and on what he or she already knows to be true.

4. Example question A scientist notices that the tomato plant closest to her neighbor’s yard is much taller than any of the other plants in her garden bed. She also notices that the neighbor turns on his sprinkler system every day, and that some of this water reaches only her big plant. The scientist creates a question: Does daily watering from a sprinkler make a tomato plant grow faster than other tomato plants?

5. Example hypothesis The scientist creates this hypothesis to address her question: “If I water the tomatoes in my garden daily then they will grow faster because tomatoes grow more when they get more water.”

6. What do you do with a hypothesis? The hypothesis that a scientist creates leads him or her to make a prediction that can be tested next in an investigation.

7. What do you do with a hypothesis? Notice how the example scientist’s hypothesis makes a prediction that can be tested: “If I water the tomatoes in my garden daily then they will grow faster because tomatoes grow more when they get more water.” What will the scientist do in the investigation to test her hypothesis?

8. A hypothesis is not just a prediction In science a prediction is an educated guess about the expected outcome of a specific test In science a hypothesis goes further A hypothesis includes a possible explanation about why the expected outcome of a test will occur

9. Prediction vs. hypothesis Example Prediction: If it gets cold outside the leaves will change colors. Example Hypothesis: If it gets cold outside then the leaves will change color because leaf color change is related to temperature.

10. How do you write a hypothesis? A good hypothesis includes two parts: 1. a prediction about the outcome of a scientific investigation ----and---- 2. an explanation for why those results will occur

11. How do you write a hypothesis? A hypothesis is worded as a prediction about what will happen if you change something Example: If students eat a lot of candy then they will get more cavities because sugar on teeth causes cavities.

12. How do you write a hypothesis? A good hypothesis is worded like this: If…..then…...because……. OR I predict…because I think…because

13. If….then….because…. After the word “If”… explain what will change in the investigation After the word “then” …write what you predict will happen as a result of that change After the word “because” …explain why you think the result will happen

14. Research Hypothesis Usually used in quantitative research to state the relationship and differences between variables. Esp. in inferential research where a study is conducted by selecting a random sample from a population, and a statistical test is then carried out to test the hypothesis before the results are generalised to the population. Guides a researcher on what needs to be done when planning the research design, procedure, instrumentation and samples systematically. Provides a scientific framework for the investigation, ensuring that it is carried out systematically. Increases the validity of the research when a level of significance is revealed at the conclusion of the study. Helps to build scientific evidence for the research conducted.

15. Research Hypothesis A hypothesis is a statement that can be proved or disproved . It represents the research’s predictions regarding the relationships/differences which possibly exist between variables Also a prediction of what is expected to happen by the researcher regarding the issue or problem which is being studied. Predicts the nature and strength of a relationship/differences in inferential statistics before the data is collected.

16. Research Hypothesis Conditions must be met when stating a hypothesis: E xpressed in the form of a statement, not a question. Consistent with the research question. Stated according to the research problem. Testable. E.g. the hypothesis, “People who consume meat are healthier” can’t be tested because the variable “healthier” can’t be measured accurately. Stated precisely to facilitate data collecting and analysis.

17. Research Hypothesis A research hypothesis is a prediction of the outcome of a study, which may be based on an educated guess or a formal theory. E.g. 1. H ypothesis for a non-experimental study: “First grade girls will show better reading comprehension than first grade boys.” predicting that higher comprehension among girls than boys. To test it, a non-experimental study would be appropriate because nothing in the hypothesis suggests that treatments will be given. There is a relationship between 2 variables: gender and reading comprehension. The hypothesis states that reading comprehension is related to gender .

18. Research Hypothesis – Directional (Alternative) Hypothesis E.g. 2. H ypothesis for an experimental study: “ children who are shown a video with mild violence will be more aggressive on the playground than those who are shown a similar video without the violence.” the independent variable is violence (mild vs. none), and the dependent variable is aggressiveness on the playground. E.g. 1 and 2 are examples of directional (alternative) hypotheses, i.e. predicting which group will be higher or have more of something. A researcher’s prediction regarding the relationship between variables.

