Data Analysis Chapter on "Norway Brand Statistical Summary and Hypotheses Decisions"

Data Analysis Chapter 5 pages (1712 words) Sources: 0

[EXCERPT] . . . .

Norway Brand

Statistical Summary and Hypotheses Decisions

The statistical method used to compare the experimental group to the control group was straightforward and fairly standard. First, with an established confidence interval of 95% and a significance or alpha of .05, the Critical't score for the control group was established using Excel's built-in function. For each instrument item compared, the mean, variance, and standard deviation of the control group's responses were calculated (after being numerically coded as described below), all using Excel's functions (AVERAGE, VAR, and STDEV). From this, the standard error was also calculated through simple arithmetic (standard deviation divided by the square root of N, and in the control group N=42). The mean for the experimental group was also calculated, and with these preliminary statistics in place the t-score could be calculated for each item (the absolute value of the difference of the control and experimental means divided by the standard error). Excel's built-in t-table function (TDIST) was then used to calculate the p-value by putting the t-value, the degrees of freedom (N-1), and the numeral 2 for a two-tailed test (though only one direction is sought for the hypotheses, directionality itself can be determined simply by comparing means, whereas the significance of any difference is still a worthwhile finding). This probability and the resulting probability of rejecting the null hypothesis (1-p) allows for an analysis of the impact of the test variable on subject responses and the investigation of other areas.

Demographic Analysis

Prior to testing stated hypotheses, demographic analysis was used to isolate variables of difference between the control and experimental group, to ensure conformity in demographic areas and to identify any confounding variables of importance to the study. Areas of gender, education, age, and the importance of healthy diet were all tested. The same basic tests for hypothesis acceptance or rejection were used, with the experimental mean for each demographic tested against summary and demographic-specific statistics from the control group.

Gender

Males were assigned a gender value of 1, females a gender value of 2. Mean for the experimental group (M=1.66, with N=38 as three participants in the experimental group did not complete this item) was not found to differ significantly from the control mean (M=1.71), with p= 0.43 meaning gender does not serve as a confounding variable to any observed differences in hypothesis tests.

Education

Level of education showed much less disparity than gender. Assigning a value of 1 for below high school, 2 for high school, and 3 for university, the control group (M=2.38) is significantly different from the experimental group (M=2.26). A p-value of 0.18 suggests education is not a confounding variable.

Age

The control and experimental groups are highly similar in age, with a calculated t-value for the experimental group of 0.19 leading to a p-value of 0.85 -- a high probability that the groups are similar leaving a very low R. value or probability of rejecting the null hypothesis, and thus a low probability that age could be a confounding variable.

Importance of Healthy Diet

Unlike age, the t-value for the importance of healthy diet to the experimental group in comparison with the control group was quite high -- so high that the p-value is effectively zero and meaning it is almost certain statistically speaking that the two groups differ in this regard. This must then be considered a confounding variable in this study.

Initial Tests

Of primary importance to establish before testing individual hypotheses are first, the country from which subjects thought the product was from (determining whether or not the presence of the flag -- the changed variable in the experimental group -- has the desired effect of altering this perception), and second, whether or not subjects would purchase the product in the future (a basic determination of perceived quality, health, and all of the other variables identified in the individual hypotheses). Testing these as hypotheses in and of themselves results in a determination of whether or not further hypothesis testing is worthwhile and provides a preliminary analysis of results.

Perceptions of Country of Origin

Perceptions of country of origin were unquestionably influenced by the variable of the flag's addition to the packaging. To perform a test on this item, responses of any country other than Norway were valued as 1, whereas responses of Norway were valued as 2. This was done so as to limit potential noise from other perceived countries of origin, when truly the "Norway/not Norway" question is the only one of importance. A very high calculated t-value again leads to a probability of effectively 0, meaning that the null hypothesis in this case should also be rejected and that the groups are dissimilar -- in other words, this suggests that the experimental variable (i.e. The addition of the flag) created a difference in perception. This also makes further testing of the stated hypotheses worthwhile, as the experimental variable as been confirmed to create the change that serves as a premise for the identified hypotheses.

Would Purchase in Future

Due to the low response rate for both the control group (N=24) and the experimental group (N=7) for this item, the calculated associations are not as meaningful or as applicable to the broader population as for other items. With the data available, however, a calculated p value of .1 puts the experimental group just within the 95% confidence interval established, and can be considered similar to the control group in this regard. In light of the above analysis, this suggests that perceptions regarding country of origin of the product did not significantly affect decisions regarding future purchases.

Hypothesis Tests

For all hypothesis tests, the mean responses for several items were combined. Means were taken of the collected means from all items identified as Low, Low-Medium, Medium, Medium-High, and/or High. Full study populations were used (N=42 for the control group; N=41 for the experimental group). The only identified confounding variable was a desire to eat healthily, and this could have a major effect on certain responses. For the purposes of this analysis, however, it is primarily assumed that the flag inclusion is responsible for statistically significant changes, and thus any improvement in ratings noted from the control group to the experimental group in any of these areas that surpasses the significance level is considered reason to reject the null hypothesis.

Quality

Test statistics in this area do not demonstrate a strong likelihood that flag inclusion affected perceptions of quality. Comparison of means shows that the slight change that took place was negative, which itself would controvert the assertion of the alternative hypothesis that change would be positive, however this negative shift is not shown to be statistically significant. Instead, the null hypothesis is not rejected (p=.71).

Taste

Perceptions of taste fared similarly to perceptions of quality, with a very slight negative change in the experimental group seen in the raw data and a straightforward mean comparison. The probability of rejecting the null hypothesis is somewhat higher (p=.25), yet it is still very safe to say that the null hypothesis is not rejected in this case, and that flag inclusion did not affect results to a statistically significant degree.

Environ.

Environmental impacts of the product were seen as slightly more positive by the experimental group, but the statistical analysis carried out shows that this change was also not significant. The null hypothesis continues to be accepted (p=.29), and it cannot be stated that the flag inclusion had any real effect on responses to this item.

Authenticity

As might be guessed at this point, no statistically significant change was seen for this item. The null hypothesis is not rejected (p=.39), and again though there was a slight positive change observed in the means this change was not validated by statistical analysis. The flag inclusion appears to have had no effect.

Purity (Raw Materials)

Purity is the first of the areas discussed here in which the experimental group diverged significantly from the control group. A t-score of 4.60 correlates to a p-value of essentially 0, however this does not mean that the null hypothesis is rejected in this case. Though the groups can be said to have significantly different responses in this area, the mean of the experimental group is actually lower than that of the control group, meaning perception of purity was actually lower in the group exposed to the flag rather than higher -- the opposite direction of that suggested by the alternative hypothesis. The null hypothesis is thus still not rejected.

Healthiness

Healthiness moved in the same direction as perceptions of purity, and again the change was highly significant (once more, so significant that the p-value of failing to reject the null hypothesis is effectively 0). But, again, because the change was in a negative direction the alternative hypothesis cannot be accepted -- rather than having more positive perceptions of healthiness, the experimental group actually had a lower perception of product healthiness. This is one area where the confounding variable of a desire to eat healthy might be… READ MORE

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