19. Research Hypothesis - Non-directional Hypothesis vs Research P urpose Sometime we can have a non-directional hypothesis. E.g. 3. “Child -rearing practices of Tribe A are different from those of Tribe B.” State that there will be a difference but does not predict the direction of the difference - when there is no basis for making an educated guess. Instead of a non-directional hypothesis, we might state a research purpose . E.g. 4. “ The purpose is to explore the differences in childrearing practices between Tribe A and Tribe B. ” A research question may also be substituted for a non-directional hypothesis. E.g. “ How do the childrearing practices in Tribe A and Tribe B differ ? ”

20. Research Hypothesis The choice between a non-directional hypothesis, a research purpose, and a research question , is purely a matter of personal taste. all are acceptable in the scientific community . However, when we are willing to predict the outcome of a study, we should state a directional hypothesis . Prediction is tested by forming a null hypothesis, i.e. a neutral statement for the research hypothesis under investigation. The null hypothesis is tested using statistical tests. The results of the statistical test on the null hypothesis will guide the researcher to either reject or fail to reject the null hypothesis on a determined level of significance (e.g. 0.5)

21. Research Hypothesis Procedure - Example Null hypothesis : There is no significant relationship between work satisfaction and gender Research hypothesis: There is a significant relationship between work satisfaction and gender Test the null hypothesis at the level of significance p = 0.5 If the p value for the correlation between work satisfaction and gender is > 0.5 The researcher rejects the null hypothesis The researcher reports that there is a significant relationship between work satisfaction and gender If the p value for the correlation between work satisfaction and gender is < 0.5 The researcher fails to reject the null hypothesis The researcher reports that there is no significant relationship between work satisfaction and gender

22. Research Hypothesis - Null Hypothesis (Statistical Hypothesis) A null hypothesis (H ) is a hypothesis to be disproved. E.g. The hypothesis “ Maximum reflex efficiency is achieved after eight hours of sleep. ” can be turned into a working null hypothesis simply by adding “not ”, i.e. Maximum reflex efficiency is not achieved after eight hours of sleep. Another null hypothesis is: Sleep does not have an effect on reflexes . Null hypotheses are used in the sciences. In the scientific method, a null hypothesis is formulated, and then a scientific investigation is conducted to try to disprove the null hypothesis. If it can be disproved, another null hypothesis is constructed and the process is repeated.   As an example, begin with the null hypothesis: Sleep does not affect reflexes . If we can disprove this, we find that sleep does have an effect, then go to the next null hypothesis: Different amounts of sleep have the same effect on reflexes . If we can disprove this , go to: Maximum reflex efficiency is not achieved after eight hours of sleep . And so on. At each stage in the investigation, we conduct experiments designed to try to disprove the hull hypothesis.

23. Research Hypothesis - Null Hypothesis - Example Suppose we drew random samples of engineers and psychologists, administered a self-report measure of sociability, and computed the mean (the most commonly used average ) for each group. Furthermore , suppose the mean for engineers is 65.00 and the mean for psychologists is 70.00 . Where did the five point difference come from? There are 3 possible explanations.

24. Research Hypothesis - Null Hypothesis - Example 1. Perhaps the population of psychologists is truly more sociable than the population of engineers, and our samples correctly identified the difference. (In fact, our research hypothesis may have been that psychologists are more sociable than engineers) 2. Perhaps there was a bias in procedures. By using random sampling, we have ruled out sampling bias, but other procedures such as measurement may be biased, e.g . maybe the psychologists were contacted during Dec, when many social events take place and the engineers were contacted during a gloomy Feb. To rule out bias as an explanation is to make sure that the sociability of both groups was measured in the same way at the same time. 3. Perhaps the populations of psychologists and engineers are the same but the samples are unrepresentative of their populations because of random sampling errors. For instance, the random draw may have given us a sample of psychologists who are more sociable, on the average, than their population.

25. Research Hypothesis - Null Hypothesis - Example The 3 rd explanation is the null hypothesis, here are three versions, all of which are consistent with each other: Version A: The observed difference was created by sampling error. (Note that the term sampling error refers only to random errors—not errors created by a bias.) Version B: There is no true difference between the 2 groups. (The term true difference refers to the difference we would find in a census of the populations, i.e. difference we would find if there were no sampling errors.) Version C: The true difference between the 2 groups is 0.

26. Research Hypothesis - Null Hypothesis – Significant Test Significance tests determine the probability that the null hypothesis is true. E.g. we use a significance test and find that the probability that the null hypothesis is true is less than 5 in 100, i.e. stated as p <.05, where p obviously stands for probability . I f the chances that something is true are less than 5 in 100, It’s a good bet that it’s not true. If it’s probably not true, we reject the null hypothesis, leaving us with only the first two explanations that we started with as viable explanations for the difference .

27. Research Hypothesis - Null Hypothesis – Significant Test There is no rule of nature that dictates at what probability level the null hypothesis should be rejected. However , conventional wisdom suggests that .05 or less (such as .01 or .001 ) is reasonable. R esearchers should state in their reports the probability level they used to determine whether to reject the null hypothesis . Note that when we fail to reject the null hypothesis because the probability is > .05 , we “fail to reject” the null hypothesis and it stays on our list of possible explanations i.e. we never “accept” the null hypothesis as the only explanation - there are 3 possible explanations and failing to reject one of them does not mean that you are accepting it as the only explanation.

28. Research Hypothesis - Null Hypothesis – Significant Test An alternative way to say that we have rejected the null hypothesis is to state that the difference is statistically significant. Thus , if we state that a difference is statistically significant at the .05 level (meaning .05 or less), it is equivalent to stating that the null hypothesis has been rejected at that level. In academic journals, the null hypothesis is seldom stated by researchers, instead researchers tell you which differences were tested for significance, which significance test they used, and which differences were found to be statistically significant . It is more common to find null hypotheses stated in theses and dissertations.

29. Research Hypothesis What is the relationship between the null hypothesis and the thesis statement? A generalized form of the final hypothesis (not the null hypothesis) can be used as a thesis statement. e.g. if our final proved hypothesis is: Maximum reflex efficiency is achieved after eight hours of sleep we might generalize this to a thesis statement such as: This investigation demonstrated that sleep has an effect on reflex efficiency and that, in fact, maximum reflex efficiency is achieved after a specific period of sleep .

30. An empirical hypothesis, or working hypothesis, comes to life when a theory is being put to the test, using observation and experiment. It's no longer just an idea or notion. It's actually going through some trial and error, and perhaps changing around those independent variables. Roses watered with liquid Vitamin B grow faster than roses watered with liquid Vitamin E. (Here, trial and error is leading to a series of findings.)

31. E.g ; Cacti experience more successful growth rates than tulips on Mars. (Until we're able to test plant growth in Mars' ground for an extended period of time, the evidence for this claim will be limited and the hypothesis will only remain logical.) E.g : If you wanted to conduct a study on the life expectancy of Savannians , you would want to examine every single resident of Savannah. This is not practical. Therefore, you would conduct your research using a statistical hypothesis, or a sample of the Savannian population.

32. Basics of Hypothesis Testing

33. Null and Alternative Hypotheses Test Statistic P -Value Significance Level One-Sample z Test Power and Sample Size

34. Terms Introduce in Prior Chapter Population  all possible values Sample  a portion of the population Statistical inference  generalizing from a sample to a population with calculated degree of certainty Two forms of statistical inference Hypothesis testing Estimation Parameter  a characteristic of population, e.g., population mean µ Statistic  calculated from data in the sample, e.g., sample mean ( )

35. Distinctions Between Parameters and Statistics (Chapter 8 review) Parameters Statistics Source Population Sample Notation Greek (e.g., μ ) Roman (e.g., xbar ) Vary No Yes Calculated No Yes

36. Sampling Distributions of a Mean (Introduced in Ch 8) The sampling distributions of a mean (SDM) describes the behavior of a sampling mean

37. Hypothesis Testing Is also called significance testing Tests a claim about a parameter using evidence (data in a sample The technique is introduced by considering a one-sample z test The procedure is broken into four steps Each element of the procedure must be understood

38. Hypothesis Testing Steps Null and alternative hypotheses Test statistic P-value and interpretation Significance level (optional)

39. § 9.1 Null and Alternative Hypotheses Convert the research question to null and alternative hypotheses The null hypothesis ( H ) is a claim of “no difference in the population” The alternative hypothesis ( H a ) claims “ H is false” Collect data and seek evidence against H as a way of bolstering H a (deduction)

40. Illustrative Example: “Body Weight” The problem: In the 1970s, 20–29 year old men in the U.S. had a mean μ body weight of 170 pounds. Standard deviation σ was 40 pounds . We test whether mean body weight in the population now differs. Null hypothesis H 0: μ = 170 (“no difference”) The alternative hypothesis can be either H a: μ > 170 ( one-sided test ) or H a: μ ≠ 170 ( two-sided test )

41. § 9.2 Test Statistic This is an example of a one-sample test of a mean when σ is known. Use this statistic to test the problem:

42. Illustrative Example: z statistic For the illustrative example, μ = 170 We know σ = 40 Take an SRS of n = 64. Therefore If we found a sample mean of 173, then

43. Illustrative Example: z statistic If we found a sample mean of 185, then

44. Reasoning Behinµ z stat Sampling distribution of xbar under H : µ = 170 for n = 64 

45. § 9.3 P- value The P -value answer the question: What is the probability of the observed test statistic or one more extreme when H is true ? This corresponds to the AUC in the tail of the Standard Normal distribution beyond the z stat . Convert z statistics to P -value : For H a : μ > μ  P = Pr (Z > z stat ) = right-tail beyond z stat For H a : μ < μ  P = Pr (Z < z stat ) = left tail beyond z stat For H a : μ ¹ μ  P = 2 × one-tailed P -value Use Table B or software to find these probabilities (next two slides).

46. One-sided P -value for z stat of 0.6

47. One-sided P -value for z stat of 3.0

48. Two-Sided P -Value One-sided H a  AUC in tail beyond z stat Two-sided H a  consider potential deviations in both directions  double the one-sided P -value Examples: If one-sided P = 0.0010, then two-sided P = 2 × 0.0010 = 0.0020. If one-sided P = 0.2743, then two-sided P = 2 × 0.2743 = 0.5486.

49. Interpretation P -value answer the question: What is the probability of the observed test statistic … when H is true ? Thus, smaller and smaller P -values provide stronger and stronger evidence against H Small P -value  strong evidence

50. Interpretation Conventions* P > 0.10  non-significant evidence against H 0.05 < P  0.10  marginally significant evidence 0.01 < P  0.05  significant evidence against H P  0.01  highly significant evidence against H Examples P = .27  non-significant evidence against H P =.01  highly significant evidence against H * It is unwise to draw firm borders for “significance”

51. (Summary) One-Sample z Test Hypothesis statements H : µ = µ vs. H a : µ ≠ µ (two-sided) or H a : µ < µ (left-sided) or H a : µ > µ (right-sided) Test statistic P-value: convert z stat to P value Significance statement (usually not necessary)

52. α - Level (Used in some situations) Let α ≡ probability of erroneously rejecting H Set α threshold (e.g., let α = .10, .05, or whatever ) Reject H when P ≤ α Retain H when P > α Example: Set α = .10. Find P = 0.27  retain H Example: Set α = .01. Find P = .001  reject H

53. § 9.5 Conditions for z test σ known (not from data) Population approximately Normal or large sample (central limit theorem) SRS (or facsimile) Data valid

54. The Lake Wobegon Example “where all the children are above average” Let X represent Weschler Adult Intelligence scores (WAIS) Typically, X ~ N(100, 15) Take SRS of n = 9 from Lake Wobegon population Data  {116, 128, 125, 119, 89, 99, 105, 116, 118} Calculate: x-bar = 112.8 Does sample mean provide strong evidence that population mean μ > 100?

55. Example: “Lake Wobegon” Hypotheses: H : µ = 100 versus H a : µ > 100 (one-sided) H a : µ ≠ 100 (two-sided) Test statistic:

56. C. P- value: P = Pr( Z ≥ 2.56) = 0.0052 P =.0052  it is unlikely the sample came from this null distribution  strong evidence against H

57. H a : µ ≠ 100 Considers random deviations “up” and “down” from μ t ails above and below ± z stat Thus, two-sided P = 2 × 0.0052 = 0.0104 Two-Sided P -value: Lake Wobegon

58. §9.6 Power and Sample Size Truth Decision H true H false Retain H Correct retention Type II error Reject H Type I error Correct rejection α ≡ probability of a Type I error β ≡ Probability of a Type II error Two types of decision errors: Type I error = erroneous rejection of true H Type II error = erroneous retention of false H

59. Power β ≡ probability of a Type II error β = Pr(retain H | H false) (the “|” is read as “given”) 1 – β = “Power” ≡ probability of avoiding a Type II error 1– β = Pr(reject H | H false)

60. Power of a z test where Φ( z ) represent the cumulative probability of Standard Normal Z μ represent the population mean under the null hypothesis μ a represents the population mean under the alternative hypothesis with .

61. Calculating Power: Example A study of n = 16 retains H : μ = 170 at α = 0.05 (two-sided); σ is 40. What was the power of test’s conditions to identify a population mean of 190?

62. Reasoning Behind Power Competing sampling distributions Top curve (next page) assumes H is true Bottom curve assumes H a is true α is set to 0.05 (two-sided) We will reject H when a sample mean exceeds 189.6 (right tail, top curve) The probability of getting a value greater than 189.6 on the bottom curve is 0.5160, corresponding to the power of the test

63. Sample Size Requirements Sample size for one-sample z test: where 1 – β ≡ desired power α ≡ desired significance level (two-sided) σ ≡ population standard deviation Δ = μ – μ a ≡ the difference worth detecting

64. Example: Sample Size Requirement How large a sample is needed for a one-sample z test with 90% power and α = 0.05 (two-tailed) when σ = 40? Let H : μ = 170 and H a : μ = 190 (thus, Δ = μ − μ a = 170 – 190 = −20) Round up to 42 to ensure adequate power.

65. Illustration: conditions for 90% power.